## THERMAL SCIENCE

International Scientific Journal

### THERMAL NON-EQUILIBRIUM HEAT TRANSFER IN A POROUS CAVITY IN THE PRESENCE OF BIO-CHEMICAL HEAT SOURCE

**ABSTRACT**

This paper is concerned with thermal non-equilibrium natural convection in a square cavity filled with a porous medium in the presence of a biomass which is transported in the cavity. The biomass can consume a secondary moving substrate. The physics of the presented problem is related to the analysis of heat and mass transfer in a composting process that controlled by internal heat generation. The intensity of the bio-heat source generated in the cavity is equal to the rate of consumption of the substrate by the biomass. It is assumed that the porous medium is homogeneous and isotropic. A two-field model that represents the fluid and solid phase temperature fields separately is used for energy equation. A simplified Monod model is introduced along with the governing equations to describe the consumption of the substrate by the biomass. In other word, the transient biochemical heat source which is dependent on a solute concentration is considered in the energy equations. Investigation of the biomass activity and bio-chemical heat generation in the case of thermal non-equilibrium assumption has not been considered in the literature and they are open research topics. The effects of thermal non-equilibrium model on heat transfer, flow pattern and biomass transfer are investigated. The effective parameters which have a direct impact on the generated bio-chemical heat source are also presented. The influences of the non-dimensional parameters such as fluid-to-solid conductivity ratio on the temperature distribution are presented.

**KEYWORDS**

PAPER SUBMITTED: 2011-10-10

PAPER REVISED: 2013-10-01

PAPER ACCEPTED: 2013-10-28

PUBLISHED ONLINE: 2014-02-09

**THERMAL SCIENCE** YEAR

**2015**, VOLUME

**19**, ISSUE

**2**, PAGES [579 - 590]

- Baytas, A. C., Pop I., Free convection in a square porous cavity using a thermal non-equilibrium model, Int. J. Therm. Sci., 41 (2002), pp. 861-870
- Varol, Y., Oztop, H. F., Pop, I., Numerical analysis of natural convection for a porous rectangular enclosure with sinusoidally varying temperature profile on the bottom wall, Int. J. Heat Mass Transfer, 35 (2008), pp. 56-64
- El-Fadel, M., Findikakis, A. N., Leckie, J. O., Numerical modeling of Generation and transport of gas and heat in landfill I Model Formulation, Waste Manag. Res., 14 (1996), pp. 483-504
- Larsen, K. L., McCartney, D. M., Effect of C:N ratio on microbial activity and N retention: bench-scale study using pulp and paper biosolids, Compost Sci. Util., 8 (2000), pp. 147-159
- Chamkha, A.J., Double-diffusive convection in a porous Enclosure with cooperating temperature and concentration Gradients and heat generation or absorption Effect, Num. Heat Transfer, Part A, 41 (2002), pp. 65-87
- Prud'homme, M., Jasmin, S., Determination of a heat source in porous medium With convective mass diffusion by an inverse method Mass Transfer, Int. J. Heat Mass Transfer, 46 (2003), pp. 2065-2075
- Jasmin, S., Prud'homme, M., Inverse determination of a heat source from a solute Concentration generation model in porous medium, Int. J. Heat Mass Transfer, 32 (2005), pp. 43-53
- Saghir, M. Z., Heat and mass transfer in a multi-porous cavity, Int. Comm. Heat Mass Transfer, 25 (1998), 7, pp.1019-1030
- Bilgen, E., Ben Yedder, R., Natural convection in enclosure with heating and cooling by sinusoidal temperature profiles on one side, Int. J. Heat Mass Transfer, 50 (2007), pp. 139-150
- Storesletten, L., Pop, I., Free convection in a vertical porous layer with walls at non-uniform temperature, Fluid Dyn. Res., 17 (1996), pp.107-119
- Bradean, R., Ingham, D. B., Heggs, P. J., Pop, I., Free convection fluid flow due to a periodically heated and cooled vertical flat plate embedded in a porous media, Int. J. Heat Mass Transfer, 39 (1996), pp. 2545-2557
- Baytas, A. C., Pop, I., Free convection in oblique enclosures filled with a porous medium, Int. J. Heat Mass Transfer, 42 (1999), pp. 1047-1057
- Bhadauria, B. S., Srivastava, A.K., Magneto-double diffusive convection in an electrically conducting-fluid-saturated porous medium with temperature modulation of the boundaries, Int. J. Heat Mass Transfer, 53 (2010), pp. 2530-2538
- Patankar, S., Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corp., New York, 1980
- Kayhani, M. H., Nazari, M., Shakeri Nejad, E., The Effects of Fluid-to-Solid Conductivity Ratio, Rayleigh Number and Interstitial Heat Transfer Coefficient on the TNE Free Convection in a Porous Enclosure, Transp Porous Med, 87 (2011), pp. 625-633l heat source, monod model