Exact analysis for minimum shape of porous fins under convection and radiation heat exchange with surrounding

An analysis is presented for determining the minimum shape of porous fins with convection and radiation modes of heat transfer taken place on its surfaces. A variable heat transfer coefficient as a function of temperature is considered for an actual case study. An analytics based on the calculus of variation is used to establish a mathematical model. The optimum shape of porous fins for a constraint heat transfer rate is not only dependent on the thermophysical parameters of fluid flow but also a strong function with porosity. The volume of optimum profile fins monotonically increases with the porosity whatever the variation of convective heat transfer coefficient takes place. However, the requirement of solid material declines always with the porosity which may be an extremely important where gain in weight with the attachment of fins opposes always to the implementation of a final design.