COURSE MATERIAL

III Year B. Tech II- Semester

MECHANICAL ENGINEERING
AY: 2024-25

Heat Transfer
(R22A0318)

Prepared by:
Dr. Desu Damodara Reddy
Associate Professor

MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY

DEPARTMENT OF MECHANICAL ENGINEERING
(Autonomous Institution-UGC, Govt. of India)
Secunderabad-500100, Telangana State, India.
www.mrcet.ac.in
MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY
(Autonomous Institution – UGC, Govt. of India)
DEPARTMENT OF MECHANICAL ENGINEERING

CONTENTS

1. Vision, Mission and Quality Policy

2. POs, PSOs & PEOs

3. Blooms Taxonomy

4. Course Syllabus

5. Course Outline.

6. Mapping of Course Objectives

7. Unit wise course Material

a. Objectives and Outcomes

b. Detailed Notes

c. Industry applications relevant to the concepts covered

d. Tutorial Questions

e. Question bank for Assignments: 05/Unit

8. Previous Question papers: 05

MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY
(Autonomous Institution – UGC, Govt. of India)

VISION
❖ To establish a pedestal for the integral innovation, team spirit, originality and
competence in the students, expose them to face the global challenges and become
technology leaders of Indian vision of modern society.

MISSION
❖ To become a model institution in the fields of Engineering, Technology and
Management.
❖ To impart holistic education to the students to render them as industry ready
engineers.
❖ To ensure synchronization of MRCET ideologies with challenging demands of
International Pioneering Organizations.

QUALITY POLICY

❖ To implement best practices in Teaching and Learning process for both UG and PG
courses meticulously.
❖ To provide state of art infrastructure and expertise to impart quality education.

❖ To groom the students to become intellectually creative and professionally

competitive.

❖ To channelize the activities and tune them in heights of commitment and sincerity,
the requisites to claim the never - ending ladder of SUCCESS year after year.

For more information: www.mrcet.ac.in

MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY
(Autonomous Institution – UGC, Govt. of India)
www.mrcet.ac.in
Department of Mechanical Engineering

VISION

To become an innovative knowledge center in mechanical engineering through state-of-

the-art teaching-learning and research practices, promoting creative thinking professionals.

MISSION

The Department of Mechanical Engineering is dedicated for transforming the students into
highly competent Mechanical engineers to meet the needs of the industry, in a changing
and challenging technical environment, by strongly focusing in the fundamentals of
engineering sciences for achieving excellent results in their professional pursuits.

Quality Policy

✓ To pursuit global Standards of excellence in all our endeavors namely teaching,

research and continuing education and to remain accountable in our core and
support functions, through processes of self-evaluation and continuous
improvement.

✓ To create a midst of excellence for imparting state of art education, industry-

oriented training research in the field of technical education.
MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY
(Autonomous Institution – UGC, Govt. of India)
www.mrcet.ac.in
Department of Mechanical Engineering
PROGRAM OUTCOMES
Engineering Graduates will be able to:
1. Engineering knowledge: Apply the knowledge of mathematics, science, engineering
fundamentals, and an engineering specialization to the solution of complex engineering
problems.
2. Problem analysis: Identify, formulate, review research literature, and analyze complex
engineering problems reaching substantiated conclusions using first principles of
mathematics, natural sciences, and engineering sciences.
3. Design/development of solutions: Design solutions for complex engineering problems
and design system components or processes that meet the specified needs with appropriate
consideration for the public health and safety, and the cultural, societal, and environmental
considerations.
4. Conduct investigations of complex problems: Use research-based knowledge and
research methods including design of experiments, analysis and interpretation of data, and
synthesis of the information to provide valid conclusions.
5. Modern tool usage: Create, select, and apply appropriate techniques, resources, and
modern engineering and IT tools including prediction and modeling to complex engineering
activities with an understanding of the limitations.
6. The engineer and society: Apply reasoning informed by the contextual knowledge to
assess societal, health, safety, legal and cultural issues and the consequent responsibilities
relevant to the professional engineering practice.
7. Environment and sustainability: Understand the impact of the professional engineering
solutions in societal and environmental contexts, and demonstrate the knowledge of, and
need for sustainable development.
8. Ethics: Apply ethical principles and commit to professional ethics and responsibilities and
norms of the engineering practice.
9. Individual and teamwork: Function effectively as an individual, and as a member or
leader in diverse teams, and in multidisciplinary settings.
10. Communication: Communicate effectively on complex engineering activities with the
engineering community and with society at large, such as, being able to comprehend and
write effective reports and design documentation, make effective presentations, and give
and receive clear instructions.
11. Project management and finance: Demonstrate knowledge and understanding of the
engineering and management principles and apply these to one’s own work, as a member
and leader in a team, to manage projects and in multidisciplinary environments.
MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY
(Autonomous Institution – UGC, Govt. of India)
www.mrcet.ac.in
Department of Mechanical Engineering
12. Life-long learning: Recognize the need for and have the preparation and ability to engage
in independent and life-long learning in the broadest context of technological change.

PROGRAM SPECIFIC OUTCOMES (PSOs)

PSO1 Ability to analyze, design and develop Mechanical systems to solve the
Engineering problems by integrating thermal, design and manufacturing Domains.

PSO2 Ability to succeed in competitive examinations or to pursue higher studies or

research.

PSO3 Ability to apply the learned Mechanical Engineering knowledge for the
Development of society and self.

Program Educational Objectives (PEOs)

The Program Educational Objectives of the program offered by the department are broadly listed
below:

PEO1: PREPARATION

To provide sound foundation in mathematical, scientific and engineering fundamentals necessary

to analyze, formulate and solve engineering problems.

PEO2: CORE COMPETANCE

To provide thorough knowledge in Mechanical Engineering subjects including theoretical

knowledge and practical training for preparing physical models pertaining to Thermodynamics,
Hydraulics, Heat and Mass Transfer, Dynamics of Machinery, Jet Propulsion, Automobile
Engineering, Element Analysis, Production Technology, Mechatronics etc.

PEO3: INVENTION, INNOVATION AND CREATIVITY

To make the students to design, experiment, analyze, interpret in the core field with the help of
other inter disciplinary concepts wherever applicable.

PEO4: CAREER DEVELOPMENT

To inculcate the habit of lifelong learning for career development through successful completion
of advanced degrees, professional development courses, industrial training etc.
MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY
(Autonomous Institution – UGC, Govt. of India)
www.mrcet.ac.in
Department of Mechanical Engineering

PEO5: PROFESSIONALISM

To impart technical knowledge, ethical values for professional development of the student to solve
complex problems and to work in multi-disciplinary ambience, whose solutions lead to significant
societal benefits.
MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY
(Autonomous Institution – UGC, Govt. of India)
www.mrcet.ac.in
Department of Mechanical Engineering

Blooms Taxonomy
Bloom’s Taxonomy is a classification of the different objectives and skills that educators set for
their students (learning objectives). The terminology has been updated to include the following
six levels of learning. These 6 levels can be used to structure the learning objectives, lessons, and
assessments of a course.

1. Remembering: Retrieving, recognizing, and recalling relevant knowledge from long‐ term
memory.
2. Understanding: Constructing meaning from oral, written, and graphic messages through
interpreting, exemplifying, classifying, summarizing, inferring, comparing, and explaining.
3. Applying: Carrying out or using a procedure for executing or implementing.
4. Analyzing: Breaking material into constituent parts, determining how the parts relate to
one another and to an overall structure or purpose through differentiating, organizing, and
attributing.
5. Evaluating: Making judgments based on criteria and standard through checking and
critiquing.
6. Creating: Putting elements together to form a coherent or functional whole; reorganizing
elements into a new pattern or structure through generating, planning, or producing.
MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY
(Autonomous Institution – UGC, Govt. of India)
www.mrcet.ac.in
Department of Mechanical Engineering
 MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY
III Year B.Tech. ME- II Sem L/T/P/C
2/1/-/3

(R22A0318) HEAT TRANSFER

*Note: Heat and Mass Transfer data books are permitted

COURSE OBJECTIVES:

1. Students can learn about heat transfer and conduction heat transfer mode.
2. Students can learn types of convection and dimensional analysis.
3. Students can learn the phases of heat transfer
4. Students can learn about heat exchanger performance.
5. Students can learn different laws of radiation and its applications.
UNIT-I
Introduction: Basic modes of heat transfer- Fourier Heat transfer equation– Differential heat
conduction equation in Cartesian and Cylindrical coordinate systems. Steady-state one-
dimensional heat conduction solutions for plain and composite slabs and cylinders, Critical
thickness of insulation.
UNIT-II
Heat conduction through extended surfaces (Fins) -Long Fin, Fin with insulated tip, and Short Fin
- Fin effectiveness and efficiency.
Unsteady state Heat Transfer-Conduction: One Dimensional Transient Conduction Heat Transfer
- Lumped system analysis, and solutions by use of Heisler charts.
UNIT-III
Convection: Dimensional analysis - Buckingham π theorem - Application of dimensional analysis
to free and forced convection problems - Dimensionless numbers and Empirical correlations.
Free and Forced convection: Continuity, momentum and energy equations - Boundary layer
theory concept - Approximate solution of the boundary layer equations - Laminar and turbulent
heat transfer correlation
UNIT- IV
Heat Exchangers: Classification of heat exchangers- Parallel flow- Counter flow- Cross flow heat
exchangers- Overall heat transfer coefficient- Fouling factor - Concepts of LMTD and NTU methods
Problems using LMTD and NTU methods - Heat exchangers with phase change.
UNIT- V
Boiling and Condensation: Different regimes of boiling- Pool, Nucleate, Transition and Film
boiling.
Condensation: Film-wise and drop-wise condensation - Nusselt's theory of condensation on a
vertical plate.
Radiation Heat Transfer: Emission characteristics and laws of Black body radiation- Laws of
Kirchhoff, Planck, Wien, Stefan Boltzmann – concepts of shape factor – Radiation shields
TEXT BOOKS:

1. Heat Transfer, by J.P.Holman, Int.Student edition, McGraw Hill Book Company.

2. Fundamentals of Heat and Mass Transfer- Sachdeva, New Age Publications

REFERENCE BOOKS:

1. Heat Transfer by S.P.Sukhatme.

2. Heat transfer by Yunus A Cengel.
3. Heat transfer by Arora and Domakundwar, Dhanpat Rai & sons, New Delhi

COURSE OUTCOMES:

1. To identify the modes of heat transfer and calculate the conduction in various solids.
2. To solve the heat transfer rate in convection for various geometric surfaces.
3. To evaluate the heat transfer rate in a phase change process,
4. To design heat exchange equipment based on the need that fits to application.
5. To learn about the radiation and its use in real life.
 COURSE OUTLINE
UNIT – 1
NO OF LECTURE HOURS: 12
LECTURE LECTURE TOPIC KEY ELEMENTS LEARNING OBJECTIVES

(2 to 3 objectives)

1. Introduction to Basic modes of heat transfer Definition of heat transfer Understanding of heat transfer (B2)

Rate equations

2. Differential heat conduction equation in Cartesian Derivation of equation Understanding of heat conduction equation.
(B2)

3. Cylindrical-coordinate systems Derivation of equation Understanding of heat conduction equation.

(B2)

4. Spherical coordinate systems Derivation of equation Understanding of heat conduction equation.

(B2)
5. Steady-state one-dimensional heat conduction Steady-state one-dimensional Application of heat conduction equation
solutions for plain and composite slabs heat conduction, plains
6. Steady-state one-dimensional heat conduction cylinders Application of heat conduction equation
solutions for cylinders
7. Steady-state one-dimensional heat conduction spheres Application of heat conduction equation
solutions for spheres
8. Electrical resistance concept - Electrical analogy Analyze the effect of heat transfer

9. Critical thickness of insulation insulation Analyze the effect of heat transfer

10. Heat conduction through fins of uniform and Heat conduction through fins Application of HT to fins
variable cross-section
11. Fin effectiveness effectiveness Finding effectiveness

12. Fin efficiency efficiency Finding efficiency

13 Introduction: Unsteady state Heat Transfer Unsteady state Understanding unsteady state heat transfer
conduction
14 Lumped system analysis Newtonian heating or cooling Analyzing heating & cooling

15 Criteria for lumped system analysis Biot Number & Fourier Numbers Understanding dimensionless numbers

16 Response time of thermocouple Response time, thermocouple, Understanding response time

source temperature, sensitivity
17 I-D Transient heat conduction in large plane walls, 1Dimensional Transient heat Application of unsteady state heat conduction
when Bi>0.1 conduction equation
18 I-D Transient heat conduction in long cylinders, when 1Dimensional Transient heat Application of unsteady state heat conduction
Bi>0.1 conduction equation
 UNIT – 2
NO OF LECTURE HOURS: 12
LECTURE LECTURE TOPIC KEY ELEMENTS LEARNING OBJECTIVES

(2 to 3 objectives)

1. Convection: Dimensional analysis Rayleigh’s method, Buckingham’s Understanding Dimensional analysis

pi-theorem
Application of convective heat transfer

2. Continuity, momentum and energy equations Governing equations Understanding fundamental laws

3. Boundary layer theory concept- Hydrodynamic & thermal Understanding concepts

boundary layer
4. Free, and Forced convection Empirical correlations Understanding correlations

5. Approximate solution of the boundary layer equations boundary layer equations Understanding boundary layer equations

6. Laminar and turbulent heat transfer correlation Laminar and turbulent Evaluate the Laminar and turbulent heat transfer

7. Application of dimensional analysis dimensional analysis Application

8. Dimensionless numbers & Empirical correlations Re, Nu, Pr & Gr Understanding Dimensionless numbers
9. Problems NUMERICAL SOLVED EXAMPLES ANALYSING & SOLVING Problems

10. Problems NUMERICAL SOLVED EXAMPLES ANALYSING & SOLVING Problems

11. Problems NUMERICAL SOLVED EXAMPLES ANALYSING & SOLVING Problems

12. Problems NUMERICAL SOLVED EXAMPLES ANALYSING & SOLVING Problems

 UNIT – 3
NO OF LECTURE HOURS: 12
LECTURE LECTURE TOPIC KEY ELEMENTS LEARNING OBJECTIVES

(2 to 3 objectives)

1. Boiling: Different regimes of boiling Nucleate, Transition and Film Understanding regimes of boiling
boiling.

2. Condensation: Laminar film condensation- Empirical Evaluate the type of condensation

relations
3. Condensation on vertical flat plates and horizontal tubes Flat plate & horizontal tubes Analyze condensation

4. Condensation: Dropwise condensation Evaluate the type of condensation

5. Problems Numerical Solved Examples Analysing & Solving Problems

6. Problems Numerical Solved Examples Analysing & Solving Problems

 UNIT – 4
NO OF LECTURE HOURS: 12
LECTURE LECTURE TOPIC KEY ELEMENTS LEARNING OBJECTIVES

(2 to 3 objectives)

1. Heat Exchangers: Types of heat exchangers Parallel flow- Counter flow- Cross Understanding of heat exchangers
flow heat exchangers

2. Overall heat transfer coefficient Definition & Formula Understanding the concept

3. LMTD derivation Evaluate the LMTD

4. NTU methods derivation Evaluate the NTU

5. Fouling factor Definition & impact of fouling Understanding fouling factor

factor
6. Heat exchangers with phase change

7. Problems Numerical Solved Examples Analysing & Solving Problems

8. Problems Numerical Solved Examples Analysing & Solving Problems

 UNIT – 5
NO OF LECTURE HOURS: 12
LECTURE LECTURE TOPIC KEY ELEMENTS LEARNING OBJECTIVES

(2 to 3 objectives)

1. Radiation: Black body radiation Absorptivity, reflectivity & Understanding basic definitions
transmissivity

2. Kirchhoff’s laws definition Understanding law

3. Shape factor Algebra, salient features Understanding salient features of

4. Stefan Boltzmann equation Total emissive power To find out Emissive power

5. Heat radiation through absorbing media Black bodies, gray bodies Evaluate the heat loss

6. Radiant heat exchange parallel and perpendicular surfaces, Evaluate the heat exchange
long concentric cylinders, small gray
bodies
7. Radiation shields Infinite parallel planes Evaluate the heat exchange

8. Problems Numerical Solved Examples Analysing & Solving Problems

9. Problems Numerical Solved Examples Analysing & Solving Problems

 UNIT 1
HEAT CONDUCTION
INTRODUCTION

Course Contents
1.1 Introduction
1.2 Thermodynamics and heat transfer
1.3 Application areas of heat transfer
1.4 Heat transfer mechanism
1.5 Conduction
1.6 Thermal conductivity
1.7 Convection
1.8 Radiation
1.9 References
1.1 Introduction
− Heat is fundamentally transported, or “moved,” by a temperature gradient; it flows or
is transferred from a high-temperature region to a low-temperature one. An
understanding of this process and its different mechanisms is required to connect
principles of thermodynamics and fluid flow with those of heat transfer.

1.2 Thermodynamics and Heat Transfer

− Thermodynamics is concerned with the amount of heat transfer as a system undergoes
a process from one equilibrium state to another, and it gives no indication of how long
the process will take. A thermodynamic analysis simply tells us how much heat must be
transferred to realize a specified change of state to satisfy the conservation of energy
principle.
− In practice we are more concerned about the rate of heat transfer (heat transfer per unit
time) than we are with the amount of it. For example, we can determine the amount of
heat transferred from a thermos bottle as the hot coffee inside cools from 90°C to 80°C
by a thermodynamic analysis alone.
− But a typical user or designer of a thermos is primarily interested in how long it will be
before the hot coffee inside cools to 80°C, and a thermodynamic analysis cannot answer
this question. Determining the rates of heat transfer to or from a system and thus the
times of cooling or heating, as well as the variation of the temperature, is the subject of
heat transfer (Figure 1.1).

Fig. 1.1 Heat transfer from the thermos

− Thermodynamics deals with equilibrium states and changes from one equilibrium state
to another. Heat transfer, on the other hand, deals with systems that lack thermal
equilibrium, and thus it is a nonequilibrium phenomenon. Therefore, thestudy of heat
transfer cannot be based on the principles of thermodynamics alone.
− However, the laws of thermodynamics lay the framework for the science of heat
transfer. The first law requires that the rate of energy transfer into a system be equal
 to the rate of increase of the energy of that system. The second law requires that heat
be transferred in the direction of decreasing temperature (Figure 1.2).

Fig. 1.2 Heat transfer from high temperature to low temperature

1.3 Application Areas of Heat Transfer

− Many ordinary household appliances are designed, in whole or in part, by using the
principles of heat transfer. Some examples:
− Design of the heating and air-conditioning system, the refrigerator and freezer, the
water heater, the iron, and even the computer, the TV, and the VCR
− Energy-efficient homes are designed on the basis of minimizing heat loss in winter and
heat gain in summer.
− Heat transfer plays a major role in the design of many other devices, such as car
radiators, solar collectors, various components of power plants, and even spacecraft.
− The optimal insulation thickness in the walls and roofs of the houses, on hot water or
steam pipes, or on water heaters is again determined on the basis of a heat transfer
analysis with economic consideration (Figure 1.3)

Fig. 1.3 Application of heat transfer

II UNIT
Heisler Charts
III - UNIT
Dimensional Analysis
• Dimensional analysis is a mathematical method
that makes use of the study of the dimensions
for solving several engineering problems.
• This method can be applied to all types of fluid
resistances, heat flow problems, and many other
problems in fluid mechanics and
thermodynamics.
• In dimensional analysis, the various physical
quantities used in fluid phenomena can be
expressed in terms of fundamental quantities.
These fundamental quantities are mass (M),
length (L), time (T), and temperature (θ or t)
IV - UNIT
HEAT EXCHANGERS
 HEAT EXCHANGERS
• A heat exchanger is a system used to transfer heat
between two or more fluids.
• Heat exchangers are used in both cooling and
heating processes.
• The fluids may be separated by a solid wall to
prevent mixing or they may be in direct contact.
• They are widely used in space
heating, refrigeration, air conditioning, power
stations, chemical plants, petrochemical
plants, petroleum refineries, natural gas processing,
and sewage treatment.
Shell and Tube HE
One pass shell and tube HE
Two pass HE
V - UNIT
Boiling and Condensation
Boiling Heat Transfer Phenomenon
• Boiling is a liquid-to-vapor change process just
like evaporation.
• Boiling is a phenomenon that occurs at a solid-
liquid interface when a liquid is brought in
contact with a surface maintained at a
temperature sufficiently above the saturation
temperature of the liquid.
• As the heat is conducted to the liquid-vapor
interface, bubbles are created by the
expansion of entrapped gas or vapor at small
cavities in the surface.
• The bubbles grow to a certain size, depending
on the surface tension at the liquid-vapor
interface and temperature and pressure.
• Boiling heat transfer is heat transferred by the
boiling of water.
• Heat Transfer, Q = h ( Ts - Tsat )
where Tsat is the saturation temperature of the
liquid.
 Classification of Boiling
• Pool Boiling
• Flow Boiling
• Sub cooled Boiling
• Saturated Boiling
• Pool Boiling:
✓ Boiling is called pool boiling when bulk fluid
motion is absence.
✓ Fluid motion is due to natural convection and
bubble-induced mixing.

• Flow Boiling:
✓ Boiling in the presence of bulk fluid motion is
called flow boiling (Forced Convection Boiling).
✓ Fluid motion is induced by external means such
as pump, as well as by bubble-induced mixing.
Sub cooled Boiling:
❖ When the temperature of the liquid is below
the saturation temperature.
❖ The term sub cooling refers to a liquid existing
at a temperature below its normal boiling
point.
Saturated Boiling:
❖ When the temperature of the liquid is equal
to the saturation temperature.
➢ Sub cooled and saturated boiling can exist in
both nucleate and film boiling.
 The Boiling Curve
• In a typical boiling curve, four different boiling
regimes are observed: natural convection
boiling, nucleate boiling, transition boiling,
and film boiling depending on the excess
temperature ΔTexcess=Ts−Tsat.
Natural Convection Boiling (to Point A)

➢ The liquid is slightly superheated in this case

(a metastable condition) and evaporates when
it rises to the free surface.
➢ Liquid motion is due to natural convection.
➢ In region 1 called the free convection zone,
the excess temperature is very small.
➢ Here the liquid near the surface is
superheated slightly, the convection currents
circulate the liquid and evaporation takes place
at the liquid surface.
Nucleate Boiling (between Points A and C)
• Bubbles start forming at point A and increases
number of nucleation sites as we move towards
point C.
• Region A–B –– isolated bubbles are formed and
heat flux rise sharply with increasing ΔTexcess.
This region is the beginning of nucleate boiling.
• Region B–C –– Increasing number of nucleation
sites causes bubble interactions and coalescence
into jets and column. Heat flux increases
at lower rate and maximum at point C. The
maximum heat flux known as critical heat flux
occurs at point C.
• Critical Heat Flux - CHF, (Te 30ºC) 
Maximum attainable heat flux in nucleate
boiling.
• q   1 MW/m for water at atmospheric
pressure.
• Point C on the boiling curve is also called
the burnout point, and the heat flux at this
point the burnout heat flux.
Transition Boiling(between Points C and D)
• When ΔTexcess increases past point C, heat
flux decreases because a large fraction of the
heater surface is covered by a vapor film,
which acts as an insulation.

• The transition boiling regime, which is also

called the unstable film boiling regime.
Film Boiling (beyond Point D)

• At point D, where the heat flux reaches a

minimum is called the Leidenfrost point.
• Heat transfer is by conduction and radiation
across the vapor blanket, therefore, heat
transfer rate increases with increasing excess
temperature.
• The Leidenfrost effect is a physical
phenomenon in which a liquid, close to a
surface that is significantly hotter than the
liquid's boiling point.
• The phenomenon of stable film boiling can be
observed when a drop of water falls on a red
hot stove. The drop does not evaporate
immediately but moves a few times on the
stove.
 Condensation
• The process of condensation is the reverse of
boiling.
• Condensation occurs when the temperature
of a vapor is reduced below its saturation
temperature.
Two forms of condensation:
• – Film condensation,
• – Drop wise condensation.
• Film-wise condensation generally occurs on
clean uncontaminated surfaces.
• In this type of condensation, the film covering
the entire surface grows in thickness as it
moves down the surface by gravity.
• There exists a thermal gradient in the film and
so it acts as a resistance to heat transfer.
• Ref = dH ρ V / (μ)
• dH = Hydraulic diameter
• ρ = density of liquid
• V = average velocity of flow
• μ = viscosity of fluid
• In drop-wise condensation the vapor
condenses into small liquid droplets of various
sizes which fall down the surface in a random
fashion.
• A large portion of the plate is directly exposed
to the vapor, making heat transfer rates much
larger than those in film condensation (5 to 10
times).
• Drop-wise condensation is achieved
by Adding a promoting chemical into
the vapor.
• Treating the surface with a promoter chemical,
Coating the surface with a polymer such as
Teflon or a noble metal such as Au, Ag, Rh, Pd, Pt
V - UNIT
Radiation
• Thermal radiation is an electromagnetic
phenomenon generated by the thermal
motion of particles in matter.
• All matter with a temperature greater
than absolute zero emits thermal radiation.
• All bodies emit radiation to their surroundings
through electromagnetic waves due to the
conversion of the internal energy of the body
into radiation.
• Particle motion results in the charge
acceleration which produces electromagnetic
radiation.
• Since electromagnetic waves can also travel
through a vacuum hence, in contrast to the
conduction and convection heat transfer, it
can take place through a perfect vacuum.
• Thus, when no medium is present, radiation
becomes the only mode of heat transfer.
• Common examples are the solar radiation
reaching the earth and the heat dissipation
from the filament of an incandescent lamp.
• Thus, heat is transferred between two bodies
over a great distance.
• Waves falling in the range of 0.1 to 100μm
wave length are called thermal radiation.
• According to the quantum theory, the thermal
radiation propagates in the form of discrete
quanta, each quantum having an energy of
E=hν
Where h = Planck’s constant = 6.625*10-34 J-s
ν = Frequency of quantum
 Reflection, Absorption, and
Transmission of Radiation
• When radiation falls on a body, a part of it may
be absorbed, a part may be reflected and the
remaining may pass through the body.
• The fraction of the incident radiation
absorbed by the body is transformed into
heat.
• The reflectivity is defined as the fraction of
incident radiation reflected from the surface
of the body.
• The transmissivity is defined as the fraction of
the incident radiation transmitted through the
body.
• The absorptivity is defined as the fraction of
incident radiation absorbed by the body.
• Bodies that do not transmit radiation are
called opaque.
• A body with reflectivity of unity will reflect
the whole of the incident radiation and is
termed a white body.
Concept of a Black body
• No actual body is perfectly black, the concept of a
black body is an idealization with which the
radiation characteristics of real bodies can be
conveniently compared.
• Real bodies do not emit as much energy as the
black body and hence their emissivity is less than
one.
• A black body plays a role in thermal radiation
similar to the idealized Carnot cycle in
thermodynamics with which real cycles are
compared.
• A black body is regarded as a perfect absorber of
incident radiation.
• The total radiation emitted by a black body is
a function of temperature.
• The emissivity of a substance is a measure of
its ability to emit radiation in comparison with
a black body.
• A black body is a perfect emitter.
• Intensity of radiation is defined as the
radiation emitted in any direction.
• The radiation intensity of a surface is defined
as the rate of heat flux emitted by it per unit
area.
 Laws of Radiation
1. Planck’s Law:
• Electromagnetic radiation consists of flow of quanta or
particles and the energy content (E) of each quantum is
proportional to the frequency.
• It is given by the following equation:
• E = hv
Where, E = Energy content
h = Planck’s constant = 6.625 x 10-34 J.s
v = Frequency
• It is clear that the greater the frequency, the shorter the
wavelength and the greater the energy content of the
quantum. In other words, the shorter the wavelength
greater is the energy of the quantum. Therefore, quanta of
ultraviolet light are more energetic than are quanta of red
light.
2. Kirchoff’s Law:
• Kirchoff law states that the absorptivity (a) of a
substance for radiation of a specific wavelength is
equal to its emissivity for the same wavelength
and is given by the following equation:
a (λ) = e(λ)
• Any grey object (other than a perfect black body)
which receives radiation, disposes of a part of it
in reflection and transmission.
• The absorptivity, reflectivity, and
transmissivity are each less than or equal to
unity.
▪ Monochromatic radiations are such radiations that
are characterized by a single frequency.
▪ In practice, radiation of a very small range of
frequencies can be described by stating a single
frequency.
 Wien's Displacement Law

• When the temperature of a blackbody

radiator increases, the overall radiated energy
increases, and the peak of the radiation curve
moves to shorter wavelengths.
• When the maximum is evaluated from the
Planck radiation formula, the product of the
peak wavelength and the temperature is
found to be a constant.
• Wavelength (λmax) of maximum intensity of
emission (µ) = b/T
Where,
• λmax is the wavelength at which maximum
radiation is emitted. It decreases as the
temperature increases.
b is constant = 2897
T is the temperature of the surface in Kelvin
Hence, λmax (µ) = 2897 T-1
• The temperature of the sun is 6000 °K for
which the value of maximum wavelength is
0.5µ, and that of the earth the average
temperature is 300 °K for which the value of
maximum wavelength is 10µ.
• Out of the total energy emitted by the sun, 7
percent is with a wavelength less than 0.4µ, 44
percent is with a wavelength ranging from 0.4
– 0.7µ and 49 percent is having wavelength
greater than 0.7µ.
Stefan-Boltzmann Law:
This law states that the intensity of radiation
emitted by a radiating body is proportional to
the fourth power of the absolute temperature of
that body.
Radiation Heat Transfer, Q = ƐσT4
Where,
σ = Stefan-Boltzmann constant =6.25*10-34 Js
Ɛ = Emissivity of a body (0 < s > 1.0)
T = Absolute temperature of the surface in °K.
 Radiation Shape Factor
• Radiation shape factor is defined as the fraction of
radiant energy that is diffused from one surface
element and strikes the other surface directly with
no intervening reflections.
• It is also called view factor or configuration factor.
• If A11 is the total area of radiating surface of body-1
having shape factor F12F12 w.r.t. receiver body-2
then the total radiant energy leaving surface-1 and
directly intercepted by surface-2 is =A1F12
The shape factor of a radiant body depends on the
1. Geometrical dimensions i.e. surface area
2. Configuration of radiating surface
concerning receiver & Inter-spatial
instance of the radiant body concerning
receiver.
• The shape factor of a radiating body is inversely
proportional to its surface area emitting radiant
energy i.e.
Shape factor ∝ 1/Surface area of emitter
• The shape factor of a radiating body is directly
proportional to the surface area of receiving body
i.e.
Shape factor ∝ Surface area of receiver

• The shape factor of a radiating body is inversely

proportional to inter-spatial distance between
emitter and receiver bodies i.e.
Shape factor ∝ 1 / Inter-spatial distance
• For steady state condition of radiation heat
transfer,
Rate of radiant energy lost by body-1 = rate of
radiant energy received by body-2
• A1F12=A2F21
Thank you
 R15
Code No: R15A0323
MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY
(Autonomous Institution – UGC, Govt. of India)
III B.Tech II Semester Regular/supplementary Examinations, April/May 2019
Heat Transfer
(ME)
Roll No

Time: 3 hours Max. Marks: 75

Note: This question paper contains two parts A and B
Part A is compulsory which carriers 25 marks and Answer all questions.
Part B Consists of 5 SECTIONS (One SECTION for each UNIT). Answer FIVE
Questions, Choosing ONE Question from each SECTION and each Question carries
10 marks.
Heat and mass transfer data books are permitted.
*******

PART – A (25 Marks)

1. (a) State Fourier's law of heat conduction. Why negative sign is used? (2M)
(b) What is lumped heat capacity method? Explain. (3M)
(c) Differentiate between natural and forced convection (2M)
(d) What is the significance of non dimensional numbers (3M)
(e) State Stefan Boltzmann’s law (2M)
(f) ) What are the various radiation properties (3M)
(g) What is NTU method of a heat exchanger. (2M)
(h) What are the differences between film wise and drop wise condensation. (3M)
(i) List some industrial and day-to-day applications of mass transfer (2M)
(j) State Fick’s law of diffusion. What are its limitations? (3M)
PART – B (50 Marks)
SECTION – I
2. A furnace wall is built up of two layers laid of fireclay 12cm thick and red brick 25 cm
thick while the annular space between the two is filled with diatomite brick (15cm).
What should be the thickness of the red brick layer if the wall is to be constructed
without diatomite brick, so that the heat flow through the wall remains constant? The
thermal conductivities of fireclay, diatomite and red brick being 0.929, 0.129 and 0.699
W/m0c respectively. (10M)
(OR)
3. Derive the general heat conduction equation in Spherical coordinates. (10M)
SECTION – II

4. Determine the heat transfer rate by free convection from a plate 0.3m × 0.3m for which
one surface is insulated and the other surface is maintained at 1100C and exposed to
atmosphere air at 300C for the following arrangements:
a) The plate is vertical
b) The plate is horizontal with the heating surface facing up
c) The plate is horizontal with the heating surface facing down. (10 M)
(OR)

DEPARTMENT OF MECHANICAL ENGINEERING

5. Derive the expression for boundary layer thickness for free convection heat transfer on
a vertical flat plate. (10M)
SECTION – III
6. (a). Explain what do you mean by absorptivity, reflectivity and transmissivity (5M)
|(b). Obtain the expression for blackbody radiation (5M)

(OR)
7. Two parallel plate 3m × 2m are spaced at 1m apart one plate is maintained at 5000C
and other at 2000C. The emissivity of the plates are 0.3 and 0.5. The plates are located
in a large room and room walls are maintained at 400C. If the plates exchange heat
with each other and with the room, find the heat lost by the hotter plate. (10M)
SECTION – IV

8. (a) Derive an expression for effectiveness of counter flow heat exchanger. (5M)
(b) Explain about the Regime’s of boiling with a neat sketch. (5M)
(OR)
9. (a) Derive the expression for LMTD in a parallel flow double pipe heat exchanger
(5M)
(b) A hot fluid enters a heat exchanger at a temperature of 2000C at a flow rate of
2.8 kg/sec (sp. heat 2.0 kJ/kg-K) it is cooled by another fluid with a mass flow rate
of 0.7 kg/sec (Sp. heat 0.4 kJ/kg-K). The overall heat transfer coefficient based on
outside area of 20 m2 is 250 W/m2-K.Calculate the exit temperature of hot fluid when
fluids are in parallel flow.(5M)

SECTION – V
10. (a) Derive the equation for mass transfer coefficient. (5M)
(b) Derive an expression for Fick's law of diffusion. (5M)
(OR)
11. (a) Explain the various modes of mass transfer (5M)
(b) Define various concentrations, velocities and fluxes in mass trasnfer (5M)

*******

DEPARTMENT OF MECHANICAL ENGINEERING

 R15
Code No: R15A0323
MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY
(Autonomous Institution – UGC, Govt. of India)
III B.Tech II Semester supplementary Examinations, Nov/Dec 2018
Heat Transfer
(ME)
Roll No

Time: 3 hours Max. Marks: 75

Note: This question paper contains two parts A and B
Part A is compulsory which carriers 25 marks and Answer all questions.
Part B Consists of 5 SECTIONS (One SECTION for each UNIT). Answer FIVE
Questions, Choosing ONE Question from each SECTION and each Question carries
10 marks.
******
PART – A (25 Marks)
1. (a) Describe the mechanism of heat transfer by convection (2M)
(b) A metallic plate of 3 cm thick is maintained at 400 0C on one side and 100 0C on the
other. How much heat is transferred through the plate per unit area? If thermal conductivity
of the plate is (K) = 370 W/mK (3M)
(c) Distinguish between laminar and turbulent flow (2M)
(d) Explain about hydro thermal boundary layer concept (3M)
(e) State Stefan Boltzmann’s law (2M)
(f) ) what is a black body? How does it differ from a grey body? (3M)
(g) How are the heat exchangers classified? (2M)
(h) What are fouling factors? Explain their effect in heat exchanger design. (3M)
(i) Explain briefly the term mass transfer. (2M)
(j) List the various modes of mas transfer and briefly explain about any one type of mass
transfer. (3M)
PART – B (50 Marks)
SECTION – I
2. What is the critical thickness of insulation on a small diameter wire or pipe? Explain
its physical significance and derive an expression for the same. (10M)
(OR)
3. Derive the equation for a heat transfer through a composite wall as Q= ΔT/∑R in
which ΔT is the temperature difference and is the ∑R total resistance (10M)
SECTION – II
4. An air stream at 0 C is flowing along a heated plate at 90 oC at a speed of 75 m/sec
o

the plate is 45 cm long and 60 cm wide. Assuming the transition of the boundary layer
to take place at Recx = 5X105 calculate the average values of friction coefficient and
heat transfer coefficient for the full length of the plate. Hence calculate the rate of
energy dissipation from the plate (10M)
(OR)
5. Air stream at 27 0C is moving at 0.3m/sec across a 100 W electric bulb at 127 0C. if the
bulb is approximated by a 60 mm diameter sphere, estimate the heat transfer rate and
the percentage of power loss due to convection (10M)
SECTION – III
6. Two parallel plates of size 1.0 mX1.0 m spaced 0.5 m apart are located in a large room,
the walls of which are maintained at a temperature of 27 0C. One plate is maintained at
a temperature of 900 0C and the other at 400 0C and their emissivities

DEPARTMENT OF MECHANICAL ENGINEERING

 are 0.2 and 0.5 respectively. If the plates exchange heat between themselves and
surroundings, find the net heat transferred to each plate and the room. Consider only
the plate surfaces facing each other. (10M)
(OR)
7. Calculate the net radiant heat exchange per m2 area for two large parallel plates at
temperature of 427 0C and 27 0C respectively. ε (hot plate) = 0.9 and ε(cold plate ) =
0.6. If a polished aluminum shield is placed between them, find the percentage
reduction in the heat transfer, ε (shied) = 0.4. (10M)
SECTION – IV
8. Hot oil with a capacity rate of 2500 W/K flows through a double pipe heat exchanger.
It enters at 360 0C and leaves at 300 0C. Cold fluid enters at 30 0C and leaves at 200 0C.
If the overall heat transfer coefficient is 800W/m2K. Determine the heat exchanger area
required for a) parallel flow and b) counter flow.(10M)
(OR)
9. Distinguish between film wise and drop wise condensation. Which of the two gives a
higher heat transfer heat transfer coefficient? Why? (10M)
SECTION – V
10. .Derive the general mass transfer equation in Cartesian coordinates. (10M)
(OR)
11. The molecular weights of the two components A and B of the gas mixture are 24 and
28 respectively. The molecular weight of gas mixture found to be 30. If the mass
concentration of the mixture is 1.2 kgm3, determine the following. i). Molar fractions,
ii).mass fractions and iii). Total pressure if the temperature of the mixture is 290K.
(10M)

*******

DEPARTMENT OF MECHANICAL ENGINEERING

 R15
Code No: R15A0323
MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY
(Autonomous Institution – UGC, Govt. of India)
III B.Tech II Semester Regular Examinations, April/May 2018
Heat Transfer
(ME)
Roll No

Time: 3 hours Max. Marks: 75

Note: This question paper contains two parts A and B
Part A is compulsory which carriers 25 marks and Answer all questions.
Part B Consists of 5 SECTIONS (One SECTION for each UNIT). Answer FIVE
Questions, Choosing ONE Question from each SECTION and each Question carries
10 marks.
*******

PART – A (25 Marks)

1. (a) Describe the mechanism of heat transfer by conduction (2M)
(b) What are the assumptions for lumped capacity analysis? (3M)
(c) Distinguish between laminar and turbulent flow (2M)
(d) Explain about thermal boundary layer concept (3M)
(e) State Stefan Boltzmann’s law (2M)
(f) ) State and prove the Kirchoff’s law α=ε (3M)
(g) Sketch the temperature variations in parallel flow and counter flow heat
exchangers. (2M)
(h) What are fouling factors? Explain their effect in heat exchanger design. (3M)
(i) Enumerate applications of mass transfer (2M)
(j) State Fick’s law of diffusion. What are its limitations? (3M)

PART – B (50 Marks)

SECTION – I

2. (a) What are Biot and Fourier Numbers? Explain their physical significance. (3M)

(b) A door of a cold storage plant is made from 6mm thick glass sheet separated by a
uniform air gap of 2mm. The temperature of the air inside the room is -200 C and the
ambient air temperature is 30 0C. Assuming that the heat transfer coefficient between
glass and the air 23.26 W/m2K. Determine the rate of heat leaking in the room per unit
area of the door. Neglect the convection effects in the air gap. Kglass = 0.75 W/mK, Kair
= 0.02W/mK. (7M).

(OR)

3. Derive the general heat conduction equation in Cartesian coordinates. (10M)

SECTION – II

DEPARTMENT OF MECHANICAL ENGINEERING

4. Assuming that the man can be represented by a cylinder 30 cm in diameter and 1.7 m
high with the surface temperature of 30 0C, Calculate the heat he would lose while
standing in a 36 Kmph wind at 10 0C. (10 M)

(OR)
5. Air stream at 27 C is moving at 0.3 m/sec across a 100 W electric bulb at 127 0C. If the
0

bulb is approximated by a 60 mm diameter sphere, estimate the heat transfer rate and the
percentage of power loss due to convection (10M)
SECTION – III

6. (a). Explain the concept of black body and gray body (5M)

|(b). Write a short notes on radiation shields (5M)

(OR)

7. The radiation shape factor of the circular surface of a thin hollow cylinder of 10 cm
diameter and 10 cm length is 0.1716. What is the shape factor of the curved surface of the
cylinder with respect to itself? (10M)
SECTION – IV

8. (a) Why a counter flow heat exchanger is more effective than a parallel flow heat
exchanger.(4M)

(b) Write a short notes on Regime’s of boiling with a neat sketch. (6M)

(OR)
9. In a counter flow double pipe heat exchanger; water is heated from 25 0C to 65 0C by
oil with a specific heat of 1.45 kJ/kg K and mass flow rate of 0.9kg/sec. the oil is cooled
from 230 0C to 160 0C. if the overall heat transfer coefficient is 420 W/m2K, calculate
i) the rate of heat transfer ii) mass flow rate of water iii) the surface area of heat
exchanger. (10M)

SECTION – V

10. (a) Derive the equation for mass transfer coefficient. (6M)
(b) Write a short notes on Equi molal diffusion and Isothermal equimass. (4M)
(OR)
11. A vessel contains a binary mixture of o2 and n2 with partial pressures in the ratio of
0.21 and 0.79 at 15C. The total pressure of the mixture is 1.1 bar. Calculate the
following i). Molar concentrations, ii) .Mass densities, iii). Mass fractions, iv). Molar
fractions of each species. (10M)

*******

DEPARTMENT OF MECHANICAL ENGINEERING

DEPARTMENT OF MECHANICAL ENGINEERING
Code No: 136CA
R16
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
B. Tech III Year II Semester Examinations, May - 2019
HEAT TRANSFER
(Mechanical Engineering)
Time: 3 hours Max. Marks: 75

Note: This question paper contains two parts A and B.

Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B
consists of 5 Units. Answer any one full question from each unit. Each question carries
10 marks and may have a, b, c as sub questions.

PART - A
(25 Marks)

1.a) Define Newton's law of cooling. [2]

b) Explain the term boundary conditions. [3]
c) Discuss the physical interpretation of thermal diffusivity. [2]
d) How does the fin efficiency differ from fin effectiveness? [3]
e) What is the difference between local and average convection heat transfer? [2]
f) Draw a neat sketch showing laminar and turbulent regions of the boundary layer during
flow over a flat plate. [3]
g) Define Reynolds analogy. [2]
h) List out the assumptions made during derivation of expression for LMTD. [3]
i) State and explain the Wien – Displacement Law. [2]
j) Differentiate between film wise and drop wise condensation. [3]

PART - B
(50 Marks)

2.a) What is meant by thermal resistance? Explain the electrical analogy for solving heat transfer
problem.
b) A mild steel tank of wall thickness 10mm contains water at 900C. Calculate the rate of
heat loss per m2 of tank surface area when the atmospheric temperature is 150C. The
thermal conductivity of mild steel is 50 W/m K and the heat transfer co-efficient for
inside and outside the tank is 2800 and 11 W/m2K respectively. Calculate also the
temperature of the outside surface of the tank. [5+5]
OR
3. a) What is the critical thickness of insulation on a small diameter wire or pipe. Explain its
physical significance and derive the expression for same.
b) The wall of a cold room is composed of three layers. The outer layer is brick 30cm thick.
The middle layer is cork 20 cm thick, the inside layer is cement 15 cm thick. The
temperatures of the outside air is 250C and on the inside air is -200C. The film co- efficient
for outside air and brick is 55.4 W/m2K. Film co-efficient for inside air and cement is 17
W/m2K. Find heat flow rate. [5+5]
Assume
k for brick = 2.5 W/mK
k for cork = 0.05 W/mK
k for cement = 0.28 W/mK
4. A 12 cm diameter cylindrical bar initially at a uniform temperature of 400C is placed in
a medium at 6500C with a convective heat transfer coefficient of 22 w/m2 K. Determine
the time required for centre to reach 2550C. Also calculate the temp of the surface. Take
k=0.2 w/mK; P = 580 kg/m3, Cp = 1050 kJ/kg. [10]
OR
5. a) Develop an expression for temperature distribution in a slab made of single material.
b) Sheets of brass and steel, each of thickness 1cm, are placed in contact. The outer surface
of brass is kept at 1000C and the outer surface of steel is kept at 00C. What is the
temperature of the common interface? The thermal conductivities of brass and steel are
in the ratio of 2:1. [5+5]

6. a) Explain the Raleigh’s method of dimensional analysis giving an example.

b) How do you determine Grasshof number? State its physical significance. [5+5]
OR
7. a) What do you understand by hydrodynamic and thermal boundary layers? Illustrate with
reference to flow over a heated flat plate. How is the boundary layer thickness defined?
b) A water heater is fabricated by a resistance wire wound uniformly over a 10 mm diameter
and 4m long tube. The resistance element maintains a uniform heat flux of 1000W/m2.
The mass flow rate of water is 12kg/hr and its inlet temperature is 100C. Estimate the
surface temperature of tube at the exit. [5+5]

8. a) Discuss how the geometric parameter of the pipe, physical properties of the fluid and
its velocity influence the heat transfer coefficient in the fluid flow in a pipe.
b) Water at 300C is flowing through a pipe of 25 mm inner diameter at a rate of 1 m 3/hr.
Find the heat transfer coefficient in water if the length of the pipe is 50 cm. The thermal
conductivity, density and kinematic viscosity of water are 0.63 W/m0K, 980 Kg/m3, and
0.6 × 10 –6 m2/s respectively. [5+5]
OR
9. In a heat exchanger, water flows through a 0.02 m inner diameter copper tube at a velocity
of 1.5 m/s. The water entering the tube at 150C is heated by steam condensing at 1000C
on the outside surface of the tube. What would be heat transfer coefficient for water if it
is to leave the pipe at 450C? The physical properties of water at the bulk temperature
300C are as follows. Thermal conductivity is 0.6172 W/(m.K)
Kinematic Viscosity 0.805 10-6 m2/s
Density 995 kg/m3.
Specific heat 4171 J/(kg.K). [10]

10. a) A black body is kept at a temperature of 1000k. Determine the fraction of thermal radiation
emitted by the surface in the wavelength band 1.0 to 6.0μ.
b) Estimate the rate of solar radiation on a plate normal to the sun rays. Assume the sun to
be a black body at a temperature of 55270C. The diameter of the sun is 1.39 × 106km and
its distance from the earth is 1.5 × 108 km. [5+5]
OR
11.a) Define the terms
i) Absorptivity
ii) Reflectivity and
iii) Transmissivity.
b) Differentiate between specular and diffuse reactions.
c) Derive Stefan-Boltzmann's law from Plank's law. [10]

---ooOoo---
Code No: 136CA R16
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
B. Tech III Year II Semester Examinations, November/December - 2020
HEAT TRANSFER
(Mechanical Engineering)
Time: 2 hours Max. Marks: 75
Answer any five questions
All questions carry equal marks
---

1. a) Derive general heat conduction equation in radial coordinates and state the assumption
made.
b) A pipe carrying steam at 250 0C has an internal diameter of 12 cm and the pipe thickness
is 7.5 mm. The conductivity of the pipe material is 49 W/m K the convective heat transfer
coefficient on the inside is 85 W/m2 K. The pipe is insulated by two layers of insulation
one of 5 cm thickness of conductivity 0.15 W/m K and over it another 5 cm thickness
of conductivity 0.48 W/m K. The outside is exposed to air at 35 0C with a convection
coefficient of 18 W/m2 K. Determine the heat loss for 5 m length. Also determine the
interface temperatures and the overall heat transfer coefficient based on inside and
outside areas. [8+7]

2. A truncated cone like solid has its circumferential surface insulated. The base is at
300 0C and the area along the flow direction at x is given by A = 1.3 (1 – 1.5x). Where x
is measured from the base in the direction of flow in m and A is in m 2. If the thermal
conductivity is 2.6 W/m K and the plane at x = 0.2 m is maintained at 100 0C, determine
the heat flow and also the temperature at x = 0.1 m. Calculate the temperature gradients
at the three sections. [15]

3. Derive an expression for heat dissipation in a straight triangular fin. [15]

4. A cylinder of radius 0.2 m generates heat uniformly at 2 × 106 W/m3. If the thermal
conductivity of the material has a value of 200 W/m K, determine the maximum
temperature gradient. Also find the centre temperature if the surface is at 100 0C. What
is the value of heat flux at the surface and heat flux per m length? [15]

5. a) Air flows over a flat plate of 80 m × 0.5 m at a velocity of 2 m/s. The temperature of air
is 50 0C, calculate i) the boundary layer thickness, ii) the drag coefficient both at a
distance of 0.8 m from the leading edge of the plate, and iii) the drag force on the plate
over the entire length. Take  = 1.003 kg/m3 and =17.95 × 10-6 m 2 /s for air at 50 0C.
b) Define (i) boundary layer thickness, (ii) velocity and momentum displacement thickness,
and (iii) enthalpy and conduction thicknesses. [8+7]

6. Wind blows at 20 kmph parallel to the wall of adjacent rooms. The first room extends to
10 m and the next one to 5 m. The wall is 3.2 m high. The room inside is at 20 0C and
the ambient air is at 40 0C. The walls are 25 cm thick and the conductivity or the material
is 1.2 W/m K. On the inside convection coefficient has a value of 6 W/m2 K. Determine
the heat gain through the walls of each room. [15]
7. a) Derive equation of LMTD for counter flow heat exchanger.
b) A cross flow heat exchanger with both fluids unmixed is used to heat water flowing at a
rate of 20 kg/s from 25 0C to 75 0C using gases available at 300 0C to be cooled to
180 0C. The overall heat transfer coefficient has a value of 95 W/m2 K. Determine the
area required. For gas Cp = 1005 J/kg K. [8+7]

8. A vertical tube, 1.2 m long and having 50 mm outer diameter is exposed to steam at
1.2 bar. If the tube surface is maintained at 85 0C by flowing cooling water through it,
determine the rate of heat transfer to the cooling water and the rate of condensation of
steam. If the tube is held in horizontal position, estimate the condensation rate. [15]

---ooOoo---
Code No: 136CA R16
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
B. Tech III Year II Semester (Special) Examinations, January/February - 2021
HEAT TRANSFER
(Mechanical Engineering)
Time: 2 hours Max. Marks: 75
Answer any five questions
All questions carry equal marks
---
1. A long Cylindrical rod of radius 5 cm and K = 10 W/m K contains radio active material
which generates heat uniformly with in the cylinder at a constant rate of 3 MW/m3. The
rod is cooled by convection from its cylindrical surface into ambient air at 500C with heat
transfer coefficient of 60 W/m2 K. Calculate the temperature at the centre and outer
surface of the cylindrical rod. [15]

2. A 0.75 m high and 1.25 m wide double pane window consists of two 3 mm thick layers
of glass (85 W/m K) separated by a 10 mm wide stagnant air space (0.022 W/m K).
Determine the rate of heat transfer through this window and the temperature of the inner
surface, when the room is maintained at 240C. Take the convective heat transfer
coefficients on the inside and the outside surfaces of the window as 15 and 50 W/m 2K
respectively. [15]

3. An thin copper rod (K= 95 W/m K) is 12 mm in diameter and spans between two plates
150 mm apart. Air flows over the plates providing the convective heat transfer coefficient
equal to 50 W/m2 K. If the surface temperature of the plates exceeds the air temperature
by 450C, calculate excess temperature at mid length of the rod over that of air and the
heat loss from the rod. [15]

4. State and explain Buckingham Pi theorem and apply the same for natural convection heat
transfer. [15]

5. a) What is the significance of Reynolds number and Nusselt number in forced convection
heat transfer? Explain.
b) Air at 2 bar and 400C is heated as it flows through a 30 mm diameter tube at a velocity of
10 m/sec. If the wall temperature is maintained at 1000C all along the length of tube,
make calculations for the heat transfer per unit length of the tube. [8+7]

6. Draw the velocity profile on vertical flat plate for natural convection and discuss the
importance in evaluating the heat transfer coefficient. [15]

7. In a counter flow double pipe heat exchanger water is heated from 250C to 650C by oil
with a specific heat of 1.45 kJ/kg K and the mean flow rate of 0.9 kg/s. The oil is cooled
from 230C to 160C. If the overall heat transfer coefficient is 420 W/m2 K. Calculate a)
rate of heat transfer, b) mean flow rate of water and c) surface area of the heat exchanger.
[15]

8.a) A square room 4 m × 4 m and height 3 m has all its walls perfectly insulated. The floor
and ceiling are maintained at 300 K and 280 K respectively. Assuming an emissivity
value 0.75 for all surfaces, determine the wall temperature and the net heat interchange
between the floor and the ceiling. Take floor to ceiling shape factor as 0.28.
b) What is the need of radiation shields? Explain the significance and their applications.
[7+8]
---ooOoo---