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

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 maximum level of inventory of item is $$100$$ and it is achieved with infinite replenishment rate. The inventory becomes zero over one and half month due to consumption at a uniform rate. This cycle continuous throughout the year. Ordering cost is Rs.$$100$$ per order and inventory carrying cost is Rs. $$10$$ per item per month. Annual cost (in Rs. ) of the plan, neglecting material cost, is