Combined Conduction–Convection–Radiation Heat Transfer of Slip Flow Inside a Micro-Channel Filled with a Porous Material

• Published in: Transport in porous media Vol. 108; no. 2; pp. 413 - 436
• Main Authors: Dehghan, Maziar, Mahmoudi, Yasser, Valipour, Mohammad Sadegh, Saedodin, Seyfolah
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.06.2015; Springer Nature B.V
• Subjects: Civil Engineering; Classical and Continuum Physics; Coefficient of variation; Coefficients; Computational fluid dynamics; Conduction heating; Dimensionless numbers; Earth and Environmental Science; Earth Sciences; Fluid flow; Geotechnical Engineering & Applied Earth Sciences; Heat flux; Heat transfer; High temperature; Hydrogeology; Hydrology/Water Resources; Industrial Chemistry/Chemical Engineering; Mathematical models; Microchannels; Nusselt number; Parameters; Porous materials; Porous media; Slip; Slip flow; Temperature dependence; Temperature distribution; Temperature profiles; Thermal conductivity; Thermodynamic properties; Velocity; Viscosity; Cellular porous medium; Slip regime; Temperature jump; Micro-channel; Radiative heat transfer
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1007/s11242-015-0483-z

Combined conduction–convection–radiation heat transfer is investigated numerically in a micro-channel filled with a saturated cellular porous medium, with the channel walls held at a constant heat flux. Invoking the velocity slip and temperature jump, the thermal behaviour of the porous–fluid system are studied by considering hydrodynamically fully developed flow and applying the Darcy–Brinkman flow model. One energy equation model based on the local thermal equilibrium condition is adopted to evaluate the temperature field within the porous medium. Combined conduction and radiation heat transfer is treated as an effective conduction process with a temperature-dependent effective thermal conductivity. Results are reported in terms of the average Nusselt number and dimensionless temperature distribution, as a function of velocity slip coefficient, temperature jump coefficient, porous medium shape parameter and radiation parameters. Results show that increasing the radiation parameter ( T r ) and the temperature jump coefficient flattens the dimensionless temperature profile. The Nusselt numbers are more sensitive to the variation in the temperature jump coefficient rather than to the velocity slip coefficient. Such that for high porous medium shape parameter, the Nusselt number is found to be independent of velocity slip. Furthermore, it is found that as the temperature jump coefficient increases, the Nusselt number decrease. In addition, for high temperature jump coefficients, the Nusselt number is found to be insensitive to the radiation parameters and porous medium shape parameter. It is also concluded that compared with the conventional macro-channels, wherein using a porous material enhances the rate of heat transfer (up to about 40 % compared to the clear channel), insertion of a porous material inside a micro-channel in slip regime does not effectively enhance the rate of heat transfer that is about 2 %.