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Chapter 2 Slide

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(i.e.

the rate of heat conduction in


the x-direction per unit area normal
to the x-direction)
1. An annealing chamber has a composite wall made of a 17 cm thick firebrick layer (k =
1.1 W/m °C) and a 13 cm thick ordinary brick layer (k = 0.70 W/m °C). The inside and
outside surface temperatures of the walls are 400°C and 45°C, respectively. Calculate
the heat loss from 25 m2 of furnace wall. Also, determine the temperature between the
ordinary brick and the firebrick layers.
2. The walls of a house in a cold region consist of three layers-an outer brickwork of 15 cm
thickness and an inner wooden panel of 1.2 cm thickness. The intermediate layer is made of
an insulating material 7 cm thick. The thermal conductivities of the brick and the wood
used are 0.70 W/m °C and 0.18 W/m °C, respectively. The inside and outside temperatures
of the composite wall are 21°C and -15°C, respectively. If the layer of insulation offers
twice the thermal resistance of the brick wall, calculate (a) the rate of heat loss per unit area
of the wall and (b) the thermal conductivity of the insulating material.
3. A 15 cm schedule 40 steam main carries saturated steam at 10.7 bar (gauge), and the
temperature is 190°C. The inside and outside diameters of the pipe are 15.4 cm and 16.8
cm, respectively. The thermal conductivity of the pipe wall is 51 W/m °C. The pipe is
insulated with a 10 cm thick fibre glass blanket (k = 0.072 W/m °C). If the outer surface
temperature of the insulation is 41°C, calculate the rate of heat loss over a 10 m section of
the pipe. Also, calculate the fraction of the total thermal resistance offered by the pipe
wall. Is it justified to neglect the resistance of the metal wall in this type of problem?
4. A spherical vessel of 3 m inside diameter is made of AISI 316 stainless steel sheet of 9
mm thickness (k = 14 W/m °C). The inside temperature is - 80°C. The vessel is layered with
a 10 cm thick polyurethane foam (k = 0.02 W/m °C) followed by a 15 cm outer layer of
cork (k = 0.045 W/m °C). If the outside surface temperature is 30°C, calculate (a) the total
thermal resistance of the insulated vessel wall, (b) the rate of heat flow to the vessel, (c) the
temperature and heat flux at the interface between the polyurethane and the cork layers, and
(d) the percentage error in calculation if the heat transfer resistance of the metal wall is
neglected.
5. Consider a composite wall consisting of four different materials as shown in Figure 1.
The following data are given: LA = 0.1 m, LC = 0.2 m, LD = 0.12 m, H = 2 m, HB = 1 m,
kA = 20 W/m °C, kB = 10 W/m °C, kc = 7 W/m °C, kD = 25 W/m °C, T1 = 120°C, and T2 =
50°C.
Calculate the rate of heat flow through the assembly per unit breadth. Assume one -
dimensional heat flow only. Show the electric analogue of the problem.

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