Consider a solid slab (thermal conductivity, k = 10 W∙m^-1∙K^-1) with thickness 0.2 m and of infinite extent in the other two directions as shown in the figure. Surface 2, at 300 K, is exposed to a fluid flow at a free stream temperature (T_∞) of 293 K, with a convective heat transfer coefficient (h) of 100 W∙m^-2∙K^-1. Surface 2 is opaque, diffuse and gray with an emissivity (ε) of 0.5 and exchanges heat by radiation with very large surroundings at 0 K. Radiative heat transfer inside the solid slab is neglected. The Stefan-Boltzmann constant is 5.67 × 10^-8 W∙m^-2∙K^-4. The temperature T₁ of Surface 1 of the slab, under steady-state conditions, is _________ K (round off to the nearest integer).

Heat is generated uniformly in a long solid cylindrical rod ( diameter $$ = 10\,\,mm$$) at the rate of $$4 \times {10^7}\,\,W/{m^3}.$$ The thermal conductivity of the rod material is $$25$$ $$W/m.K.$$ Under steady state conditions, the temperature difference between the center and the surface of the rod is ________________ $${}^ \circ C.$$

A brick wall $$\,\left( {k = 0.9{W \over {m.K}}} \right)$$ of thickness $$0.18$$ $$m$$ separates the warm air in a room from the cold ambient air. On a particular winter day, the outside air temperature is −$${5^ \circ }C.\,$$ and the room needs to be maintained at $${27^ \circ }C.\,$$ The heat transfer coefficient associated with outside air is $$20\,\,W/{m^2}K.$$ Neglecting the convective resistance of the air inside the room, the heat loss, in $$\left( {{W \over {{m^2}}}} \right)$$ is

A cylindrical uranium fuel rod of radius 5 mm in a nuclear reactor is generating heat at the rate of $$4 \times {10^7}\,\,W/{m^3}.$$ The rod is cooled by a liquid (convective heat transfer coefficient $$1000W/{m^2}$$-$$K$$) at $${25^ \circ }C$$. At steady state, the surface temperature (in $$K$$) of the rod is