The Effect of Thermophoresis on MHD Stream of a Micropolar Liquid Through a Porous Medium with Variable Heat and Mass Flux and Thermal Radiation
DOI:
https://doi.org/10.37934/cfdl.14.5.106124Keywords:
Thermal Radiation, Thermophoresis, MHD, Micropolar, Porous Medium, Heat and Mass fluxAbstract
In this paper, the combined possessions of thermal radiation and thermophoresis on stable Magnetohydrodynamic free convection stream of a micropolar liquid past an erect porous laminate during a porous medium in the occurrence of variable heat and mass fluxes are engaged into report is measured. The leading non-linear partial differential equations of the crisis are changed into a scheme of nonlinear ordinary differential equations during suitable similarity conversion and Runge–Kutta Fourth order with shooting procedure scheme. The possessions of a variety of substantial parameters on the dimensionless stream, microrotation, temperature, and concentration profiles are discussed and offered graphically. In the end, numerical ideals of the substantial quantities, such as the limited skin factor, the combine stress coefficient, the local Nusselt quantity and the local Sherwood quantity are tabulated with the variant of magnetic constraint, coupling invariable, Darcy constraint, modified Forchheimer number, radiation constraint, and thermophoretic constraints.
References
Eringen, A. Cemal. "Theory of micropolar fluids." Journal of Mathematics and Mechanics 16 (1966): 1-18. https://doi.org/10.1512/iumj.1967.16.16001
Eringen, A. Cemal. "Theory of thermomicrofluids." Journal of Mathematical Analysis and Applications 38, no. 2 (1972): 480-496. https://doi.org/10.1016/0022-247X(72)90106-0
Eringen, A. Cemal. Microcontinuum field theories: II. Fluent media. Vol. 2. Springer Science & Business Media, 2001.
Lukaszewicz, Grzegorz. Micropolar fluids: theory and applications. Springer Science & Business Media, 1999. https://doi.org/10.1007/978-1-4612-0641-5_5
Chiu, C-P., and H-M. Chou. "Free convection in the boundary layer flow of a micropolar fluid along a vertical wavy surface." Acta Mechanica 101, no. 1 (1993): 161-174. https://doi.org/10.1007/BF01175604
Hassanien, I. A., and R. S. R. Gorla. "Heat transfer to a micropolar fluid from a non-isothermal stretching sheet with suction and blowing." Acta Mechanica 84, no. 1 (1990): 191-199. https://doi.org/10.1007/BF01176097
Gorla, R. S. R. "Mixed convection boundary layer flow of a micropolar fluid on a horizontal plate." Acta Mechanica 108, no. 1 (1995): 101-109. https://doi.org/10.1007/BF01177331
Ahmadi, Goodarz. "Self-similar solution of imcompressible micropolar boundary layer flow over a semi-infinite plate." International Journal of Engineering Science 14, no. 7 (1976): 639-646. https://doi.org/10.1016/0020-7225(76)90006-9
Gorla, Rama Subba Reddy, Richard Pender, and John Eppich. "Heat transfer in micropolar boundary layer flow over a flat plate." International Journal of Engineering Science 21, no. 7 (1983): 791-798. https://doi.org/10.1016/0020-7225(83)90062-9
Soundalgekar, V. M., and H. S. Takhar. "Flow of micropolar fluid past a continuously moving plate." International Journal of Engineering Science 21, no. 8 (1983): 961-965. https://doi.org/10.1016/0020-7225(83)90072-1
Takhar, H. S., and V. M. Soundalgekar. "Flow and heat transfer of micropolar fluid past a porous plate." Indian Journal of Pure and Applied Mathematics 16, no. 5 (1985): 552-558.
Hassanien, I. A., and R. S. R. Gorla. "Heat transfer to a micropolar fluid from a non-isothermal stretching sheet with suction and blowing." Acta Mechanica 84, no. 1 (1990): 191-199. https://doi.org/10.1007/BF01176097
Takhar, Harmindar S., R. S. Agarwal, Rama Bhargava, and S. Jain. "Mixed convection flow of a micropolar fluid over a stretching sheet." Heat and Mass Transfer 34, no. 2 (1998): 213-219. https://doi.org/10.1007/s002310050252
Mansour, M. A., and R. S. R. Gorla. "Micropolar fluid flow past a continuously moving plate in the presence of magnetic field." Applied Mechanics and Engineering 4, no. 4 (1999): 663-672.
Mansour, M. A., A. A. Mohammadein, S. MM El-Kabeir, and Rama Subba Reddy Gorla. "Heat transfer from moving surfaces in a micropolar fluid." Canadian Journal of Physics 77, no. 6 (1999): 463-471. https://doi.org/10.1139/p99-046
Nayan, Asmahani, Nur Izzatie Farhana Ahmad Fauzan, Mohd Rijal Ilias, Shahida Farhan Zakaria, and Noor Hafizah Zainal Aznam. "Aligned Magnetohydrodynamics (MHD) Flow of Hybrid Nanofluid Over a Vertical Plate Through Porous Medium." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 92, no. 1 (2022): 51-64. https://doi.org/10.37934/arfmts.92.1.5164
Hanafi, Hajar, and Sharidan Shafie. "Unsteady Free Convection MHD Flow over a Vertical Cone in Porous Media with Variable Heat and Mass Flux in Presence of Chemical Reaction." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 92, no. 2 (2022): 1-12. https://doi.org/10.37934/arfmts.92.2.112
Sannad, Mohamed, Youcef Mehdi, Afaf Zaza, Youness El Hammami, Youssef Idihya, and Othmane Benkortbi. "A Numerical Simulation Under Milk Fouling in A Plate Heat Exchanger in The Presence of a Porous Medium." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 91, no. 1 (2022): 1-17. https://doi.org/10.37934/arfmts.91.1.117
Yang, Yue-Tzu, and Sae-Jan Wang. "Free convection heat transfer of non-Newtonian fluids over axisymmetric and two-dimensional bodies of arbitrary shape embedded in a fluid-saturated porous medium." International Journal of Heat and Mass Transfer 39, no. 1 (1996): 203-210. https://doi.org/10.1016/S0017-9310(96)85016-2
Rastogi, S. K., and D. Poulikakos. "Double-diffusion from a vertical surface in a porous region saturated with a non-Newtonian fluid." International Journal of Heat and Mass Transfer 38, no. 5 (1995): 935-946. https://doi.org/10.1016/0017-9310(94)00198-5
Kim, Youn J. "Heat and mass transfer in MHD micropolar flow over a vertical moving porous plate in a porous medium." Transport in Porous Media 56, no. 1 (2004): 17-37. https://doi.org/10.1023/B:TIPM.0000018420.72016.9d
Reddy, T. Sankar, V. Ramachandra Prasad, P. Roja, and N. Bhaskar Reddy. " Radiation consequences on MHD mixed convection stream of a micropolar liquid past a semi-infinite moving porous plate in a porous medium with heat absorption." International Journal of Applied Mathematics and Mechanics 6, no. 18 (2010): 80-101.
Cogley, Allen C., Walter G. Vincent, and Scott E. Gilles. "Differential approximation for radiative transfer in a nongrey gas near equilibrium." AIAA Journal 6, no. 3 (1968): 551-553. https://doi.org/10.2514/3.4538
Kim, Youn J., and Andrei G. Fedorov. "Transient mixed radiative convection flow of a micropolar fluid past a moving, semi-infinite vertical porous plate." International Journal of Heat and Mass Transfer 46, no. 10 (2003): 1751-1758. https://doi.org/10.1016/S0017-9310(02)00481-7
Makinde, Oluwole D. "Free convection flow with thermal radiation and mass transfer past a moving vertical porous plate." International Communications in Heat and Mass Transfer 32, no. 10 (2005): 1411-1419. https://doi.org/10.1016/j.icheatmasstransfer.2005.07.005
Ibrahim, F. S., A. M. Elaiw, and A. A. Bakr. "Influence of viscous dissipation and radiation on unsteady MHD mixed convection flow of micropolar fluids." Applied Mathematics & Information Sciences 2, no. 2 (2008): 143-162.
Rahman, M. M., and M. A. Sattar. "Transient convective flow of micropolar fluid past a continuously moving vertical porous plate in the presence of radiation." International Journal of Applied Mechanics and Engineering 12, no. 2 (2007): 497-513.
Dutta, B. K., P. Roy, and A. S. Gupta. "Temperature field in flow over a stretching sheet with uniform heat flux." International Communications in Heat and Mass Transfer 12, no. 1 (1985): 89-94. https://doi.org/10.1016/0735-1933(85)90010-7
Elbashbeshy, Elsayed M. A. "Heat transfer over a stretching surface with variable surface heat flux." Journal of Physics D: Applied Physics 31, no. 16 (1998): 1951-1956. https://doi.org/10.1088/0022-3727/31/16/002
Elbashbeshy, E. M. A., and M. A. Bazid. "The mixed convection along a vertical plate with variable surface heat flux embedded in porous medium." Applied Mathematics and Computation 125, no. 2-3 (2002): 317-324. https://doi.org/10.1016/S0096-3003(00)00134-X
Rahman, M. M., and Tamanna Sultana. "Radiative heat transfer flow of micropolar fluid with variable heat flux in a porous medium." Nonlinear Analysis: Modelling and Control 13, no. 1 (2008): 71-87. https://doi.org/10.15388/NA.2008.13.1.14590
Ishak, Anuar, Roslinda Nazar, and Ioan Pop. "Heat transfer over a stretching surface with variable heat flux in micropolar fluids." Physics Letters A 372, no. 5 (2008): 559-561. https://doi.org/10.1016/j.physleta.2007.08.003
Mandal, Iswar Chandra, and Swati Mukhopadhyay. "Heat transfer analysis for fluid flow over an exponentially stretching porous sheet with surface heat flux in porous medium." Ain Shams Engineering Journal 4, no. 1 (2013): 103-110. https://doi.org/10.1016/j.asej.2012.06.004
Ganesan, P., and G. Palani. "Finite difference analysis of unsteady natural convection MHD flow past an inclined plate with variable surface heat and mass flux." International Journal of Heat and Mass Transfer 47, no. 19-20 (2004): 4449-4457. https://doi.org/10.1016/j.ijheatmasstransfer.2004.04.034
Talbot, L., R. K. Cheng, R. W. Schefer, and D. R. Willis. "Thermophoresis of particles in a heated boundary layer." Journal of Fluid Mechanics 101, no. 4 (1980): 737-758. https://doi.org/10.1017/S0022112080001905
Batchelor, G. K., and C. Shen. "Thermophoretic deposition of particles in gas flowing over cold surfaces." Journal of Colloid and Interface Science 107, no. 1 (1985): 21-37. https://doi.org/10.1016/0021-9797(85)90145-6
Mills, A. F., Hang Xu, and F. Ayazi. "The effect of wall suction and thermophoresis on aerosol particle deposition from a laminar boundary layer on a flat plate." International Journal of Heat and Mass Transfer 27, no. 7 (1984): 1110-1113. https://doi.org/10.1016/0017-9310(84)90127-3
Goren, Simon L. "Thermophoresis of aerosol particles in the laminar boundary layer on a flat plate." Journal of Colloid and Interface Science 61, no. 1 (1977): 77-85. https://doi.org/10.1016/0021-9797(77)90416-7
Epstein, Michael, G. M. Hauser, and R. E. Henry. "Thermophoretic deposition of particles in natural convection flow from a vertical plate." Journal of Heat Transfer 107, no. 2 (1985): 272-276. https://doi.org/10.1115/1.3247410
Garg, Vijay K., and S. Jayaraj. "Thermophoresis of aerosol particles in laminar flow over inclined plates." International Journal of Heat and Mass Transfer 31, no. 4 (1988): 875-890. https://doi.org/10.1016/0017-9310(88)90144-5
Opiolka, S., F. Schmidt, and H. Fissan. "Combined effects of electrophoresis and thermophoresis on particle deposition onto flat surfaces." Journal of Aerosol Science 25, no. 4 (1994): 665-671. https://doi.org/10.1016/0021-8502(94)90007-8
Selim, A., M. A. Hossain, and D. A. S. Rees. "The effect of surface mass transfer on mixed convection flow past a heated vertical flat permeable plate with thermophoresis." International Journal of Thermal Sciences 42, no. 10 (2003): 973-982. https://doi.org/10.1016/S1290-0729(03)00075-9
Wang, Chi-Chang. "Combined effects of inertia and thermophoresis on particle deposition onto a wafer with wavy surface." International Journal of Heat and Mass Transfer 49, no. 7-8 (2006): 1395-1402. https://doi.org/10.1016/j.ijheatmasstransfer.2005.09.036
Alam, M. S., M. M. Rahman, and M. A. Sattar. "Effects of variable suction and thermophoresis on steady MHD combined free-forced convective heat and mass transfer flow over a semi-infinite permeable inclined plate in the presence of thermal radiation." International Journal of Thermal Sciences 47, no. 6 (2008): 758-765. https://doi.org/10.1016/j.ijthermalsci.2007.06.006
Duwairi, H. M., and Rebhi A. Damseh. "Effect of thermophoresis particle deposition on mixed convection from vertical surfaces embedded in saturated porous medium." International Journal of Numerical Methods for Heat & Fluid Flow 18, no. 2 (2008): 202-216. https://doi.org/10.1108/09615530810846347
Pakravan, Hossein Ali, and Mahmood Yaghoubi. "Combined thermophoresis, Brownian motion and Dufour effects on natural convection of nanofluids." International Journal of Thermal Sciences 50, no. 3 (2011): 394-402. https://doi.org/10.1016/j.ijthermalsci.2010.03.007
Jena, S. Ko, and M. N. Mathur. "Similarity solutions for laminar free convection flow of a thermomicropolar fluid past a non-isothermal vertical flat plate." International Journal of Engineering Science 19, no. 11 (1981): 1431-1439. https://doi.org/10.1016/0020-7225(81)90040-9
Peddieson, J., and R. P. McNitt. "Boundary-layer theory for a micropolar fluid Recent." Adv. Eng. Sci. 5 (1970): 405-476.
Brewster, M. Quinn. Thermal radiative transfer and properties. John Wiley & Sons, 1992.
