Heat transfer related questions that can be used for an examination.

1. MMB 421 HEAT TRANSFER
ASSIGNMENT 1
DUE DATE: FRIDAY 14 SEPTEMBER 2018; 1700 HRS
Solve the following problems following as much as possible the formal procedure for
solving heat transfer problems.
1. A glass window of width W = 1m and height H = 2m is 5 mm thick and has a thermal
conductivity of kg = 1.4W/m·K. If the inner and outer surface temperatures of the
glass are 15°C and -20°C, respectively, on a cold winter day, what is the rate of heat
loss through the glass? To reduce heat loss through windows, it is customary to use
a double pane construction in which adjoining panes are separated by an air space.
If the spacing is 10mm and the glass surfaces in contact with the air have
temperatures of 10°C and -15°C, what is the rate of heat loss from a 1m X 2m
window? The thermal conductivity of air is ka = 0.024 W/m·K. [10 marks]
2. The door of a domestic refrigerator has an area of 0.7 m2
and is essentially made of
a thin metal sheet with a 2.5 cm thick layer of insulation on the inside. The thermal
conductivity of the insulation is 0.25 W/m°C and the heat transfer coefficients to the
surrounding air on each side of the door are both 10 W/m2
°C. The inside of
refrigerator (cold chamber) and the kitchen (where the refrigerator is placed) are to
be maintained at 0°C and 20°C respectively. Assuming the thermal resistance
through the metal sheet to be negligible, determine
a. the heat flow rate through the door. [5 marks]
b. the surface temperature of the metal sheet. [5 marks]
3. A steam main 75 mm inside dia. and 90 mm outside dia. is lagged with two
successive layers of insulation. The layer in contact with the pipe is 38 mm asbestos
( 0.14 / °Ck W m  ). The asbestos layer is covered with 25 mm thick magnesia
insulation ( 0.07 / °Ck W m  ). The surface coefficients for inside and outside
surfaces are 227 W/m2
°C and 6.8 W/m2
°C respectively and the thermal conductivity
of the pipe material = 45 W/m°C. If the steam temperature is 375°C and the ambient
temperature is 35°C, calculate the steady state loss of heat from steam for 60m
length of pipe. [10 marks]
4. A leading manufacturer of household appliances is proposing a self-cleaning oven
design that involves use of a composite window separating the oven cavity from the
room air. The composite is to consist of two high-temperature plastics (A and B) of
thicknesses LA = 2LB and thermal conductivities kA = 0.15 W/m·K and kB = 0.08
W/m·K. During the self-cleaning process, the oven wall and air temperatures, Tw; and
Ta, are 400°C, while the room air temperature T∞ is 25°C. The inside convection and
radiation heat transfer coefficients hi, and hr., as well as the outside convection
coefficient ho; are each approximately 25 W/m2
·K. What is the minimum window
thickness, L = LA + LB, needed to ensure a temperature that is 50°C or less at the

2. outer surface of the window? This temperature must not be exceeded for safety
reasons. [15 marks]
5. A simple thermal conductivity measuring device is shown in figure below. The centre
rod is a metal with unknown thermal conductivity k which is to be determined. The
upper surface of the rod is maintained at 80 °C with an electric heater, while the
lower end surface is held at 22°C with a cooling water flow through a plate-type heat
exchanger. Assume that over this temperature range, 22 to 80 °C, the conductivity is
constant, determine the value of k if the electric power input is 18.45 W and the
specimen length and diameter are 0.1 m and 0.03 m, respectively. Using tables of
material thermal properties, state the metal with the closest value of conductivity to
this metal. [10 marks]
6. A steel pipe (k = 45.0 W/m·K) having a 5.0 cm outside dia. is covered with a 4.2 cm
thick layer of magnesia (k = 0.07 W/m·K) which is in turn covered with a 2.4 cm layer
of fiberglass insulation (k = 0.048W/m·K). The pipe wall outside temperature is 370K
and the outside surface temperature of the fiberglass is 305 K. What is the interfacial
temperature between the magnesia and the fiberglass? [10 marks]
7. A hole of diameter D = 0,25 m is drilled through the centre of a solid block of square
cross section with W = 1 m on a side. The hole is drilled along the length, L = 2 m, of
the block, which has a thermal conductivity of k =150 W/m·K. A warm fluid passing
through the hole maintains an inner surface temperature of T1, = 75°C, while the
outer surface of the block is kept atT2 = 25°C.
1. Using the flux plot method, determine the shape factor for the system. [10 marks]
2. What is the rate of heat transfer through the block? [5 marks]