Fully developed free convection in open-ended vertical channels partially filled with porous material

Analytical solutions for fully developed natural convection in open-ended v ertical channels partially filled with porous substrates are presented Four fundamental boundary conditions have been investigated and the correspondi ng fundamental solutions computed These four fundamental boundary condition s were obtained by combining each of the two conditions of one boundary mai ntained at uniform heat flux and one at uniform wall temperature; in each c ondition the opposite boundary is kept adiabatic or isothermal at the inlet fluid temperature. Expressions for the fully developed velocity, temperatu re, mixing cup temperature, volumetric flow rate, friction coefficient, and Nusselt number are given for each fundamental solution. Such fully develop ed values are approached, in a given channel, when the height-to-gap width ratio is sufficiently large. These values represent the limiting conditions and provide analytical checks on numerical solutions for steady and transi ent developing flows.