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1. Transpiration Cooling in a Planar System Two large flat porous horizontal plates are separated by a distance L, separating a gas phase. The upper plate at y=L is at temperature T and the lower plate at y=0 is to be maintained at a lower temperature T.. To reduce the amount of heat that must be removed from the lower plate, a gas at temperature T. is blown through the gaps. The flow between the plates can be idealized as plug flow with a constant velocity v., with no velocity in the x- or z-directions. Assume that all material properties are constant. porous plate T(y=L)=TL gas with conductivityk, density pand heat capacity C per unit mass (i) (ii) T(y=0)=To porous plate Gas flow with uniform velocity Vy TOTL Write the heat equation for the gas between the plates. Simplify the equation to remove any terms that are equal to zero. Write the physical meaning of each remaining term. Write the boundary conditions. Non-dimensionalize the governing equation and boundary conditions, choosing appropriate expressions for the non-dimensional temperature () and y-coordinate (Y). The following ratio should appear in the non-dimensionalized heat equation: Pe = (pu vyL)/k (Pclet number). What is the physical meaning of Pe? What is the physical significance of Pe >>I and Pe