On the thermally developing forced convection through a porous material under the local thermal non-equilibrium condition: An analytical study

• Thermally developing convective heat transfer inside a porous-channel is studied.
• Analysis is based on small local thermal non-equilibrium intensity assumption.
• Expressions for Nu number and local thermal non-equilibrium intensity are presented.
• LTNE intensity decreases by increasing the Biot number and conductivity ratio.
• An expression for the thermal entrance length is proposed.

The aim of the present analytical study is to investigate a thermally developing forced convective heat transfer inside a channel filled with a porous medium whose walls are imposed to a constant heat flux (i.e. the iso-flux thermal boundary condition). The Darcy’s law of motion and the two-energy equation (i.e. local thermal non-equilibrium, LTNE) model are considered. A perturbation analysis is conducted to avoid using any model for the iso-flux thermal boundary condition. Thermally developing forced convection inside a porous-filled channel has previously not been analyzed without implementing a heuristic model for the iso-flux thermal boundary condition. The temperature difference between the fluid and solid phases (called the LTNE intensity) is analytically obtained. Results concerning the LTNE intensity is compared with the available models of the iso-flux thermal boundary condition. In addition, the Nusselt number of a thermally developing convection through a porous material is obtained for the LTNE condition. Also, an expression representing the developing length, i.e. the dimensionless axial location at which the flow becomes fully developed, for a porous-filled channel is proposed for the first time.