## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Combined effects of variable viscosity and thermophoretic transportation on mixed convection flow around the surface of a sphere

**ABSTRACT**

The physical behavior of the combined effect of temperature dependent viscosity and thermophoretic motion on mixed convection flow around the surface of a sphere is investigated. The set of nonlinear coupled partial differential equations is formulated andthen nondimenisonalized by using an appropriate set of dimensionless variables. The dimensionless model is then transformed to convenient form for integration by employing a suitable set of primitive variables formulation and then discretized by using an efficient implicite finite difference scheme for numerical simulation. The effect of controlling parameters on velocity profile, temperature profile, and mass concentration as well as skin friction, rate of heat transfer, mass transfer rate are analyzed. The obtained numerical results for different values of controlling parameters indicate that, velocity profile gains its largest magnitude at position x=1.5 radian and slows down at postion x=π radian. It is also predicted that the temperature distribution and mass concentarion are diluted at position x=1.5 radian due to rapid motion of fluid. The numerical results are highlighted in graphical as well as in tabular form.

**KEYWORDS**

PAPER SUBMITTED: 2019-05-18

PAPER REVISED: 2020-03-16

PAPER ACCEPTED: 2020-03-19

PUBLISHED ONLINE: 2020-04-04

- Potter, J. M., Riley, N.,Free convection from a heated sphere at large Grashof number, J. Fluid Mech.,100(1980), 4, pp. 769-783
- Epstein M., Hauser G. M., Henry R. E., Thermophoretic deposition of particles in natural convection flow from a vertical plate, Int. J. Heat Transfer,107(1985),2, pp. 272-276
- Attia, H. A., Unsteady hydromagnetic channel flow of dusty fluid with temperature dependent viscosity and thermal conductivity, Heat Mass Transfer, 42 (2006), 9, pp. 779-787
- Chin, K. E., Nazar, R., Arifin, N. M., Pop, T, Effect of variable viscosity on mixed convection boundary layer in porous medium, Int. Communications in Heat and Mass Transfer, 34 (2007), 4, pp. 464-473
- El-Hakiem, M. A., Rashad, A. M., Effect of radiation on non-Darcy free convection from a vertical cylinder embedded in a fluid-saturated porous medium with a temperature-dependent viscosity, J. Porous Media, 10(2007), pp. 209-218
- Enzo, Z., Mixed convection with variable viscosity in a vertical annulus with uniform wall temperatures, Int. J. Heat and Mass Transfer, 51 (2008), 1-2, pp. 30-40
- Perez, C. E., Thomas, J. M., Blancer, S., Creff, R., The steady Navier-Stokes/energy system with temperature-dependent viscosity-Part-1: Analysis of the continuous problem, Int. J. Numer. Meth. Fluids, 56(2008), 1, pp. 63-89
- Perez, C. E., Thomas, J. M., Blancer, S., Creff, R., The steady Navier-Stokes/energy system with temperature-dependent viscosity-Part-2: The discrete problem and numerical experiments, Int. J. Numer. Meth. Fluids, 56(2008), 1, 91-114
- Abe-El Aziz, M. S., Rania, F., Effects of variable viscosity and suction/injection on thermal boundary layer of non-Newtonian power-law fluids past a power-law stretched surface, Thermal Science,14 (2010), 4, pp. 1111-1120
- Chamkha, A. J., El-Kabeir, S. M. M., Rashad, A. M., Heat and mass transfer by non-Darcy free convection from a vertical cylinder embedded in porous media with temperature dependent viscosity, Int. J. Numerical Methods for Heat and Fluid Flow, 21 (2011), 7, pp. 847-863
- Rashad, A. M., Chamkha, A. J., El-Kabeir, S. M. M., Effect of chemical reaction on heat and mass transfer by mixed convection flow about a sphere in a saturated porous media, Int. J. Numerical Methods for Heat and Fluid Flow, 21(2011), 4, pp. 418-433
- Chinyoka, T., Makinde. O. D., Unsteady hydromagnetic flow of a reactive variable viscosity third-grade fluid in a channel with convective cooling, Int. J. Numer. Meth. Fluids, 69(2012), 2, pp. 353-365
- Hayat, T., Abbas, F. M., Ahmad, B., Alsaedi, A., MHD mixed convection peristaltic flow with variable viscosity and thermal conductivity, Sains Malaysiana, 43 (2014),10, pp. 1583-1590
- Crosby, A., Lister, J. R., Creeping axisymmetric plumes with strongly temperature-dependent viscosity, J. Fluid Mech.,745 (2014), doi:10.1017/jfm.2014.128.
- Dhiman, J. S., Sharma, N., Effects of temperature dependent viscosity on thermal convection of nanofluids: steady case, J. Thermophysics and Heat Transfer, 29 (2015), 1, pp. 90-101.
- Lee , J., Jung, S. Y., Sung, H. J., Zaki, T. A., Turbulent thermal boundary layers with temperature dependent viscosity, Int. J. Heat and Fluid Flow, 14 (2014), pp. 43-52
- Umavathi, J. C., Ojjela. O., Effects of variable viscosity on free convection in a vertical rectangular duct, Int. J. Heat and Mass Transfer, 84 (2015), 1, pp. 1-15
- Ashraf, M., Chamkha, A. J., Iqbal, S. Masud, A., Effects of temperature dependent viscosity and thermal conductivity on mixed convection flow along a magnetized verticsl surface, Int. J. Numerical Methods for Heat and Fluid Flow, 26(2015), 5, pp. 1580-1592
- Thoray, C., Michaut, C., Elastic-plate gravity currents with a temperature-dependent viscosity, J. Fluid of Mechanics, 805 (2016), 1, pp. 88-117
- Makinde, O. D., Khan, W. A., Chulham, J. R., MHD variable reacting flow over a convectively heated plate in a porous medium with thermophoresis and radiative heat transfer, Int. J. Heat and Mass Transfer, 93 (2016), 1, pp. 595-604
- Malikarjuna, B., Rashad, A. M., Hussein, A. K., Raju, S. H., Transpiration and thermophoresis effects on non-Darcy convective flow past a rotating cone with thermal radiation, Arabian Journal for Science and Engineering, 41(2016), 11, pp. 4691-4700
- Ashraf, M., Fatima, A., Gorla, R. S. R., Periodic momentum and thermal boundary layer mixed convection flow around the surface of heated sphere in the presence of viscous dissipation, Cand. J. Phys.,95(2017), 10, pp.976-986
- Ashraf, M., Fatima, A.,Numericalsimulation of the effect of transient shear stress and the rate of heat transfer around different positions of sphere in the presence of viscous dissipation, J. Heat Transfer, (ASME),140(2018), 6, pp. 701-7012
- Ashraf, M., Anwar, K., and Gorla, R. S. R., Natural convection boundary layer flow of nanofluids around different stations of sphere and into plume above the sphere, Heat Transfer-Asian Research, 48(2019), 3, pp. 1127-1148