# FORCED CONVECTION IN A SELF HEATING POROUS CHANNEL: LOCAL THERMAL NONEQUILIBIUM MODEL

## Main Article Content

## Abstract

Laminar forced convection flow through a parallel plates channel completely filled with a saturated porous medium where occurs a uniform heat generation per unit volume with volumetric heat generation is investigated numerically. The Darcy-Brinkman model is used to describe the fluid flow. The energy transport mathematical model is based on the two equations model which assumes that there is no local thermal equilibrium **(LTNE) **between the fluid and the solid phases. The dimensionless governing equations with the appropriate boundary conditions are solved by direct numerical simulation. The effect of the controlling parameters, Biot number, thermal conductivities ratio, heat generation rate and the Reynolds number on the LTE needed and sufficient condition is analysed. The results reveal essentially that the LTE condition is unfavourably affected by the increase in the heat generation rate, the thermal conductivities ratio and the decrease in the Biot number. In addition, for a given heat generation rate, the effect of Reynolds number on the LTE condition is reversed depending on the conductivities ratio threshold.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2115>. Date accessed: 18 oct. 2017. doi: https://doi.org/10.2298/TSCI150201110A.

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Accepted 2017-03-13

Published 2017-03-13

## References

[2] Chauhan, D. S. and V, Kumar., Heat transfer effects in a couette flow through a composite channel partly filled by a porous medium with a transverse sinusoidal injection velocity and heat source, Thermal Sciences., 15 suppl. 2 (2011), pp. S175-S186.

[3] Younsi. R., Computational analysis of MHD flow, heat and mass transfer in trapezoidal porous cavity, Thermal Sciences., 15 (2009), N°1, pp. 13-22.

[4] Xu, J., Qu, Z. G., Tao, W. Q., Analytical solution of forced convective heat transfer in tubes partially filled with metallic foam using the two-equation model, Int. J. Heat Mass Transfer., 54 (2011), pp. 3846-3855.

[5] Chen, C. C., Huang, P. C., Hwang, H. Y., Enhanced forced convective cooling of heat sources by metal-foam porous layers, Int. J. Heat Mass Transfer., 58 (2013), pp. 356-373.

[6] Phanikumar, M. S., Mahajan, R.L., Non-Darcy natural convection in high porosity metal foams, Int. J. Heat Mass Transfer., 45 (2002), pp. 3781–3793.

[7] Pippal, S., Bera, P., A thermal non-equilibrium approach for 2D natural convection due to lateral heat flux: Square as well as slender enclosure, Int. J. Heat Mass Transfer., 56 (2013), pp.501– 515.

[8] Lee, D.Y., Vafai, K., Analytical characterization and conceptual assessment of solid and fluid temperature differentials in porous media, Int. J. Heat Mass Transfer., 42(1999), pp. 423-435.

[9] Khashan, S. A., AL-Nimr, M. A., Validation of the local thermal equilibrium assumption in forced convection of non-Newtonian fluids through porous channels, Transport in Porous Media., 61 (2005), pp. 291–305.

[10] Marafie, A., Vafai, K., Analysis of non-darcian effects on temperature differentials in porous media, Int. J Heat Mass Transfer., 44 (2001), pp. 4401-4411.

[11] Jaballah, S., Sammouda, H., Bennacer, R., Study of the mixed convection in a channel with porous layers using a thermal nonequilibrium model, J. Porous Media., 15.1 (2012), pp. 51-62.

[12] Nield, D. A., Bejan, A., Convection in porous media, Springer-Verlag., 3rd Edition New York, 2006.

[13] Kaviany, M., Principles of heat transfer in porous media, Springer-Verlag, 2nd edition corrected., New York, 1999.

[14] Wakaoo, N., Kaguei, S., Funazkri, T., Effect of fluid dispersion coefficients on particle to fluid heat transfer coefficients in packed beds, Chem. Engng Sci., 34 (1979), pp. 325-336.

[15] Patankar, S. V., Numerical heat transfer and fluid flow, Hemisphere, New York (1980).

[16] Stone, H.L., Iterative solution of implicit approximations of multidimensional partial differential equations, SIAM J. Num. Anal., 5 (1968), N°. 3.

[17] Hooman, B., Guergenci, H., Effects of viscous dissipation and boundary conditions on forced convection in a channel occupied by a saturated porous medium, Transp. Porous Med., 68 (2007), pp. 301-319.