Characterization and regulation of isothermal surfaces are key issues in a number of thermal management devices. The surface temperature uniformity can be controlled utilizing a variable area channel heat exchanger filled with a porous medium. A comprehensive analytical investigation of forced convection through a generic variable area channel is carried out to design a compact heat exchanger in producing an isothermal surface subject to a constant heat flux, which may be required in the biological, electronics, optical, laser, manufacturing, and solidification applications. Exact solutions for the fluid and solid phases and the wall surface temperature distributions as well as the Nusselt number correlations are established while incorporating local thermal nonequilibrium and transverse conduction contributions. The channel temperature field is adjusted utilizing either an adiabatic or a constant temperature on the inclined surface. The effects of the pertinent physical parameters, such as channel inlet/outlet thickness, inclination angle, Biot number, ratio of fluid and matrix thermal conductivities, working fluid properties, and imposed heat flux, on the fluid and solid temperature fields and the isothermal surface are thoroughly investigated. The results indicate that utilizing proper pertinent parameters, an isothermal surface is achieved. The validity of the utilization of the local thermal equilibrium model is also investigated and error maps are presented.