The $$LMTD$$ of a counter flow heat exchanger is $${20^ \circ }C$$. The cold fluid enters at $${20^ \circ }C$$ and the hot fluid enters at $${100^ \circ }C$$. Mass flow rate of the cold fluid is twice that of the hot fluid. specific heat at constant pressure of the fluid is twice that of the cold fluid. The exit temperature of the cold fluid is

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