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:

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

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

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