A cubic block of side $$'L'$$ and mass $$'M'$$ is dragged over an oil film across table by a string connects to a hanging block of mass $$'m'$$ as shown is fig. The Newtonian oil film of thickness $$'h'$$ has dynamic viscosity $$'\mu '$$ and the flow condition is laminar. The acceleration due to gravity is $$'g'.$$ The steady state velocity $$'v'$$ of block is :

A journal bearing has a shaft diameter of $$40$$ $$mm$$ and a length of $$40mm.$$ The shaft is rotating at $$20$$ $$rad/s$$ and the viscosity of the lubricant is $$20$$ $$mPa$$-$$s$$. The clearance is $$0.020$$ $$mm.$$ The loss of torque due to the viscosity of the lubricant is approximately:

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