Radiation · Heat Transfer · GATE ME
Marks 1
1
Wien’s law is stated as follows: λmT = C, where C is 2898 μm.K and λm is the wavelength at which the emissive power of a black body is maximum for a given temperature T. The spectral hemispherical emissivity (ελ) of a surface is shown in the figure below (1 Å = 10-10 m). The temperature at which the total hemispherical emissivity will be highest is K (round off to the nearest integer).
GATE ME 2022 Set 2
2
A flat plate made of cast iron is exposed to a solar flux of 600 W/m2 at an ambient temperature of 25 °C. Assume that the entire solar flux is absorbed by the plate. Cast iron has a low-temperature absorptivity of 0.21. Use Stefan-Boltzmann constant = 5.669 × 10-8 W/m2-K4. Neglect all other modes of heat transfer except radiation. Under the aforementioned conditions, the radiation equilibrium temperature of the plate is __________ °C (round off to the nearest integer).
GATE ME 2022 Set 1
3
The emissive power of a blackbody is $$P.$$ If its absolute temperature is doubled, the emissive power becomes
GATE ME 2017 Set 2
4
Consider the radiation heat exchange inside an annulus between two very long concentric cylinders. The radius of the outer cylinder is $${R_0}$$ and that of the inner cylinder is $${R_i}$$ . The radiation view factor of the outer cylinder onto itself is
GATE ME 2016 Set 2
5
For an opaque surface, the absorptivity $$\left( \alpha \right),$$ transmissivity $$\left( \tau \right)$$ and reflectivity $$\left( \rho \right)$$ are related by the equation:
GATE ME 2012
6
The following figure was generated from experimental data relating spectral black body emissive power to wave length at three temperatures $${T_1},{T_2}$$ and $${T_3}\left( {{T_1} > {T_2} > {T_3}} \right).$$
The conclusion is that the measurements are
GATE ME 2005
7
A plate having $$10\,\,c{m^2}$$ area each side is hanging in the middle of a room of $$100\,\,{m^2}$$ total surface area. The plate temperature and emissivity are respectively $$800$$ $$K$$ and $$0.6.$$
The temperature and emissivity values for the surfaces of the room are $$300$$ $$K$$ and $$0.3$$ respectively. Boltzmannn constant $$\sigma = 5.67 \times {10^{ - 8}}\,\,W/{m^2}{K^4}.$$ The total heat loss from the two surfaces of the plate is
GATE ME 2003
8
The shape factors with themselves of two infinitely long black body concentric cylinders with a dia ratio of $$3$$ are ....... For the inner and ..... for the outer
GATE ME 1994
9
A diffuse radiation surface has
GATE ME 1991
10
For a glass plate transitivity and reflectivity are specified as $$0.86$$ and $$0.08$$ respectively, the absorptivity of the glass plate is
GATE ME 1988
Marks 2
1
Consider a hemispherical furnace of diameter $ D = 6 \text{ m} $ with a flat base. The dome of the furnace has an emissivity of 0.7 and the flat base is a blackbody. The base and the dome are maintained at uniform temperature of 300 K and 1200 K, respectively. Under steady state conditions, the rate of radiation heat transfer from the dome to the base is _______ kW (rounded off to the nearest integer).
Use Stefan-Boltzmann constant = $5.67 \times 10^{-8} \text{ W/(m}^2 \text{ K}^4 \text{)}$
GATE ME 2024
2
A cylindrical rod of length ℎ and diameter 𝑑 is placed inside a cubic enclosure of side length 𝐿. 𝑆 denotes the inner surface of the cube.
The view-factor FS-S is
The view-factor FS-S is
GATE ME 2023
3
Two black surfaces, $$AB$$ and $$BC,$$ of lengths $$5m$$ and $$6m,$$ respectively, are oriented as shown. Both surfaces extend infinitely into the third dimension. Given that view factor $${F_{12}} = 0.5,\,\,{T_1} = 800\,\,K,\,\,{T_2} = 600\,\,K,$$ $${T_{surrounding}} = 300\,\,K$$ and Stefan Boltzmann constant, $$\sigma = 5.67 \times {10^{ - 8}}\,\,W/\left( {{m^2}{K^4}} \right),$$ the heat transfer rate from Surface $$2$$ to the surrounding environment is ____________ $$kW.$$
GATE ME 2017 Set 1
4
Two large parallel plates having a gap of $$10$$ $$mm$$ in between them are maintained at temperatures $${T_1} = 1000\,\,K$$ and $${T_2} = 400\,\,K$$
Given emissivity values, $${\varepsilon _1} = 0.5,\,\,{\varepsilon _2} = 0.25$$ and Stefan-Boltzmann constant $$\sigma = 5.67 \times {10^{ - 8}}\,$$ $$\,W/{m^2}$$-$$K,$$ the heat transfer between the plates (in $$kW/{m^2}$$) is _____________.
Given emissivity values, $${\varepsilon _1} = 0.5,\,\,{\varepsilon _2} = 0.25$$ and Stefan-Boltzmann constant $$\sigma = 5.67 \times {10^{ - 8}}\,$$ $$\,W/{m^2}$$-$$K,$$ the heat transfer between the plates (in $$kW/{m^2}$$) is _____________.
GATE ME 2016 Set 3
5
An infinitely long furnace of $$0.5m \times 0.4m$$ 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 $${T_1} = {T_3} = {927^ \circ }C,$$
while the side walls are at temperature $${T_2} = {T_4} = {527^ \circ }C.$$
The view factor, $${F_{1 - 2}}$$ is $$0.26.$$ The net radiation heat loss or gain on side $$1$$ is_________ $$W/m.$$ Stefan-Boltzman constant $$ = \,5.67 \times {10^{ - 8}}$$ $$W/{m^2}$$-$${K^4}$$
while the side walls are at temperature $${T_2} = {T_4} = {527^ \circ }C.$$
The view factor, $${F_{1 - 2}}$$ is $$0.26.$$ The net radiation heat loss or gain on side $$1$$ is_________ $$W/m.$$ Stefan-Boltzman constant $$ = \,5.67 \times {10^{ - 8}}$$ $$W/{m^2}$$-$${K^4}$$
GATE ME 2016 Set 1
6
The total emissive power of a surface is $$500$$ $$W/{m^2}$$ at a temperature $${T_1}$$ and $$1200$$ $$W/{m^2}$$ at a
temperature $${T_2}$$, where the temperatures are in Kelvin. Assuming the emissivity of the surface to be constant, the ratio of the temperatures $${{{T_1}} \over {{T_2}}}$$ is
GATE ME 2015 Set 2
7
A solid sphere $$1$$ of radius $$'r'$$ is placed inside a hollow, closed hemispherical surface $$2$$ of radius $$'4r'.$$ The shape factor $${F_{2 - 1}}$$ is ...
GATE ME 2015 Set 3
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
GATE ME 2014 Set 4
9
A hemispherical furnace of $$1$$ $$m$$ radius has the inner surface (emissivity, $$\varepsilon = 1$$) of its roof maintained at $$800K,$$ while its floor $$\left( {\varepsilon = 0.5} \right)$$ is kept at $$600K$$. Stefan-Boltzmannn constant is $$\,5.668 \times {10^{ - 8}}$$ $$W/{m^2}.{K^4}.$$ The net radiative heat transfer (in $$kW$$) from the roof to the floor is __________.
GATE ME 2014 Set 2
10
A solid sphere of radius$${r_1} = 20\,\,mm$$ is placed concentrically inside a hollow sphere of radius $${r_2} = 30\,\,mm$$ as shown in the figure.
The view factor $${F_{21}}$$ for radiation heat transfer is
GATE ME 2014 Set 3
11
Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of $$400$$ $$K$$ and $$300$$ $$K.$$ If the emissivities of the surfaces are $$0.8$$ and the Stefan-Boltzmann constant is $$5.67 \times {10^{ - 8}}$$ $$W/{m^2}{K^4},$$ the net radiation heat exchange rate in $$kW/{m^2}$$ between the two plates is
GATE ME 2013
12
Consider two infinitely long thin concentric tubes of circular cross section as shown in the figure. If $${D_1}$$ and $${D_2}$$ are the diameters of the inner and outer tubes respectively, then the view factor $${F_{22}}$$ is given by
GATE ME 2012
13
Radiative heat transfer is intended between the inner surfaces of two very largen isothermal parallel metal plates. While the upper plate (designated as plate $$1$$) is a black surface and is the warmer one being maintained at $${727^ \circ }C,$$ the lower plate (plate $$2$$) is a diffuse and gray surface with an emissivity of $$0.7$$ and is kept at $${27^ \circ }C.$$ Assume that the surfaces are sufficiently large to form a two-surface enclosure and steady state conditions to exist. Stefan Boltzmann constant is given as
$$5.67 \times {10^{ - 8}}\,W/{m^2}{K^4}$$
$$5.67 \times {10^{ - 8}}\,W/{m^2}{K^4}$$
The irradiation (in $$kW/{m^2}$$) for the upper plate is
GATE ME 2009
14
Radiative heat transfer is intended between the inner surfaces of two very largen isothermal parallel metal plates. While the upper plate (designated as plate $$1$$) is a black surface and is the warmer one being maintained at $${727^ \circ }C,$$ the lower plate (plate $$2$$) is a diffuse and gray surface with an emissivity of $$0.7$$ and is kept at $${27^ \circ }C.$$ Assume that the surfaces are sufficiently large to form a two-surface enclosure and steady state conditions to exist. Stefan Boltzmann constant is given as
$$5.67 \times {10^{ - 8}}\,W/{m^2}{K^4}$$
$$5.67 \times {10^{ - 8}}\,W/{m^2}{K^4}$$
If plate is also a diffuse gray surface with an emisivity value of $$0.8,$$ the net radiant heat exchange (in $$kW/{m^2}$$) between plate $$1$$ and plate $$2$$
GATE ME 2009
15
A hollow enclosure is formed between two infinitely concentric cylinders of radii $$1m$$ and $$2m$$ respectively. Radiative heat exchange takes place between the inner surface of the larger cylinder (surface $$-2$$) and the outer surface of the smaller cylinder (surface$$-1$$) the radiating surfaces are diffuse and the medium in the enclosure is non-participating. The fraction of the thermal radiation leaving the larger surface and striking itself is
GATE ME 2008
16
A solid cylinder (surface $$2$$) is located at the center of a hollow sphere (surface $$1$$). The diameter of the sphere is $$1m,$$ while the cylinder has a diameter and length of $$0.5m$$ each. The radiation configuration factor $${F_{11}}$$ is.
GATE ME 2005
17
What is the value of the view factor for two inclined flat plates having common edge of equal width, and with an angle of $$20$$ degrees?
GATE ME 2002
18
For the circular tube of equal length and diameter shown in fig below, the view factor $${F_{13}}$$ is $$0.17.$$ The view factor $${F_{12}}$$ in this case will be.
GATE ME 2001
19
The radiative heat transfer rate per unit area $$\left( {W/{m^2}} \right)$$ between two plane parallel gray surfaces (emissivity $$=0.9$$) maintained at $$400K$$ and $$300K$$ is ($${{\sigma _b} = }$$ Stephen Boltzmann constant $$5.67 \times {10^{ - 8}}\,\,W/{m^2}{K^4}$$)
GATE ME 1993
Marks 5
1
A thin metal plate is exposed to solar radiation. The air and the surroundings are at $${30^ \circ }C\,.$$ The heat transfer coefficient by free convection from the upper surface of the plate is $$17.4$$ $$\,W/{m^2}K$$. The plate has an absorptivity of $$0.9$$ at solar wavelength and an emissivity of $$0.1$$ at the long wavelength. Neglecting any heat loss from the lower surface, determine the incident solar radiation intensity in $$kW/{m^2}$$ , if the measured equilibrium temperature of the plate is $${50^ \circ }C\,.$$ Stefan Boltzmannn constant is $$5.67 \times {10^{ - 8}}\,\,W/{m^2}{K^4}$$
GATE ME 2000
2
Consider two large parallel plates, one at $${T_1} = {727^ \circ }C$$ with emissivity $${\varepsilon _1} = 0.8$$ and the other at $${T_2} = {227^ \circ }C\,$$ with emissivity $${\varepsilon _2} = 0.4.$$ An aluminium radiation shield with an emissivity, $${\varepsilon _s} = 0.05$$ on both sides is placed between the plates. Calculate the percentage reduction in heat transfer rate between the two plates as a result of the shield.
Use $$\sigma = 5.67 \times {10^{ - 8}}W/\left( {{m^2}{K^4}} \right)$$
Use $$\sigma = 5.67 \times {10^{ - 8}}W/\left( {{m^2}{K^4}} \right)$$
GATE ME 1995
3
An object has the shape of cubical box of side $$10cm,$$ with no top cover. The box is placed inside a room whose dimensions are much larger than those of the box. All the five surfaces of box are at a temp of $${500^ \circ }C$$ and have an emissivity of $$0.6.$$ The walls of the room are at $${25^ \circ }C$$ and have an emissivity of $$0.4.$$ All these surfaces can be assumed to be diffuse-gray. Find the net radiative heat loss from the inner surface of the box to the walls of the room.
Stephen Boltzmann constant $$5.67 \times {10^{ - 8}}\,\,W/{m^2}{K^4}$$. View factor between two parallel square plates placed directly opposite to each other is $$0.2$$
Stephen Boltzmann constant $$5.67 \times {10^{ - 8}}\,\,W/{m^2}{K^4}$$. View factor between two parallel square plates placed directly opposite to each other is $$0.2$$
GATE ME 1991
4
Two black plates, each one meter square, are placed parallel to each other in such a way that the radiation shape factor for the system is $$0.4.$$ If the plates are maintained at $${800^ \circ }C$$ and $${400^ \circ }C$$ respectively, determine the net radiant heat transfer between the plates. Also calculate the net heat exchange if the plates were infinite in size. Stephen Boltzmann constant $$ = 5.67 \times {10^{ - 8}}\,\,W/{m^2}{K^4}$$
GATE ME 1989