GATE Heat Transfer

(Detailed solution) GATE ME | Heat Transfer | Radiation Questions

Question #1

Consider the radiation heat exchange inside an annulus between two very long concentric cylinders. The radius of the outer cylinder is Ro and that of the inner cylinder is R. The radiation view factor of the outer cylinder onto itself is

(A) $\large 1-\sqrt{\frac{R_{i}}{R_{o}}}$

(B) $\large \sqrt{1-\frac{R_{i}}{R_{o}}}$

(C) $\large 1-\left ( \frac{R_{i}}{R_{o}} \right )^{1/3}$

(D) $\large 1-\frac{R_{i}}{R_{o}}$

[GATE 16 S2, 1 mark]

Question #2

Two large parallel plates having a gap of 10 mm in between them are maintained at temperatures T1 = 1000 K and T2 = 400 K. Given emissivity values, $\epsilon _{1}=0.5$ ,  $\epsilon _{2}=0.25$ and Stefan-Boltzmann constant $\sigma = 5.67\times 10^{-8} w/m^2K^4$  , the heat transfer between the plates (in kW/m2) is ___________________

[GATE 16 S3, 2 marks]

Question #3

An infinitely long furnace of 0.5 m × 0. 4 m cross-section is shown in the figure below. Consider. all surfaces of the furnace to be black. The top and bottom walls are maintained at temperature T1 = T3 = 927 o C while the side walls are at temperature T2 = T4 = 527 o C. The view factor, F1-2 is 0.26. The net radiation heat loss or gain on side 1 is_________ W/m. Stefan-Boltzmann constant = 5.67 × 10−8 W/m2-K4

[GATE 16 S1, 2 marks]

Question #4

A solid sphere 1 of radius ‘r’ is placed inside a hollow, closed hemispherical surface 2 of radius ‘4r’. The shape factor F2-1 is


(A) 1/12

(B) 1/2

(C) 2

(D) 12

[GATE 15 S3, 2 marks]

Question #5

The total emissive power of a surface is 500 W/m2 at a temperature T1 and 1200 W/m2 at a temperature T2, where the temperatures are in Kelvin. Assuming the emissivity of the surface to be constant, the ratio of the temperatures T1/T2 is

(A) 0.308

(B) 0.416

(C) 0.803

(D) 0.874

[GATE 15 S2, 2 marks]

Question #6

A hemispherical furnace of 1 m radius has the inner surface (emissivity, ε = 1) of its roof maintained at 800 K, while its floor (ε = 0.5 ) is kept at 600 K. Stefan-Boltzmann constant is 5.668 × 10−8 W/m2 .K4 . The net radiative heat transfer (in kW) from the roof to the floor is _______

[GATE 14 S2, 2 marks]

Question #7

A solid sphere of radius r1 = 20 mm is placed concentrically inside a hollow sphere of radius r2 = 30 mm as shown in the figure.

The view factor F21 for radiation heat transfer is

(A) 2/3




[GATE 14 S3, 2 marks]

Question #8

Two infinite parallel plates are placed at a certain distance apart. An infinite radiation shield is inserted between the plates without touching any of them to reduce heat exchange between the plates. Assume that the emissivities of plates and radiation shield are equal. The ratio of the net heat exchange between the plates with and without the shield is
(A) 1/2 (B) 1/3 (C) 1/4 (D) 1/8

[GATE 14 S4, 2 marks]

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