## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Thermal analysis on natural convection coupled with radiative heat transfer in a saturated porous cavity

**ABSTRACT**

Porous foam is an ideal material for enhancing radiative heat transfer in numerous thermal equipment. The solid skeletons of porous foams can absorb/ release radiative energy and transfer convective energy with the surrounding fluid in the pores. In this paper, the conduction-convection-radiation coupling heat transfer in a porous cavity is investigated. A local thermal nonequilibrium model is used to represent the energy transport during the solid and fluid phases. The heat flux caused by thermal radiation is obtained by solving the radiation transfer equation. The thermal and fluid fields are studied to discern various parameters, including the Planck numbers Pl , the modified Rayleigh numbers Ra , and the interphase heat transfer coefficients H . Our study indicates the following: (1) the effect of radiation can be neglected when Pl > 20; (2) the modified Rayleigh numbers have little influence on the solid temperature when the radiative heat transfer is dominant and the convective heat transfer between the two phases is weak; and (3) the local thermal-equilibrium can be formed when H exhibits high values.

**KEYWORDS**

PAPER SUBMITTED: 2021-03-09

PAPER REVISED: 2021-06-16

PAPER ACCEPTED: 2021-07-05

PUBLISHED ONLINE: 2021-09-04

- Ingham, D. B., Pop, I., Transport phenomena in porous media Ш, 2005, Elsevier, Oxford
- Vafai, K., Handbook of porous media, second ed., 2005, Taylor and Francis, New York
- Wang, K. Y., Tien, C. L., Thermal Insulation in Flow Systems: Combined Radiation and Convection through a Porous Segment, Journal of Heat Transfer, 106 (1984), pp. 453-459
- Nemoda, S. , , et al, Numerical Simulation of Porous Burners and Hole Plate Surface Burners, Thermal Science, 8 (2004), 1, pp. 3-17
- Dupuy, J. L., Larini, M., Fire Spread through a Porous Forest Fuel Bed: a Radiative and Convective Model including Fire-induced Flow Effects, International Journal Of Wildland Fire, 9 (1999), 3, pp. 155-172
- Fend, T., et al, Porous Materials as Open Volumetric Solar Receivers: Experimental Determination of Thermophysical and Heat Transfer Properties, Energy, 29 (2004), 5-6, pp. 823-833
- Rostamiyan, Y., et al, Analytical Investigation of Nonlinear Model arising in Heat Transfer through the Porous Fin, Thermal Science, 18 (2014), 2, pp. 409-417
- Darvishi, M. T., et al, Unsteady Thermal Response of a Porous Fin under the Influence of Natural Convection and Radiation, Heat and Mass Transfer, 50 (2014), pp. 1311-1317
- Astanina, M. S., et al, Effect of Thermal Radiation on Natural Convection in a Square Porous Cavity Filled with a Fluid of Temperature-dependent Viscosity, Thermal Science, 22 (2018), 1, pp. 391-399
- Sheikholeslami, M., Shehzad, S. A., Magnetohydrodynamic Nanofluid Convection in a Porous Enclosure considering Heat Flux Boundary Condition, International Journal of. Heat and Mass Transfer, 106 (2017), pp. 1261-1269
- Shateria, A. R., Salahshour, B., Comprehensive Thermal Performance of Convection-Radiation longitudinal Porous Fins with various Profiles and Multiple Nonlinearities, International Journal of Mechanical Sciences, 136 (2018), pp. 252-263
- Chen, H., et al, Least square spectral collocation method for nonlinear heat transfer in moving porous plate with convective and radiative boundary conditions, International Journal of Thermal Science, 132 (2018), pp. 335-343
- Ghalambaz, M., et al, Free Convection in a Square Cavity filled by a Porous Medium saturated by a Nanofluid: Viscous Dissipation and Radiation Effects, Engineering Science and Technology An International Journal, 19 (2016), pp. 1244-1253
- Jamal-Abad, M. T., et al, Heat Transfer in Concentrated Solar Air-heaters filled with a Porous Medium with Radiation Effects: A Perturbation Solution, Renewable Energy, 91 (2016), pp. 147-154
- López, A., et al, Entropy Generation Analysis of MHD Nanofluid Flow in a Porous Vertical Microchannel with Nonlinear Thermal Radiation, Slip Flow and Convective-radiative Boundary Conditions, International Journal of. Heat and Mass Transfer, 107 (2017), pp. 982-994
- Barnoon, P., et al, Two Phase Natural Convection and Thermal Radiation of Non-Newtonian Nanofluid in a Porous Cavity considering Inclined Cavity and Size of inside Cylinders, International Communications in Heat and Mass Transfer, 108 (2019), pp. 104285
- Arafa, A. A. M., et al, Radiative Flow of Non-Newtonian Nanofluids within Inclined Porous Enclosures with Time Fractional Derivative, Scientific Reports, 11 (2021), pp. 5338
- Ajibade, O. A., et al, Effects of Dynamic Viscosity and Nonlinear Thermal Radiation on Free Convective Flow through a Vertical Porous Channel, International Journal of Thermofluids, 9 (2021), pp. 100062
- Olajuwon, I. B., Convection Heat and Mass Transfer in a Hydromagnetic Carreau Fluid past a Vertical Porous Plate in Presence of Thermal Radiation and Thermal Diffusion, Thermal Science, 15 (2011), 2, pp. 241-252
- Izadi, M., MHD Thermogravitational Convection and Thermal Radiation of a Micropolar Nanoliquid in a Porous Chamber, International Communications in Heat and Mass Transfer, 110 (2020), 104409.
- Talukdar, P., et al, Combined Radiation and Convection Heat Transfer in a Porous Channel Bounded by Isothermal Parallel Plates, International Journal of Heat and Mass Transfer, 47 (2004), pp. 1001-1013
- Abdesslem, J., et al, Radiative Properties Effects on Unsteady Natural Convection inside a Saturated Porous Medium: Application for Porous Heat Exchangers, Energy, 61 (2013), pp. 224-233
- Elgazery, N. S., An Implicit-Chebyshev Pseudospectral Method for the Effect of Radiation on Power-law Fluid past a Vertical Plate immersed in a Porous Medium, Communications in Nonlinear Science and Numerical Simulation, 13 (2008), pp. 728-744
- Chen, X., et al, Transient Thermal Analysis of the Coupled Radiative and Convective Heat Transfer in a Porous filled Tube Exchanger at High Temperatures, International Journal of Heat and Mass Transfer, 108 (2017), pp. 2472-2480
- Mahmoudi, Y., Effect of Thermal Radiation on Temperature Differential in a Porous Medium under Local Thermal Non-equilibrium Condition, International Journal of Heat and Mass Transfer, 76 (2014), pp. 105-121
- Xue, C., et al., Transient Thermal Analysis of the Coupled Radiative and Convective Heat Transfer in a Porous filled Tube Exchanger at High Temperatures, International Journal of Heat and Mass Transfer, 108 (2017), pp. 2472-2480
- Mesgarpour, M., Numerical Optimization of a New Concept in Porous Medium considering Thermal Radiation: Photovoltaic Panel Cooling Application, Solar Energy, 216 (2021), 5, pp. 452-467
- Raptis, A., Radiation and Free Convection Flow through a Porous Medium, International Communications in Heat and Mass Transfer, 25 (1998), 2, pp. 289-295
- Chen, Y. Y., et al, Influences of Radiative Characteristics on Free Convection in a Saturated Porous Cavity under Thermal Non-equilibrium Condition, International Communications in Heat and Mass Transfer, 95 (2018), pp. 80-91
- D. M. Manole, J. L. Lage, Numerical benchmark results for natural convection in a porous medium cavity, HTD-Vol. 216, Heat and Mass Transfer in Porous Media, ASME Conference 1992:55-60.
- S. L. Moya, E. Ramos, M. Sen, Numerical study of natural convection in a tilted rectangular porous material, Int. J. Heat Mass Transfer, 1987 (30):741-756.
- Baytas, A. C., Pop, I., Free Convection in a Square Porous Cavity using a Thermal Nonequilibrium Model, International Journal of Thermal Science, 41 (2002), pp. 861-870
- Chen, S. S., et al, Chebyshev Collocation Spectral Method for Solving Radiative Transfer with the Modified Discrete Ordinates Formulations, International Journal of Heat and Mass Transfer, 88 (2015), pp. 388-397
- Chen, Y. Y., et al, Spectral Collocation Method for Natural Convection in a Square Porous Cavity with Local Thermal Equilibrium and Non-equilibrium Models, International Journal of Heat and Mass Transfer, 96 (2016), pp. 84-96