PROBLEMS ON RADIATIVE HEAT TRANSFER

1. One side of a circular metallic plate is insulated. The radiant heat flux falling on the other side
is 900 W/m2. The heat transfer coefficient from the plate surface to air is 10 W/m 2-K. The
surface emissivity of the plate is 0.8. The surrounding air temperature is 300 K. Find the plate
surface temperature under steady state condition. Ans: 355 K

2. Determine the wavelength at which the spectral emissive power of a tungsten filament at
1400 K becomes maximum and spectral emissive power at that wave length. Ans: 2.07 µm,
176 kW/m2-µm

3. A gray, diffuse and opaque surface (α = 0.8) is at 100 0C and receives an irradiation 1 kW/m 2.
If the surface area is 0.1 m 2, determine (a) radiosity of the surface, (b) net radiant heat transfer
from the surface and (c) calculate the above quantities if the surface is black. Ans: (a) 1078
W/m2, (b) 7.8 W/m2, (c) 1097 W/m2and 9.75 W/m2

4. The spectral emissivity of an opaque surface at 800 K is given as follows:

ε = 0.3 for 0 ≤  < 3 µm

ε = 0.8 for 3 ≤  < 7 µm

ε = 0.1 for 7 µm ≤  < 

Find the effective emissivity of the surface. Ans: 0.52

5. A pipe of 20 cm diameter is carrying stream at 200°C through a room where the temperature
of air is 30°C. If the pipe is losing heat at the rate of 1.92 kW per meter of pipe, find the
emissivity of the pipe surface. Use the following correlation for convective heat transfer:

Nud  0.53 Grd . Pr  0.25

The properties of air at 115°C are as follows:

Ʋ = 0.25  10-4 m2/s, K = 0.033 W/m-°C and Pr=0.69 Ans: 0.8

6. A long pipe of 5 cm diameter passes through a room and is exposed to air at 27°C. The pipe
surface temperature is 100°C. Assuming emissivity of the pipe surface as 0.6. Calculate the
heat loss per metre length of the pipe. Ans: 60.6 W/m

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7. The diameters of the inner and the outer spheres of a Dewar vessel are 30 cm and 36 cm
respectively. Both spheres are plated to have emissivity 0.05. The temperature of the outer
sphere is 20°C. Liquid oxygen which boils at -183°C is kept inside the inner vessel.
Determine the evaporation rate of liquid nitrogen if other modes of heat transfer except
radiation are negligible. Take latent heat of evaporation at -183°C to be 215 kJ/kg. Ans: 0.06
kg/hr

8. A disc of 10 cm diameter maintained at 700 K is situated 2 m below the centre of another disc
of 2 m diameter which is maintained at 500 K. Find the radiative heat transfer from the
smaller disc to the bigger disc. The emissivities of the smaller and the bigger discs may be
taken as 0.8 and 0.6 respectively. Shape factors may be obtained from the corresponding
chart. Ans: 150.4 W

9. Two coaxial parallel circular discs of equal diameter D are placed at a distance of L. If the
view factor F12 = 0.1, without altering the diameter of the discs, determine a solution that
would increase the view factor F12 by a factor 5.

10. A cylindrical enclosure with A1, A2 and A3 as inner base, top and side
surfaces respectively has been shown in the adjacent figures. If the ratio of
the length to the diameter of the tube is K, show that the view factor
between the base and the side surface is given by the expression:

F13  2 K  K 2  1  2 K 2 Also, find F13 for K = 1. Ans: 0.828

11. A 3 mm thick glass window transmits 90% of the radiation between λ =

0.3 µm and 3.0 µm and is essentially opaque for radiation at other
wavelengths. Determine the rate of radiation through a 2 m × 2 m glass window from black
body sources at (a) 5800 K and (b) 1000 K.

12. Two very large parallel plates are maintained at uniform temperatures T 1 = 750 K and T2 =
500 K and have emissivities ε 1 = 0.85 and ε2 = 0.7 respectively. a thin aluminium sheet with
the same emissivity on both sides is placed between the plates in order to reduce the net rate
of radiation heat transfer between the plates by 90%. Find the emissivity of the aluminium
sheet.

13. A hemispherical furnace of 5 m diameter with a flat base has been

shown in the figure. The dome of the furnace is black and the base
has an emissivity of 0.7. The base and the dome are maintained at
uniform temperatures of 400 K and 1000 K respectively. Determine
the net rate of radiation heat transfer from the dome to the base
surface during steady operation.
Ans: 759 W

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14. A system is consisting of two concentric spheres having radius r 1 and
r2 (r2 > r1) as shown in the figure. Taking r 1 = 5 cm, determine the
radius r2, if it is required to have the value of shape factor F 21 equal
to 0.6. Ans: 6.45 cm

15. A steel tube, 5 cm in diameter and 2 m long is at a temperature of

500 K. This tube is located centrally in (i) a large brick room having
wall temperature 300 K and (ii) a square brick conduit of 20 cm side and at 300 K. If the
emissivities of steel and brick are 0.8 and 0.95 respectively, calculate the rate of heat loss in
each case. Ans: 774.8 W, 768 W

16. Two large parallel planes each having emissivity 0.8 is maintained at two different
temperatures. Find the number of radiation shields each having emissivities 0.05 is to be
placed between the planes to reduce the radiative heat transfer by a factor of 75. Ans: 3

17. A stainless steel (ε = 0.6) at 100°C faces a brick wall (ε = 0.75) at 500°C. Estimate the heat
flux and the radiant heat transfer coefficient. Ans: 9573 W/m2, 24W/m2-K

18. Dry saturated steam at 5 bar is passing through a steel pipe of 10 cm outside diameter and
lagged with 5 cm thick insulation. The conductivity and emissivity of the insulating material
are 0.14 W/m-K and 0.9 respectively. If the surroundings are at 25°C temperature and the
heat transfer coefficient on the outer surface of the lagged pipe is 11.5 W/m 2-K, calculate the
conduction and radiation heat loss from one metre length of the pipe. Also, calculate the
radiation and overall heat transfer coefficient and the rate of condensation of steam from 40 m
length of the pipe. Ans: 138.8 W/m, 70.68 W/m, 5.94 W/m2-K, 17.44 W/m2-K

19. Two parallel discs, each 60 cm in diameter are spaced 30 cm apart with one disc located
directly above the other disc. One disc is maintained at 500 0C and its emissivity is 0.2 and
other at 2270C and its emissivity is 0.4. The discs are located in a large room whose walls are
maintained at 600C. Determine the rate of heat loss from each disc. Ans: 1060 W, 125 W

20. Calculate the shape factor F 12 for a long duct having cross-section of
equilateral triangle as shown in the figure. Ans: 0.5

21. A cylindrical cavity of depth h and diameter d is closed on its outer surface
with a flat as shown in the figure. Find the shape factor of the cavity with
respect to itself.

22. Show that the shape factor of conical cavity with respect to itself is
1  2 sin  , where  is the semi vertical angle of the conic section. The
cavity is closed by a flat surface.