Materi Perpindahan Kalor & Massa

PERPINDAHAN KALOR DAN MASSA 2
Dr. Eng. Rizal Mahmud, S.Pd., M.T
Teknik Mesin
Institut Teknologi Adhi Tama Surabaya
Natural Convection
Contents
❑ Physical Mechanism of Natural Convection
❑ Equation of Motion and The Grashof Number
❑ Natural Convection over Surfaces
2
Natural Convection
Physical Mechanism of Natural Convection

Many familiar heat transfer applications
involve natural convection as the primary
mechanism of heat transfer. Examples?
Natural convection in gases is usually
accompanied by radiation of comparable
magnitude except for low-emissivity
surfaces.
The motion that results from the continual
replacement of the heated air in the vicinity
of the egg by the cooler air nearby is called
a natural convection current, and the heat
transfer that is enhanced as a result of this
current is called natural convection heat
transfer.
3
Natural Convection
Buoyancy force: The upward force exerted by a fluid on a body completely or
partially immersed in it in a gravitational field. The magnitude of the buoyancy force
is equal to the weight of the fluid displaced by the body.
Where ρfluid is the average density
of the fluid (not the body), g is the
gravitational acceleration, and
The net vertical force acting on a body Vbody is the volume of the portion
of the body immersed in the fluid
(for bodies completely immersed
in the fluid, it is the total volume
of the body).
Archimedes’ principle: A body immersed in a fluid will

experience a “weight loss” in an amount equal to the weight of the
fluid it displaces.
The “chimney effect” that induces the upward flow of hot
combustion gases through a chimney is due to the buoyancy effect.
4
Natural Convection
In natural convection, no blowers are used, and therefore the

flow rate cannot be controlled externally.
The flow rate in this case is established by the dynamic
balance of buoyancy and friction.
An interferometer produces a map of interference fringes,

which can be interpreted as lines of constant temperature.
The smooth and parallel lines in (a) indicate that the flow is
laminar, whereas the eddies and irregularities in (b) indicate
that the flow is turbulent.
The lines are closest near the surface, indicating a higher
temperature gradient.
5
Natural Convection
The thickness of the boundary layer increases in the

flow direction.
Unlike forced convection, the fluid velocity is zero
at the outer edge of the velocity boundary layer as
well as at the surface of the plate.
At the surface, the fluid temperature is equal to the
plate temperature, and gradually decreases to the
temperature of the surrounding fluid at a distance
sufficiently far from the surface.
In the case of cold surfaces, the shape of the
velocity and temperature profiles remains the same
but their direction is reversed.
6
Natural Convection
The Grashof Number

The governing equations of natural convection and the boundary conditions can be
nondimensionalized by dividing all dependent and independent variables by suitable constant
quantities:
Substituting them into the momentum equation and simplifying give
Grashof number: Represents the

natural convection effects in
momentum equation.
7
Natural Convection
▪ The Grashof number provides the main criterion in determining whether the fluid flow
is laminar or turbulent in natural convection.
▪ For vertical plates, the critical Grashof number is observed to be about 109 .
When a surface is subjected to external flow, the problem

involves both natural and forced convection.
The relative importance of each mode of heat transfer is
determined by the value of the coefficient 𝐺𝑟/𝑅𝑒 2 :
• Natural convection effects are negligible if 𝐺𝑟/𝑅𝑒 2 << 1.
• Free convection dominates and the forced convection effects
are negligible if 𝐺𝑟/𝑅𝑒 2 >> 1.
• Both effects are significant and must be considered if
𝐺𝑟/𝑅𝑒 2 = 1 (mixed convection).
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Natural Convection
9
Natural Convection
Natural Convection over Surfaces

Natural convection heat transfer on a surface depends on the geometry of the surface as well as its
orientation, the variation of temperature on the surface and the thermophysical properties of the fluid
involved.
With the exception of some simple cases, heat transfer relations in natural
convection are based on experimental studies.
The constants C and n depend on the geometry of the surface and the flow
regime, which is characterized by the range of the Rayleigh number.
The value of n is usually 1/4 for laminar flow and 1/3 for turbulent flow.
All fluid properties are to be evaluated at the film temperature Tf = (Ts + T∞)/2.
10
Natural Convection
Vertical Plates (Ts = constant)

For a vertical flat plate, the characteristic length is the plate height L. In Table 9–1 we give
three relations for the average Nusselt number for an isothermal vertical plate. The first two
relations are very simple. Despite its complexity, we suggest using the third one (Eq. 9–21)
recommended by Churchill and Chu (1975) since it is applicable over the entire range of
Rayleigh number. This relation is most accurate in the range of 10−1 < 𝑅𝑎𝐿 < 109 .
11
Natural Convection
12
Natural Convection
Vertical Plates (𝑞ሶ 𝑠 = constant)
The relations for isothermal plates in the table can also be used for plates subjected to uniform
heat flux, provided that the plate midpoint temperature 𝑇𝐿/2 is used for 𝑇𝑠 in the evaluation of
the film temperature, Rayleigh number, and the Nusselt number.
Inclined Plates
In the case of a hot plate in a cooler environment,
convection currents are weaker on the lower surface of
the hot plate, and the rate of heat transfer is lower relative
to the vertical plate case.
On the upper surface of a hot plate, the thickness of the
boundary layer and thus the resistance to heat transfer
decreases, and the rate of heat transfer increases relative
to the vertical orientation.
In the case of a cold plate in a warmer environment, the
opposite occurs. 13
Natural Convection
Horizontal Plates
For a hot surface in a cooler environment, the net force
acts upward, forcing the heated fluid to rise.
If the hot surface is facing upward, the heated fluid rises
freely, inducing strong natural convection currents and
thus effective heat transfer.
But if the hot surface is facing downward, the plate blocks
the heated fluid that tends to rise, impeding heat transfer.
The opposite is true for a cold plate in a warmer
environment since the net force (weight minus buoyancy
force) in this case acts downward, and the cooled fluid
near the plate tends to descend.
14
Natural Convection
Horizontal Cylinders and Spheres
The boundary layer over a hot horizontal cylinder starts to

develop at the bottom, increasing in thickness along the
circumference, and forming a rising plume at the top.
Therefore, the local Nusselt number is highest at the bottom,

and lowest at the top of the cylinder when the boundary layer
flow remains laminar.
The opposite is true in the case of a cold horizontal cylinder in a

warmer medium, and the boundary layer in this case starts to
develop at the top of the cylinder and ending with a descending
plume at the bottom.
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Natural Convection
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Natural Convection
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Natural Convection
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Natural Convection
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Natural Convection
20
Natural Convection
21

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PERPINDAHAN KALOR DAN MASSA 2

Dr. Eng. Rizal Mahmud, S.Pd., M.T

Physical Mechanism of Natural Convection

Archimedes’ principle: A body immersed in a fluid will

In natural convection, no blowers are used, and therefore the

An interferometer produces a map of interference fringes,

The thickness of the boundary layer increases in the

The Grashof Number

Substituting them into the momentum equation and simplifying give

Grashof number: Represents the

When a surface is subjected to external flow, the problem

Natural Convection over Surfaces

Vertical Plates (Ts = constant)

Horizontal Cylinders and Spheres

The boundary layer over a hot horizontal cylinder starts to

Therefore, the local Nusselt number is highest at the bottom,

The opposite is true in the case of a cold horizontal cylinder in a

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