Forced convection heat transfer inside an anisotropic porous channel with oblique principal axes: Effect of viscous dissipation

An analytical study on laminar and fully developed forced convection heat transfer in a parallel-plate horizontal channel filled with an anisotropic permeability porous medium is performed. The principal axis of the anisotropic porous medium is oriented from 0 to 90 degrees. A constant heat flux is applied on the outer wall of the channel. Both clear (Newtonian) fluid and Darcy viscous dissipations are considered in the energy equation. Directional permeability ratio parameter A¹ is defined to combine both the effect of the dimensionless permeability ratio parameter K¹=(K₁/K₂) and orientation angle φ into one parameter. The effects of the parameter A¹, the Darcy number Da and the modified Brinkman number Br¹ on the heat transfer and fluid flow characteristics in the channels are investigated and presented in graphs. The obtained results show that the parameters A¹, Da and Br¹ have strong effects on the dimensionless normalized velocity and temperature profiles as well as on the Nusselt number. It is found that for a particular value of A¹, called as critical value A_cr¹, the external heat applied to the surface of the channel is balanced by the internal heat generation due to viscous dissipation and the bulk mean temperature approaches the wall temperature. Hence, the Nusselt number approaches infinity for the critical values A_cr¹.