Consider a slab of 20 mm thickness. There is a uniform heat generation of $ \dot{q} = 100 \text{ MW/m}^3 $ inside the slab. The left and right faces of the slab are maintained at 150 °C and 110 °C, respectively. The plate has a constant thermal conductivity of 200 W/(m.K). Considering a 1-D steady state heat conduction, the location of the maximum temperature from the left face will be at ______mm (answer in 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