For air flow over a flat plate, velocity $$(U)$$ and boundary layer thickness $$\left( \delta \right)$$ can be expressed respectively, as $$${U \over {{U_\infty }}} = {3 \over 2}{y \over \delta } - {1 \over 2}{\left( {{y \over \delta }} \right)^3}\,\,\,\,;\,\,\,\,\delta = {{4.64x} \over {\sqrt {{{{\mathop{\rm Re}\nolimits} }_x}} }}$$$
If the free stream velocity is $$2$$ $$m/s$$, and air has Kinematic viscosity of $$1.5 \times {10^{ - 5}}{m^2}/s$$ and density of $$1.23$$ $$kg/{m^3}$$, then wall shear stress at $$x=1$$ $$m$$, is

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

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

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