Thermal diffusion and diffusion thermo effects on MHD thermosolutal Marangoni convection boundary layer flow over a permeable surface. (English) Zbl 1244.76119

Hamid, R. A.; Zaimi, W. M. K. A. Wan; Arifin, N. M.; Bakar, N. A. A.; Bidin, B.

J. Appl. Math. 2012, Article ID 750939, 14 p. (2012).

Summary: The problem of thermal diffusion and diffusion thermo effects on thermosolutal Marangoni convection flow of an electrically conducting fluid over a permeable surface is investigated. Using appropriate similarity transformations, the governing system of partial differential equation is transformed to a set of nonlinear ordinary differential equations, then solved numerically using the Runge-Kutta-Fehlberg method. The effects of thermal diffusion and diffusion thermo, magnetic field parameter, thermosolutal surface tension ratio, and suction/injection parameter on the flow field, heat transfer characteristic, and concentration are thoroughly examined. Numerical results are obtained for temperature and concentration profiles as well as the local Nusselt and Sherwood numbers are presented graphically and analyzed. It is found that these governing parameters affect the variations of the temperature and concentration and also the local Nusselt and Sherwood numbers.

MSC:

76W05	Magnetohydrodynamics and electrohydrodynamics
76R10	Free convection
76D10	Boundary-layer theory, separation and reattachment, higher-order effects
80A20	Heat and mass transfer, heat flow (MSC2010)

References:

[1]	L. G. Napolitano, “Microgravity fluid dynamics,” in Proceedings of the 2nd Levitch Conference, Washington, DC, USA, 1978. · Zbl 0398.76007
[2]	L. G. Napolitano, “Marangoni boundary layers,” in Proceedings of the 3rd European Symposium on Materials Sciences in Space, Grenoble, France, 1979. · Zbl 0485.76032
[3]	K. Arafune and A. Hirata, “Thermal and solutal marangoni convection in In-Ga-Sb system,” Journal of Crystal Growth, vol. 197, no. 4, pp. 811-817, 1999.
[4]	K. Arafune, K. Yamamoto, and A. Hirata, “Interactive thermal and solutal Marangoni convection during compound semiconductor growth in a rectangular open boat,” International Journal of Heat and Mass Transfer, vol. 44, no. 13, pp. 2404-2411, 2001.
[5]	Z. Galazka and H. Wilke, “Influence of Marangoni convection on the flow pattern in the melt during growth of Y3Al5O12 single crystals by the Czochralski method,” Journal of Crystal Growth, vol. 216, no. 1, pp. 389-398, 2000. · doi:10.1016/S0022-0248(00)00426-7
[6]	H. Neumann, Y. Plevachuk, and F. Allenstein, “Investigation of Marangoni convection in monotectic melts by resistance measurements,” Materials Science and Engineering A, vol. 361, no. 1-2, pp. 155-164, 2003. · doi:10.1016/S0921-5093(03)00512-4
[7]	B. Arendt and R. Eggers, “Interaction of Marangoni convection with mass transfer effects at droplets,” International Journal of Heat and Mass Transfer, vol. 50, no. 13-14, pp. 2805-2815, 2007. · Zbl 1119.80305 · doi:10.1016/j.ijheatmasstransfer.2006.10.055
[8]	Y. L. Xu, Z. B. Dong, Y. H. Wei, and C. L. Yang, “Marangoni convection and weld shape variation in A-TIG welding process,” Theoretical and Applied Fracture Mechanics, vol. 48, no. 2, pp. 178-186, 2007. · doi:10.1016/j.tafmec.2007.05.004
[9]	A. Al-Mudhaf and A. J. Chamkha, “Similarity solutions for MHD thermosolutal Marangoni convection over a flat surface in the presence of heat generation or absorption effects,” Heat and Mass Transfer, vol. 42, no. 2, pp. 112-121, 2005. · doi:10.1007/s00231-004-0611-8
[10]	D. M. Christopher and B. Wang, “Prandtl number effects for Marangoni convection over a flat surface,” International Journal of Thermal Sciences, vol. 40, no. 6, pp. 564-570, 2001. · doi:10.1016/S1290-0729(01)01244-3
[11]	I. Pop, A. Postelnicu, and T. Gro\csan, “Thermosolutal Marangoni forced convection boundary layers,” Meccanica, vol. 36, no. 5, pp. 555-571, 2001. · Zbl 1060.76109 · doi:10.1023/A:1017431224943
[12]	R. A. Hamid, N. M. Arifin, R. Nazar, F. M. Ali, and I. Pop, “Dual solutions on thermosolutal Marangoni forced convection boundary layer with suction and injection,” Mathematical Problems in Engineering, vol. 2011, Article ID 875754, 19 pages, 2011. · Zbl 1382.76230 · doi:10.1155/2011/875754
[13]	C. H. Chen, “Marangoni effects on forced convection of power-law liquids in a thin film over a stretching surface,” Physics Letters A, vol. 370, no. 1, pp. 51-57, 2007. · doi:10.1016/j.physleta.2007.05.024
[14]	E. Magyari and A. J. Chamkha, “Exact analytical results for the thermosolutal MHD Marangoni boundary layers,” International Journal of Thermal Sciences, vol. 47, no. 7, pp. 848-857, 2008. · doi:10.1016/j.ijthermalsci.2007.07.004
[15]	N. M. Arifin, F. M. Ali, R. Nazar, and I. Pop, “Thermal and solutal marangoni mixed convection boundary layer flow,” WSEAS Transactions on Mathematics, vol. 9, no. 5, pp. 376-385, 2010.
[16]	R. A. Hamid, N. M. Arifin, R. Nazar, and F. M. Ali, “Radiation effects on marangoni convection over a flat surface with suction and injection,” Malaysian Journal of Mathematical Sciences, vol. 5, no. 1, pp. 13-25, 2011. · Zbl 1244.76110
[17]	N. G. Kafoussias and E. W. Williams, “Thermal-diffusion and diffusion-thermo effects on mixed free-forced convective and mass transfer boundary layer flow with temperature dependent viscosity,” International Journal of Engineering Science, vol. 33, no. 9, pp. 1369-1384, 1995. · Zbl 0899.76325 · doi:10.1016/0020-7225(94)00132-4
[18]	P. Puvi Arasu, P. Loganathan, R. Kandasamy, and I. Muhaimin, “Lie group analysis for thermal-diffusion and diffusion-thermo effects on free convective flow over a porous stretching surface with variable stream conditions in the presence of thermophoresis particle deposition,” Nonlinear Analysis: Hybrid Systems, vol. 5, no. 1, pp. 20-31, 2011. · Zbl 1371.76108 · doi:10.1016/j.nahs.2010.08.003
[19]	E. Osalusi, J. Side, and R. Harris, “Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer of a steady MHD convective and slip flow due to a rotating disk with viscous dissipation and Ohmic heating,” International Communications in Heat and Mass Transfer, vol. 35, no. 8, pp. 908-915, 2008. · Zbl 1161.80002 · doi:10.1016/j.icheatmasstransfer.2008.04.011
[20]	A. A. Afify, “Similarity solution in MHD: effects of thermal diffusion and diffusion thermo on free convective heat and mass transfer over a stretching surface considering suction or injection,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 5, pp. 2202-2214, 2009. · Zbl 1221.76212 · doi:10.1016/j.cnsns.2008.07.001
[21]	N. T. Eldabe, A. G. El-Saka, and A. Fouad, “Thermal-diffusion and diffusion-thermo effects on mixed free-forced convection and mass transfer boundary layer flow for non-Newtonian fluid with temperature dependent viscosity,” Applied Mathematics and Computation, vol. 152, no. 3, pp. 867-883, 2004. · Zbl 1077.76066 · doi:10.1016/S0096-3003(03)00603-9
[22]	M. A. El-Aziz, “Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer by hydromagnetic three-dimensional free convection over a permeable stretching surface with radiation,” Physics Letters A, vol. 372, no. 3, pp. 263-272, 2008. · Zbl 1217.76069 · doi:10.1016/j.physleta.2007.07.015
[23]	M. M. Rashidi, T. Hayat, E. Erfani, S. A. Mohimanian Pour, and A. A. Hendi, “Simultaneous effects of partial slip and thermal-diffusion and diffusion-thermo on steady MHD convective flow due to a rotating disk,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 11, pp. 4303-4317, 2011. · Zbl 1419.76712 · doi:10.1016/j.cnsns.2011.03.015
[24]	T. Hayat, M. Nawaz, S. Asghar, and S. Mesloub, “Thermal-diffusion and diffusion-thermo effects on axisymmetric flow of a second grade fluid,” International Journal of Heat and Mass Transfer, vol. 54, no. 13-14, pp. 3031-3041, 2011. · Zbl 1217.80039 · doi:10.1016/j.ijheatmasstransfer.2011.02.045
[25]	A. Aziz, “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1064-1068, 2009. · doi:10.1016/j.cnsns.2008.05.003