THERMAL SCIENCE

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Amir Abbas

,

Muhmmad Ashraf

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 non-linear coupled PDE is formulated and then non-dimensionalized 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 implicate 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, and 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 concentration 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
thermophoretic transportation, temperature dependent viscosity, mixed convection, sphere, implicite finite difference method
PAPER SUBMITTED: 2019-05-18
PAPER REVISED: 2020-03-16
PAPER ACCEPTED: 2020-03-19
PUBLISHED ONLINE: 2020-04-04
DOI REFERENCE: https://doi.org/10.2298/TSCI190518137A
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2020, VOLUME 24, ISSUE Issue 6, PAGES [4089 - 4101]
REFERENCES
  1. Potter, J. M., Riley, N.,Free convection from a heated sphere at large Grashof number, J. Fluid Mech.,100(1980), 4, pp. 769-783
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. Crosby, A., Lister, J. R., Creeping axisymmetric plumes with strongly temperature-dependent viscosity, J. Fluid Mech.,745 (2014), doi:10.1017/jfm.2014.128.
  15. 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.
  16. 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
  17. 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
  18. 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
  19. Thoray, C., Michaut, C., Elastic-plate gravity currents with a temperature-dependent viscosity, J. Fluid of Mechanics, 805 (2016), 1, pp. 88-117
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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
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Combined effects of variable viscosity and thermophoretic transportation on mixed convection flow around the surface of a sphere

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence