A closed cylinder having a radius $$R$$ and height $$H$$ is filled with oil of density $$\rho .$$ If the cylinder is rotated about its axis at an angular velocity of $$\omega $$ , then thrust at the bottom of the cylinder is

In a condenser, water enters at $${30^ \circ }C$$ and flows at the rate $$1500$$ $$Kg/hr.$$ The condensing steam is at a temperature of $${120^ \circ }C$$ and cooling water leaves the condenser at $${80^ \circ }C$$. Specific heat of water is $$4.187 kJ/kg$$ $$K.$$ If the overall heat transfer coefficient is $$2000$$ $$W/{m^2}K,$$ the heat transfer area is

A spherical thermocouple junction of diameter $$0.706 mm$$ is to be used for the measurement of temperature of a gas stream. The convective heat transfer co-efficient on the bead surface is $$400W/{m^2}K.$$ Thermo-physical properties of thermocouple material are
$$k = 20W/mK,$$ $$C = 400J/kgK$$ and $$\rho = 8500\,\,kg/{m^3}.$$ If the thermocouple initially at $${30^ \circ }C$$ is placed in a hot stream of $${300^ \circ }C$$ the time taken by the bead to reach $${298^ \circ }C$$, is

One dimensional unsteady state heat transfer equation for a sphere with heat generation at the rate $$'{q_g}',$$ can be written as