Second Semester 1432/1433
King Saud University
College of Engineering
Chemical Engineering Dept.
ChE 317
Tutorial # 1
23/3/1433
Heat Transfer Operations
1. Find the heat loss per m2 of surface through a brick wall 0.5 m thick when the
inner surface is at 400 K and the outside at 310; the thermal conductivity of
the brick may be taken as 0.7 W/m.K.
2. *A square silicon chip 7 mm by 7 mm in size and 0.5 mm thick is mounted on
a plastic substrate. The top surface of the chip is cooled by a synthetic liquid
flowing over it. Electronic circuits on the bottom of the chip generate heat at a
rate of 5 watts that must be transferred through the chip. Estimate the steadystate temperature difference between the front and the back surfaces of the
chip. The thermal conductivity of silicone is 150 W/ m K.
3. A heat flux meter at the outer (cold) wall of a concrete building indicates that
the heat loss through a wall of 10 cm thickness is 20 W/m2. If a thermocouple
at the inner surface of the wall indicates a temperature 22 ºC while another at
the outer surface shows 6 ºC, calculate the thermal conductivity of the
concrete.
4. * Calculate the heat loss through a 1-m by 3-m glass window 7 mm thick if the
inner surface temperature is 20 ºC and the outer surface temperature is 17 ºC.
Comment on the possible effect of radiation on your answer.
5. A warehouse is to be designed for keeping perishable foods cool prior to
transportation to grocery stores. The warehouse has an effective surface area
of 20000 ft2 exposed to an ambient air temperature of 90 ºF. The warehouse
wall insulation (k = 0.1 Btu/hr ft ºF) is 3 in. thick. Determine the rate at which
heat must be moved (Btu/hr) from the warehouse to maintain the food at 40
ºF.
6. A furnace is constructed with 225 mm of firebrick, 120 mm of insulating
brick, and 225 mm of building brick. The inside temperature is 1200 K and the
outside temperature is 330 K. If the thermal conductivities are 1.4,0.2 and 0.7
W/m. K, find the heat loss per unit area and the temperature at the junction of
the firebrick and insulating brick.
7. *A wall of a furnace 0.244 m thick is constructed of material having a thermal
conductivity of 1.3 W/m. K. The wall is insulated on the outside with material
having an average k of 0.346 W/m.K, so that the heat loss from the furnace
will be equal to or less than 1830 W/m2. The inner surface temperature is 1588
K and the outer 299 K. Calculate the thickness of insulation required.
M Gaily
Office: A B 81, Building 3
1
Second Semester 1432/1433
Solved Problem
The Cost of Heat Loss through a Roof
The roof of an electrically heated home is 6 m long, 8 m wide, and 0.25 m thick, and
is made of a flat layer of concrete whose thermal conductivity is k = 0.8 W/m · °C.
The temperatures of the inner and the outer surfaces of the roof one night are
measured to be 15°C and 4°C, respectively, for a period of 10 hours. Determine:
(a) The rate of heat loss through the roof that night.
(b) The cost of that heat loss to the home owner if the cost of electricity is $0.08/kWh.
SOLUTION The inner and outer surfaces of the flat concrete roof of an electrically
heated home are maintained at specified temperatures during a night. The heat loss
through the roof and its cost that night are to be determined.
Assumptions
1 Steady operating conditions exist during the entire night since the surface
temperatures of the roof remain constant at the specified values.
2 Constant properties can be used for the roof.
Properties The thermal conductivity of the roof is given to be k = 0.8 W/m · °C.
Analysis
(a) Noting that heat transfer through the roof is by conduction and the area of the
roof is A = 6 m x 8 m = 48 m2,
The steady rate of heat transfer through the roof is determined to be
Q = kA (T1 - T2)
L
= (0.8 W/m · °C) (48 m2) (15 - 4) °C = 1690 W = 1.69 kW
0.25 m
(b) The amount of heat lost through the roof during a 10-hour period and its cost are
determined from
q =Q.Δt= (1.69 kW) (10 h) = 16.9 kWh
Cost = (Amount of energy) (Unit cost of energy)
= (16.9 kWh) ($0.08/kWh) = $1.35
Discussion The cost to the home owner of the heat loss through the roof that night
was $1.35. The total heating bill of the house will be much larger since the heat losses
through the walls are not considered in these calculations.
M Gaily
Office: A B 81, Building 3
2