## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Effect of thermal radiation on natural conviction of a nanofluid in a square cavity with a solid body

**ABSTRACT**

This investigation is to concentrate on the effect of thermal radiation on free convection of a Cu-water nanofluid in a differentially heated cavity containing a solid square block placed in the middle. The upper and lower dividers of the cavity are kept as thermally protected; The coupled equations of mass, momentum, and energy are governed the mathematical model. Finite difference method is used to solve the governing equations. All internal surfaces of the cavity are deemed as a diffused emitters and reflectors for radiation. The impacts of relevant parameters, the Rayleigh number (103 ≤ Ra ≤ 106), volume fraction of nanoparticles (0.0 ≤ f ≤ 0.04) and thermal radiation (Rd=0, 1, 5 and 10), are explored. For various values of the flow parameters, the values for local and average Nusselt number are calculated. It is observed that the local and averaged Nusselt numbers are increased with an increase in the Rayleigh number and volume fraction of nanoparticles. Also, the temperature distribution of the fluid increases with an increase in the radiation parameter.

**KEYWORDS**

PAPER SUBMITTED: 2019-10-03

PAPER REVISED: 2020-03-12

PAPER ACCEPTED: 2020-05-25

PUBLISHED ONLINE: 2020-06-07

- Choi, S.U., Eastman J.A., Enhancing thermal conductivity of fluids with nanoparticles, Argonne National Lab, IL, United States, 1995.
- Hussein, A.K., et al., Naceur, B.M. and Habib, B.A., Three-dimensional unsteady natural convection and entropy generation in an inclined cubical trapezoidal cavity with an isothermal bottom wall, Alexandria Engineering Journal, 55 (2016), 2, pp. 741-755.
- Shen, Z.G., et al., Effect of tilt angle on the stability of free convection heat transfer in an upward-facing cylindrical cavity: Numerical analysis, International Journal of Thermal Sciences, 107 (2016), pp. 13-24.
- Bilgen, E. and Oztop, H., Natural convection heat transfer in partially open inclined square cavities, International Journal of Heat and Mass Transfer, 48 (2005), 8, pp. 1470-1479.
- Iwatsu, R., et al., Mixed convection in a driven cavity with a stable vertical temperature gradient, International Journal of Heat and Mass Transfer, 36 (1993), 6, pp. 1601-1608.
- Cheong, H.T., et al., Natural convection in a wavy porous cavity with sinusoidal heating and internal heat generation, International Journal of Numerical Methods for Heat & Fluid Flow, 27 (2017), 2, pp. 287-309.
- Hayat, T., et al., Mixed convective three-dimensional flow of Williamson nanofluid subject to chemical reaction, International Journal of Heat and Mass Transfer, 127 (2018), pp. 422-429.
- Hayat, T., et al., Radiative flow of micropolar nanofluid accounting thermophoresis and Brownian moment, International Journal of Hydrogen Energy, 42 (2017), 26, pp. 16821-16833.
- Khan, M.I., et al., Behavior of stratification phenomenon in flow of Maxwell nanomaterial with motile gyrotactic microorganisms in the presence of magnetic field, International Journal of Mechanical Sciences, 131, (2017), pp. 426-434.
- Hayat, T., et al., Entropy generation in flow with silver and copper nanoparticles, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 539 (2018), pp. 335-346.
- Khanafer, K., et al., Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, Int. journal of heat and mass transfer 46 (2003), 19, pp 3639-3653.
- Sivasankaran, S., et al., Natural convection of nanofluids in a cavity with linearlyvarying wall temperature, (2010), pp. 468-482.
- Tiwari, R. K. and Das, M. K., Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids, Int. Journal of Heat and Mass Transfer 50 (2018), 9-10, pp. 2002-2018.
- Hayat, T., et al., Numerical simulation for melting heat transfer and radiation effects in stagnation point flow of carbon-water nanofluid, Computer methods in applied mechanics and engineering, 315, (2017), pp. 1011-1024.
- Hayat, T., et al., Stagnation point flow with Cattaneo-Christov heat flux and homogeneous-heterogeneous reaction,. Journal of Molecular Liquids, 220, (2016), pp. 49-55.
- Hayat, T., et al., Thermally stratified stretching flow with Cattaneo-Christov heat flux, International Journal of Heat and Mass Transfer, 106, (2017), pp. 289-294.
- Hayat, T., et al., Impact of Cattaneo-Christov heat flux model in flow of variable thermal conductivity fluid over a variable thicked surface, International Journal of Heat and Mass Transfer, 99, (2016), pp. 702-710.
- Hayat, T., et al., Mathematical modeling of non-Newtonian fluid with chemical aspects: a new formulation and results by numerical technique, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 518, (2017), pp. 263-272.
- Farooq, M., et al., MHD stagnation point flow of viscoelastic nanofluid with non-linear radiation effects, Journal of molecular liquids, 221, (2016), pp. 1097-1103.
- Khan, M.I., et al., A comparative study of Casson fluid with homogeneous-heterogeneous reactions, Journal of colloid and interface science, 498, (2017), pp. 85-90.
- Qayyum, S., et al., A framework for nonlinear thermal radiation and homogeneous-heterogeneous reactions flow based on silver-water and copper-water nanoparticles: a numerical model for probable error, Results in physics, 7, (2017), pp. 1907-1914.
- Khan, M.I., et al., Entropy optimization and quartic autocatalysis in MHD chemically reactive stagnation point flow of Sisko nanomaterial, International Journal of Heat and Mass Transfer, 127, (2018), pp. 829-837.
- Hayat, T., et al., New thermodynamics of entropy generation minimization with nonlinear thermal radiation and nanomaterials, Physics Letters A, 382, (2018), 11, pp. 749-760.
- Sivasankaran, S., et al., MHD mixed convection of Cu-water nanofluid in a two-sided lid-driven porous cavity with a partial slip, Numerical Heat Transfer 70 (2016), 12, pp. 1356-1370.
- Goodarzi, M., et al., Investigation of heat transfer and pressure drop of a counter flow corrugated plate heat exchanger using MWCNT based nanofluids, Int. communications in heat and mass transfer 66 (2015), pp.172-179.
- Esfe, M.H., et al., Numerical simulation of natural convection around an obstacle placed in an enclosure filled with different types of nanofluids, Heat Transfer Research 45 (2014), 3.
- Hayat, T., et al., Entropy generation in magnetohydrodynamic radiative flow due to rotating disk in presence of viscous dissipation and Joule heating, Physics of Fluids, 30, (2018), 1, pp. 017101.
- Karimipour, A., New correlation for Nusselt number of nanofluid with Ag/Al2O3/Cu nanoparticles in a microchannel considering slip velocity and temperature jump by using lattice Boltzmann method, Int. Journal of Thermal Sciences 91 (2015), pp. 146-146.
- Md Kasmani, R., et al., Analytical and numerical study on convection of nanofluid past a moving wedge with Soret and Dufour effects, Int. Journal of Numerical Methods for Heat & Fluid Flow 27 (2017), 10, pp. 2333-2354.
- Elbashbeshy, E. M., et al., Effects of thermal radiation and magnetic field on unsteady mixed convection flow and heat transfer over an exponentially stretching surface with suction in the presence of internal heat generation/absorption, Journal of the Egyptian Mathematical Society, 20 (2012), 3, pp. 215-222.
- Safaei, M. R., et al., The investigation of thermal radiation and free convection heat transfer mechanisms of nanofluid inside a shallow cavity by lattice Boltzmann method, Physica A: Statistical Mechanics and its Applications 509 (2018), pp. 515-535.
- Ridouane, E. H., et al., Interaction between natural convection and radiation in a square cavity heated from below, Numerical Heat Transfer, Part A: Applications 45 (2004), 3, pp. 289-311.
- Ridouane, E. H., et al., Effects of surface radiation on natural convection in a Rayleigh-Bénard square enclosure: steady and unsteady conditions, Heat and mass transfer, 42 (2006), 3, 214-225.
- Kogawa, T., Influence of radiation effect on turbulent natural convection in cubic cavity at normal temperature atmospheric gas, Int. Journal of Heat and Mass Transfer, 104 (2017), pp. 456- 466.
- Alsabery, A., Effects of finite wall thickness and sinusoidal heating on convection in nanofluid-saturated local thermal non-equilibrium porous cavity, Physica A: Statistical Mechanics and its Applications 470 (2017), pp. 20-38.
- De Vahl Davis, G. and Jones, I., Natural convection in a square cavity, International Journal for numerical methods in fluids, 3 (1983), 3, pp. 249-264.
- Bilgen, E. and Yeder, R. B., Natural convection in enclosure with heating and cooling by sinusoidal temperature profiles on one side, International Journal of Heat and Mass Transfer, 50 (2007), 1-2, pp. 139-150.
- Ho, C. J., et al., Numerical simulation of natural convection of nanofluid in a square enclosure: effects due to uncertainties of viscosity and thermal conductivity, International Journal of Heat and Mass Transfer, 51 (2008), 17-18, pp. 4506-4516.
- Cheong, H., et al., Effect of aspect ratio on natural convection in an inclined rectangular enclosure with sinusoidal boundary condition, International Communications in Heat and Mass Transfer, 45 (2013), pp. 75-85.