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

In a counter flow heat exchanger, hot fluid enters at $${65^ \circ }C$$ and cold fluid leaves at $${30^ \circ }C.$$ mass flow rate of the hot fluid is $$1$$ $$Kg/s$$ and that of cold fluid is $$2$$ $$kg/s$$. Specific heat of the hot fluid is $$10$$ $$kgK$$ and that of cold fluid is $$5$$ $$kj/kgK.$$ The $$LMTD$$ for the heat ecchanger is

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

Building has to be maintained at $${21^ \circ }C$$ (dry bulb) and $${14.5^ \circ }C$$ (wet bulb). The dew point temp under these conditions is $${10.17^0}C$$. The outside temp is $$ - {23^0}C$$ (dry bulb) and internal and external surface heat transfer coefficients are $$8\,\,W/{m^2}K$$ and $$23$$ $$W/{m^2}K$$ respectively. If the building wall has a thermal conductivity of $$1.2$$ $$W/mK,$$ the minimum thickness (m) of wall required to prevent condensation is