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

For flow of fluid over a heated plate, the following fluid properties are known: Viscosity $$=0.001Pa.s;$$ Specific heat at constant pressure $$=1$$ $$kJ/kgK;$$ Thermal conductivity $$=$$ $$W/mK,$$ The hydrodynamic boundary layer thickness at a specified location on the plate is $$1mm,$$ thermal boundary layer thickness at the same location is

For the three dimensional object shown in the fig below. Five faces are insulated. The sixth face $$(PQRS),$$ which is not insulted, interacts thermally with the ambient , with a convective heat transfer coefficient of $$10W/{m^2}K.$$ The ambient temperature is $${30^ \circ }C$$. Heat is uniformly generated inside the object at the rate of $$100W/{m^3}.$$ Assuming the face $$PQRS$$ to be at uniform temperature, its steady state temp is

Steady two dimensional heat conduction takes place in the body shown in the fig below. The normal temperature gradients over surface $$P$$ and $$Q$$ can be considered to be uniform. The temperature gradient $$\partial T/\partial x = $$ at surface $$Q$$ is equal to $$10$$ $$K/m.$$ surfaces $$P$$ and $$Q$$ are maintained at constant temperatures as shown in the fig. While the remaining part of the boundary is insulated . The body has a constant thermal conductivity of $$0.1$$ $$W/mk$$, the value of $$\partial T/\partial x$$ and $$\partial T/\partial y$$ at surface $$P$$ are