## THERMAL SCIENCE

International Scientific Journal

### EFFECTS OF PRESSURE STRESS WORK AND THERMAL RADIATION ON FREE CONVECTION FLOW AROUND A SPHERE EMBEDDED IN A POROUS MEDIUM WITH NEWTONIAN HEATING

**ABSTRACT**

The effects of pressure stress work and thermal radiation on free convection flow around a sphere embedded in a porous medium with Newtonian heating is considered. The basic equations of boundary-layer are transformed into a non-dimensional form and reduced to non-linear system of partial differential equations and solved numerically using an implicit finite difference technique with Newtons linearization method. Comparisons with previously published work are performed and excellent agreement is obtained. Numerical results have been shown graphically and tabular forms for some selected values of parameters set consisting of radiation parameter, pressure stress work parameter, Newtonian heating coefficient, and Prandtl number.

**KEYWORDS**

PAPER SUBMITTED: 2015-06-01

PAPER REVISED: 2016-08-16

PAPER ACCEPTED: 2016-08-18

PUBLISHED ONLINE: 2016-09-05

**THERMAL SCIENCE** YEAR

**2018**, VOLUME

**22**, ISSUE

**1**, PAGES [401 - 412]

- Nazar, R., Amin, N., Grosn, T., and Pop, I., Free Convection Boundary Layer on an Isothermal Sphere in Micropolar Fluid, Int. Communications in Heat and Mass Transfer, 29(2002), 3, pp.377-386
- Akhter, T. and Alim, M. A., Effects of Radiation on Natural Convection Flow around a Sphere with Uniform Surface Heat Flux, J. of Mechanical Engineering, Institution of Engineers, Bangladesh, 39 (2008), 1, pp.50-56
- Alam, M. M., Alim, M. A., and Chowdhury, M. K., Viscous Dissipation Effects with MHD Natural Convection Flow on a Sphere in The Presence of Heat Generation, Nonlinear Analysis: Modeling and Control, 12 (2007), 4, pp.447-459
- Chen, T. S., and Mucoglu, A., Analysis of Mixed Forced and Free Convection about a Sphere, Int. J. Heat Mass Transfer, 20 (1977), pp.867- 875
- Chen, T. S., and Mucoglu, A., Mixed Convection about a Sphere with Uniform Surface Heat Flux, J. Heat Transfer, 100 (1978), pp.542- 544
- Cheng, E. H., and O¨zisik, M. N., Radiation with Free Convection in an Absorbing, Emitting and Scattering Medium, Int. J. Heat Mass Transfer, 15 (1972), 1243-1252
- O¨zisik, M. N., Radiative Transfer and Interactions with Conduction and Convection, Wiley, New York, USA, 1973
- Azzam, G. A., Radiation Effects on The MHD Mixed Free-Forced Convective Flow Past a Semi Infinite Moving Vertical Plate for High Temperature Differences, Phys. Scripta, 66 (2002), pp.71 -76
- Molla, M.M., Hossain, M.A., and Siddiqa, S., Radiation Effect on Free Convection Laminar Flow from an Isothermal Sphere, Communications, 198 (2011), 12, pp.1483-1496
- Chamkha, A. J., and Al-Mudhaf, A., Simultaneous Heat and Mass Transfer from a Permeable Sphere at Uniform Heat and Mass Fluxes with Magnetic Field and Radiation Effects, Num. Heat Transfer A, 46 (2004), pp. 181-198
- Akhter, T., and Alim, M. A., Effects of Radiation on Natural Convection Flow around a Sphere with Uniform Surface Heat Flux, J. of Mechanical Engineering, Institution of Engineers, Bangladesh, 39 (2008), 1, pp. 50-56
- Miraj, M., Alim M. A., and Andallah, L. S., Effects of Pressure work and Radiation on Natural Convection Flow around a Sphere with Heat Generation, Int. Communications in Heat and Mass Transfer, 38 (2011), 7, pp. 911-916
- El-Kabeir, S. M., El-Hakiem, M. A., and Rashad, A. M., Natural Convection from a Permeable Sphere Embedded in a Variable Porosity Porous Medium Due to Thermal Dispersion, Nonlinear Analysis: Modeling and Control, 12 (2007), pp. 345-357
- Merkin, J.H., Natural Convection Boundary Layer Flow on a Vertical Surface with Newtonian Heating, Int. J Heat Fluid Flow, 15 (1994), pp.392-398
- Pop, I., Lesnic, D., and Ingham, B., Asymptotic Solutions for the Free Convection Boundary Layer Flow Along a Vertical Surface in a Porous Medium with Newtonian Heating, Journal of Porous Media, 3 (2000), pp.227-235
- Chaudhary, R. and Jain, P., Unsteady Free Convection Boundary Layer Flow Past an Impulsively Started Vertical Surface with Newtonian Heating, Romanian Journal of Physics, 51(2006), pp.911-921
- Salleh, M. Z., Nazar, R., Pop, I., Numerical Solutions of Free Convection Boundary Layer Flow on a Solid Sphere with Newtonian Heating in a Micropolar Fluid, Meccanica, 47 (2012), pp.1261-1269
- Keller, H. B., Numerical Methods in Boundary Layer Theory, Annu. Rev. Fluid Mech., 10 (1978), pp. 417-433
- Cebeci, T., and Bradshaw, P., Physical and Computational Aspects of Convective Heat Transfer, Springer, New York, USA, 1984
- Salleh, M. Z., Nazar, R., and Pop, I., Mixed Convection Boundary Layer Flow About A Solid Sphere with Newtonian Heating, Archives of Mechanics, 62 (2010), pp.283-303