Porous cooling of a pile

In this investigation the problem of a limiting case of steady state one dimensional solid-fluid Newtonian heat transfer is examined in which an incompressible non-heat generating coolant fluid is flowing through a heat generating porous plate. The effect of grain size on the Newtonian heat transfer in the porous plate with various kinds of internal heat generations is determined analytically. The temperature difference between the solid and the coolant fluid through the porous plate is determined. All the previous studies assume that in the porous plate, coolant fluid temperature and solid temperatures are approximately equal. This analysis eliminates this simplifying assumption. The cases of uniform, linear, exponential, sinusoidal and any single valued function internal heat generation are studied. The axial temperature distributions in the coolant fluid and the solid porous plate are derived in terms of internal heat generation, porosity of the porous medium, initial temperature of the coolant fluid, size of the spheres forming the porous plate, coolant mass flow rate and the specific heat of the coolant fluid. This analysis aims at better understanding of heat transfer phenomena in porous materials which are increasingly and usefully used in many important fields of science and engineering --Abstract, page ii