Book Description

Two-dimensional transpiration heat conduction is considered for a porous region bounded by four surfaces. Two opposing surfaces have no fluid flow or heat transfer across them. The other two surfaces are in contact with reservoirs at differing pressures so that fluid is forced to flow through the region. The flow exit side of the region can have an arbitrary temperature or heat flux distribution imposed along it. As a result of the boundary conditions the porous region occupies a rectangle in a suitable complex potential plane. The energy equation is transformed into the potential plane, and the general solution is found in this rectangular region. The solution can then be transformed into the geometry in the physical plane by conformal mapping. The method is illustrated by obtaining the heat-transfer characteristics of a square duct with porous walls.