Transpiration cooling in a planar system, two large flat porous horizontal plates is separated by a relatively small distance L. The upper plate at y = L is at temperature TL, and the lower one at y = 0 is to be maintained at a lower temperature T0. To reduce the amount of heat that must be removed from the lower plate, an ideal gas at T₀ is blown upward through both plates at a steady rate. Develop an expression for the temperature distribution and the amount of heat q₀ that must be removed from the cold plate per unit area as a function of the fluid properties and gas flow rate. Use the abbreviation ϕ = pC_pv_y/L/k.