Conduction · Heat Transfer · GATE PI

A metallic cylindrical casing of an exhaust pipe has inner radius $$50$$ $$mm$$ and wall thickness $$7$$ $$mm.$$ If the thermal conductivity of the material of the casing is $$50$$ $$W/m$$-$$K,$$ then the thermal resistance of the casing in $$K/kW$$ is ________________ (up to three decimal places).

A well machined steel plate of thickness $$L$$ is kept such that the wall temperature are $${T_h}$$ and $${T_c}$$ as shown in the figure below. A smooth copper plate of the same thickness $$L$$ is now attached to the steel plate without any gap as indicated in the figure below. The temperature at the interface is $${T_i},$$ The temperature of the outer walls are still the same at $${T_h},$$ and $${T_c}.$$ The heat transfer rates are $${q_1}$$ and $${q_2}$$ per unit area in the two cases respectively in the direction shown. Which of the following statements is correct?

In a $$1$$ $$m$$ thick wall, the temperature distribution at a given instant is
$$T\left( x \right) = {c_0} + {c_1}x + {c_2}{x^2}$$ where $$T$$ is in $${}^ \circ C$$ and $$x$$ is in $$m.$$ The constants are: $${c_0} = {800^ \circ }C,$$ $${c_1} = - {250^ \circ }C/m$$ and $${c_2} = - {40^ \circ }C/{m^2}.$$ The thermal conductivity of the wall is $$50$$ $$W/mK$$ and wall area is $$5\,\,{m^2}.$$ If there is a heat source generating uniform volumetric heating at the rate of $$500$$ $$W/{m^3}$$ inside the wall, then the rate of change of energy storage in the wall, in $$kW,$$ is _____________.

Heat is being transferred convectively from a cylindrical nuclear reactor fuel rod of $$50mm$$ diameter to water at $${70^ \circ }C$$, under steady state condition, the rate of heat generation within the fuel element is $$50 \times {10^6}\,\,W/{m^3}$$ and the convective heat transfer coefficient is $$1$$ $$kW/{m^2}K.$$ The outer surface temperature of the fuel element would be

A long glass cylinder of inner diameter $$=0.03m$$ and outer diameter $$=0.05m$$ carries hot fluid inside. If the thermal conductivity of glass $$=1.05$$ $$W/mK,$$ the thermal resistance $$(K/W)$$ per unit length of the cylinder is