NUMERICAL ANALYSIS ON UNSTEADY MHD FLOW AND
HEAT TRANSFER OVER AN INCLINED STRETCHING
SURFACE IN A POROUS MEDIUM WITH HEAT SOURCE
AND VARIABLE MAGNETIC FIELD ANGLE
George Buzuzi1, Gilbert Makanda2 1Department of Mathematics and Physics
Cape Peninsula University of Technology
P.O. Box 1906, Bellville 7535
SOUTH AFRICA 2Department of Mathematical and Physical Sciences
Central University of Technology, Free State
Private Bag X20539, Bloemfontein
SOUTH AFRICA
Numerical analysis on unsteady magnetohydrodynamic flow and heat transfer over an inclined stretching channel in a porous medium with heat source in the presence of an inclined magnetic field is reported. The non-linear and coupled governing equations are solved by transforming them to ordinary differential equations by using similarity transformation and are then solved numerically by applying the successive linearization method. Convergence analysis of the method is carried out to show the robustness of the method. The effects of the various flow parameters on the velocity and temperature fields as well as the skin friction coefficient and the heat transfer coefficient are presented graphically and discussed.
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References
[1] B. C. Sakiadis, Boundary layer behaviour on continuous solid surfaces:
Boundary layer equations for two dimensional and axisymmetric flow,
AIChE J., 7, No 1 (1961), 26-28.
[2] L. J. Crane, Flow past a stretching plane, Z. Angew. Math. Phys., 21
(1970), 645-647.
[3] H. Dessie, N. Kishan, MHD effects onheat transfer over stretching sheet
embedded in porous medium with variable viscosity, viscous dissipation
and heat source/sink, Ain Shams Eng. J., 5 (2014), 967-977.
[4] M. K. Choudhary, S. Chaudhary, R. Sharma, Unsteady MHD flow and
heat transfer over a stretching permeable surface with suction or injection,
Procedia Eng., 127 (2015), 703-710.
[5] P. S. Gupta, A. S. Gupta, Heat and mass transfer on a stretching sheet with
suction or blowing, Canadian J. Chem. Eng., 55, No 6 (1977), 744-746.
[6] J. Vleggaar, Laminar boundary layer behaviour on continuous solid surfaces, Chem. Eng. Sci., 32 (1977), 1517-1525.
[7] E. M. A. Elbashbeshy, D.A. Aldawody, Heat transfer over an unsteady
stretching surface with variable heat flux in the presence of a heat source
or sink, Comput. Math. with Appl., 60 (2010), 2806-2811.
[8] A. J. Chamkha, MHD flow of a uniformly stretched vertical permeable surface in the presence of heat generation/absorption and a chemical reaction,
Int. Commun. Heat Mass Transf., 30 (2003), 413-422.
[9] S. M. Imran, S. Asghar, M. Mushtaq, Mixed convection flow over an unsteady stretching surface in a porous medium with heat source, Math.
Probl. Eng., 2012 (2012), 1-16; DOI: 10.1155/2012/485418.
[10] C. S. K. Raju, N. Sandeep, C. Sulochana, V. Suganamma, M. Jayachandra,
Radiation, inclined magnetic field and cross-diffusion effects on flow over
a stretching surface, J. Nigerian Math Soc., 34 (2015), 169-180.
[11] S. O. Salawu, M. S. Dada, Radiation heat transfer of variable viscosity and
thermal conductivity effects on inclined magnetic field with dissipation in
a non-Darcy medium, J. Nigerian Math Soc., 35 (2016), 93-106.
[12] N. Sandeep and V. Sugunamma, Radiation, inclined magnetic field effects
on unsteady hydromagnetic free convection flow past an impulsively moving vertical plate in a porous medium, J. Appl. Fluid. Mech., 7, No 2
(2014), 275-286.
[13] T. Hoyat, A. Shafiq, A. Alsaedi and Asghar, Effect of inclined magnetic
field in flow of third grade fluid with variable thermal conductivity, AIP
Adv., 5 (2015), 1-13; DOI: 10.1063/1.4928321.
[14] A. A. Dar, K. Elangovan, Thermal diffusion, radiation and inclined magnetic field effects on oscillatory flow in an asymmetric channel in presence
of heat source and chemical reaction, J. Nigerian Math Soc., 35 (2016),
488-509.
[15] F. S. Ibrahim, A. M. Elaiw, A. A. Bakr, Effect of the chemical reaction
and radiation absorption on the unsteady MHD free convection flow past a
semi infinite vertical permeable moving plate with heat source and suction,
Commun. in Nonlin. Sci. and Numer. Simul., 13 (2008), 1056-1066.
[16] M. S. Alam, M. M. Rahman, A. Satter, 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, Int. J. Therm. Sci., 47, No 6 (2008), 758-765.
[17] M. S. Alam, M. M. Rahman, A. Satter, Transient magnetohydrodynamic
free convective heat and mass transfer flow with thermophoresis past a radiate inclined permeable plate in the presence of variable chemical reaction
and temperature dependent viscosity, Nonlinear Anal.: Model. Control, 14
(2009), 3-20.
[18] M. J. Uddin, Convective flow of micropolar fluids along an inclined flat
plate with variable electric conductivity and uniform surface heat flux,
Daffodil Int. Univ. J. of Sci. and Techn., 6, No 1 (2011), 69-79.
[19] G. Buzuzi, J. B. Munyakazi, K. C. Patidar, A fitted numerical method
to investigate the effect of various parameters on an MHD flow over an
inclined plate, Numer. Methods Partial Differ. Equ. (2015), 107-120; DOI:
10.1002/num.21986.
[20] G. Buzuzi, A. N. Buzuzi, Unsteady MHD convection flow and heat transfer past a vertical inclined plate in a porous medium with variable plate
temperature with suction in a slip flow regime, Int. J. Appl. Math., 32, No
2 (2019), 205-218; DOI: 10.12732/ijam.v32i2.4.
[21] G. Buzuzi, A. N. Buzuzi, T. Nyamayaro, W. Manamela, K. S. Ramolotja,
The study of magneto hydrodynamic free convective flow and heat transfer in a porous medium with heat generation, radiation absorption and
chemical reaction, Int. J. Appl. Math., 33, No 4 (2020), 733-756; DOI:
10.12732/ijam.v33i4.15.
[22] F. A. Strobel, T. S. Chen, Bouyancy effects on heat and mass transfer in
booundary layers adjacent to inclined continuous moving sheet, Numer.
Heat Transfer A, 3, No 4 (1980), 461-481.
[23] A. Moutsoglou, T. S. Chen, Bouyancy effects in boundary layer on inclined
continuous moving sheets, J. Heat Transfer, 102, No 2 (1980), 371-373.
[24] M. Ali, M. A. Alim, M. S. Alam, Similarity solution of heat and mass
transfer fow over an inclined stretching sheet with viscous dissipation and
constant heat flux in presence of magnetic field, Procedia Eng., 105 (2015),
557-569.
[25] M. Hassan, E. Karim, A. Samad, MHD free convection flow past an inclined
stretching sheet with considering viscous dissipation and radiation, Open
J. Fluid Dyn., 7 (2017), 152-168.
[26] G. Makanda, D. Makinde, P. Sibanda, Natural convection of viscoelastic
fluid from a cone-embedded in a porous mwdium with viscous dissipation,
Math. Probl. Eng., 2013, (2013), 1-11; DOI: 10.1155/2013/934712.