The velocity profile of a fully developed laminar flow in a straight circular pipe, as shown in the figure, is given by the expression. $$$u\left( r \right) = {{ - {R^2}} \over {4\mu }}\left( {{{dp} \over {dx}}} \right)\left( {1 - {{{r^2}} \over {{R^2}}}} \right)$$$
Where $${{dp} \over {dx}}$$ is a constant.

The average velocity of fluid in the pipe is

Consider steady-state heat conduction across the thickness in a plane composite wall as shown in fig exposed to convection conditions on both sides.

Assuming negligible contact resistance between the wall surfaces, the interface temp $$T(C)$$ of the two walls will be

A coolant fluid at $${30^ \circ }C$$ flows over a heated flat plate maintained at a constant temperature of $${100^ \circ }C$$. The boundary layer temp distribution at a given location on the plate may be approximated as $$T=30+70exp(-y),$$ where $$y$$ (in $$m$$) is the distance normal to the plate and $$T$$ is in $$^ \circ C.$$ If thermal conductivity of the fluid is $$1.0W/mk,$$ the local convective heat transfer (in $$W/{m^2}K$$) at that location will be

Radiative heat transfer is intended between the inner surfaces of two very largen isothermal parallel metal plates. While the upper plate (designated as plate $$1$$) is a black surface and is the warmer one being maintained at $${727^ \circ }C,$$ the lower plate (plate $$2$$) is a diffuse and gray surface with an emissivity of $$0.7$$ and is kept at $${27^ \circ }C.$$ Assume that the surfaces are sufficiently large to form a two-surface enclosure and steady state conditions to exist. Stefan Boltzmann constant is given as
$$5.67 \times {10^{ - 8}}\,W/{m^2}{K^4}$$

The irradiation (in $$kW/{m^2}$$) for the upper plate is