The ratios of the laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness of flows of two fluids $$P$$ and $$Q$$ on a flat plate are $${1 \over 2}$$ and $$2$$ respectively. The Reynolds number based on the plate length for both the flows is $${10^4}.$$ The Prandtl and Nusselt numbers for $$P$$ are $${1 \over 8}$$ and $$35$$ respectively. The Prandtl and Nusselt number for $$Q$$ are respectively

Match the following

List-$${\rm I}$$
$$P.$$ Compressible flow
$$Q.$$ Free surface flow
$$R.$$ Boundary layer flow
$$S.$$ Pipe flow
$$T.$$ Heat convection

List-$${\rm II}$$
$$U.$$ Renolds number
$$V.$$ Nussult number
$$W.$$ Weber number
$$X.$$ Froude number
$$Y.$$ Mach number
$$Z.$$ Skin friction coefficient

The temp distribution within the Laminar thermal boundary layer over a heated isothermal flat plate is given by
$$\left( {T - {T_w}} \right)/\left( {{T_\infty } - {T_w}} \right) = \left( {3/2} \right)\,\,\left( {y/{\delta _t}} \right) - \left( {1/2} \right){\left( {y/{\delta _t}} \right)^3},$$
where $${{T_w}}$$ and $${{T_ \propto }}$$ are the temp of plate and free stream respectively, and $$'y'$$ is the normal distance measuread from the plate. The ratio of Average to the local Nussult number based on the thermal boundary layer thickness $${{\delta _t}}$$ is given by

The average heat transfer coefficient on a thin hot vertical plate suspended in still air can be determined from observations of the change in plate temperature with time as it cools. Assume the plate temp to be uniform at any instant of time and radiation heat exchange with the surroundings is negligible. The ambient temperature is $${25^ \circ }C,$$ the plate has a total surface area of $$0.1{m^2}$$ and a mass of $$4$$ kg.

The specific heat of the plate material is $$2.5KJ/KgK.$$ The convective heat transfer coefficient in $$W/{m^2}K,$$ at instant when the plate temp is $${225^ \circ }C$$ and the change in plate temp with time $$dT/dt=-0.02K/s,$$ is