ORIGINAL ARTICLE
Analytical solutions of triple-diffusive magnetohydrodynamic fluid flowing through a stretching/shrinking sheet
Sangamesh,
Vinod Y.,
K. R. Raghunatha,
Suma Nagendrappa Nagappanavar,
Sangamesh
Department of Mathematics, Davangere University, Davanagere, India
Search for more papers by this authorVinod Y.
Department of Mathematics, Davangere University, Davanagere, India
Search for more papers by this authorCorresponding Author
K. R. Raghunatha
Department of Mathematics, Davangere University, Davanagere, India
Correspondence K. R. Raghunatha, Department of Mathematics, Davangere University, Davanagere, Karnataka 577007, India.
Email: [email protected]
Search for more papers by this authorSuma Nagendrappa Nagappanavar
Department of Mathematics, Davangere University, Davanagere, India
Search for more papers by this author Sangamesh,
Vinod Y.,
K. R. Raghunatha,
Suma Nagendrappa Nagappanavar,
Sangamesh
Department of Mathematics, Davangere University, Davanagere, India
Search for more papers by this authorVinod Y.
Department of Mathematics, Davangere University, Davanagere, India
Search for more papers by this authorCorresponding Author
K. R. Raghunatha
Department of Mathematics, Davangere University, Davanagere, India
Correspondence K. R. Raghunatha, Department of Mathematics, Davangere University, Davanagere, Karnataka 577007, India.
Email: [email protected]
Search for more papers by this authorSuma Nagendrappa Nagappanavar
Department of Mathematics, Davangere University, Davanagere, India
Search for more papers by this authorFirst published: 27 February 2024
Abstract
The aim of this article is to investigate the dual nature solutions of the triple diffusive magnetohydrodynamic flow due to stretching/shrinking surfaces. The system of nonlinear partial differential equations is transformed into nonlinear ordinary differential equations with the help of compatible transforms. Analytical dual solutions are obtained for every unknown velocity, temperature, and concentration profile in terms of known physical parameters. Heat and mass transfer analyses have been carried out in the presence of convective boundary conditions. The graphic interpretation of the possible dual solutions of dimensionless velocity, temperature, concentration, skin-friction coefficient, and Nusselt and Sherwood numbers is analyzed under the influence of different known physical parameters. The obtained results are validated against previously published results for a special case of the problem.
Open Research
DATA AVAILABILITY STATEMENT
The data that supports the findings of this study are available in the supplementary material of this article
REFERENCES
- 1Chen CF, Johnson DH. Double-diffusive convection: a report on an engineering foundation conference. J Fluid Mech. 1984; 138: 405-416.
- 2Hill AA, Malashetty MS. An operative method to obtain sharp nonlinear stability for systems with spatially dependent coefficients. Proc R Soc A. 2012; 468: 323-336.
10.1098/rspa.2011.0137 Google Scholar
- 3Shyy W, Chen MH. Double-diffusive flow in enclosures. Phys Fluids A. 1991; 3: 2592-2607.
- 4Kuznetsov AV, Nield DA. Double-diffusive natural convective boundary-layer flow of a nanofluid past a vertical plate. Int J Therm Sci. 2011; 50: 712-717.
- 5Badruddin IA, Khan TM, Kamangar S. Effect of variable heating on double diffusive flow in a square porous cavity. AIP Conf Proc. 2016; 1728: 1.
- 6Turner JS. Multicomponent convection. Annu Rev Fluid Mech. 1985; 17: 11-44.
- 7Huppert HE, Turner JS. Double-diffusive convection. J Fluid Mech. 1981; 106: 299-329.
- 8Nasir M, Waqas M, Kausar MS, Bég OA, Zamri N. Cattaneo-Christov dual diffusive non-newtonian nanoliquid flow featuring nonlinear convection. Chin J Phys. 2022. doi:10.1016/j.cjph.2022.05.005
10.1016/j.cjph.2022.05.005 Google Scholar
- 9Platten JK, Legros JC. Convection in Liquids. Springer-Verlag; 2011.
- 10Griffiths RW. The influence of a third diffusing component upon the onset of convection. J Fluid Mech. 1979; 92: 659-670.
- 11Terrones G. Cross diffusion effects on the stability criteria in a triply diffusive system. Phys Fluids A. 1993; 5: 2172-2182.
- 12Straughan B, Tracey J. Multi-component convection-diffusion with internal heating or cooling. Acta Mech. 1999; 133: 219-238.
- 13Alhefthi RK, Vinod Y, Raghunatha KR, Inc M. Couple stress effects on the MHD triple-diffusive oscillatory flow in a fluid-saturated porous layer. Mod Phys Lett B. 2023:2450116.
- 14Alhefthi RK, Vinod Y, Raghunatha KR, Pallavi G, Inc M. Viscoelastic effect on the triple diffusive oscillatory flow in a fluid-saturated porous layer. Mod Phys Lett B. 2023:2450098.
- 15Crane LJ. Flow past a stretching plate. Zeitschrift für angewandte Mathematik und Physik ZAMP. 1970; 21: 645-647.
- 16Pavlov KB. Magnetohydrodynamic flow of an incompressible viscous fluid caused by the deformation of a plane surface. Magn Gidrod. 1974; 4: 146-148.
- 17Gupta PS, Gupta AS. Heat and mass transfer on a stretching sheet with suction or blowing. Canad J Chem Eng. 1977; 55: 744-746.
- 18Rajagopal KR, Na TY, Gupta AS. Flow of a viscoelastic fluid over a stretching sheet. Rheol Acta. 1984; 23: 213-215.
- 19Chen CK, Char MI. Heat transfer of a continuous stretching surface with suction or blowing. J Math Anal Appl. 1988; 135: 568-580.
- 20Vajravelu K, Rollins D. Heat transfer in an electrically conducting fluid over a stretching surface. Int J Non Linear Mech. 1992; 27: 265-277.
- 21Maranna T, Sneha KN, Mahabaleshwar US, Souayeh B. An impact of heat and mass transpiration on magnetohydrodynamic viscoelastic fluid past a permeable stretching/shrinking sheet. Heat Transfer. 2023; 52: 2231-2248.
- 22Kopp MI, Yanovsky VV, Anusha T, Mahabaleshwar US. MHD flow and heat transfer of a ternary hybrid ferrofluid over a Stretching/Shrinking porous sheet with the effects of brownian diffusion and thermophoresis. East Eur J Phys. 2023; 1: 7-18.
- 23Mahabaleshwar US, Vanitha GP, Pérez LM, Aly EH, Pop I. Exact solutions for magnetohydrodynamic nanofluids flow and heat transfer over a permeable axisymmetric radially stretching/shrinking sheet. Chin Phys B. 2024; 33:020204.
- 24Ishak A, Nazar R, Pop I. Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet. Heat Mass Transfer. 2008; 44: 921-927.
- 25Salleh MZ, Nazar R, Pop I. Boundary layer flow and heat transfer over a stretching sheet with Newtonian heating. J Taiwan Inst Chem Eng. 2010; 41: 651-655.
- 26Qasim M, Noreen S. Heat transfer in the boundary layer flow of a casson fluid over a permeable shrinking sheet with viscous dissipation. Eur Phys J Plus. 2014; 129: 7.
- 27Nadeem S, Ul Haq R, Khan ZH. Heat transfer analysis of water-based nanofluid over an exponentially stretching sheet. Alex Eng J. 2014; 53: 219-224.
10.1016/j.aej.2013.11.003 Google Scholar
- 28Makinde OD, Khan WA, Khan ZH. Buoyancy effects on MHD stagnation point flow and heat transfer of a nanofluid past a convectively heated stretching/shrinking sheet. Int J Heat Mass Transfer. 2013; 62: 526-533.
- 29Fang T, Zhang J. Closed-form exact solutions of MHD viscous flow over a shrinking sheet. Commun Nonlin Sci Num Simul. 2009; 14: 2853-2857.
- 30Yao S, Fang T, Zhong Y. Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions. Commun Nonlin Sci Num Simul. 2011; 16: 752-760.
- 31Fang T, Yao S, Pop I. Flow and heat transfer over a generalized stretching/shrinking wall problem—exact solutions of the Navier–Stokes equations. Int J Non Linear Mech. 2011; 46: 1116-1127.
- 32Qasim M. Heat and mass transfer in a Jeffrey fluid over a stretching sheet with heat source/sink. Alex Eng J. 2013; 52: 571-575.
10.1016/j.aej.2013.08.004 Google Scholar
- 33Madhu M, Kishan N, Chamkha AJ. Unsteady flow of a Maxwell nanofluid over a stretching surface in the presence of magnetohydrodynamic and thermal radiation effects. Propul Power Res. 2017; 6: 31-40.
- 34Krishna MV, Ahammad NA, Chamkha AJ. Radiative MHD flow of Casson hybrid nanofluid over an infinite exponentially accelerated vertical porous surface. Case Stud Thermal Eng. 2021; 27:101229.
- 35Chamkha AJ, Khaled ARA. Similarity solutions for hydromagnetic simultaneous heat and mass transfer by natural convection from an inclined plate with internal heat generation or absorption. Heat Mass Transfer. 2001; 37: 117-123.
- 36Kumar B, Seth GS, Nandkeolyar R, Chamkha AJ. Outlining the impact of induced magnetic field and thermal radiation on magneto-convection flow of dissipative fluid. Int J Therm Sci. 2019; 146:106101.
- 37Chamkha AJ, Al-Naser H. Hydromagnetic double-diffusive convection in a rectangular enclosure with opposing temperature and concentration gradients. Int J Heat Mass Transfer. 2002; 45: 2465-2483.
- 38Chamkha AJ, Issa C. Effects of heat generation/absorption and thermophoresis on hydromagnetic flow with heat and mass transfer over a flat surface. Int J Num Methods Heat Fluid Flow. 2000; 10: 432-449.
- 39Chamkha AJ. Coupled heat and mass transfer by natural convection about a truncated cone in the presence of magnetic field and radiation effects. Num Heat Transfer A Appl. 2001; 39: 511-530.
- 40Pavlov KB. Magnetohydrodynamic flow of an incompressible fluid caused by deformation of a plane surface. MHD. 1974; 10: 507-510.
- 41Chakrabarti A, Gupta AS. Hydromagnetic flow and heat transfer over a stretching sheet. Q Appl Math. 1979; 37: 73-78.
- 42Turkyilmazoglu M. Analytic heat and mass transfer of the mixed hydrodynamic/thermal slip MHD viscous flow over a stretching sheet. Int J Mech Sci. 2011; 53: 886-896.
- 43Bhattacharyya K. Dual solutions in boundary layer stagnation-point flow and mass transfer with chemical reaction past a stretching/shrinking sheet. Int Commun Heat Mass Transfer. 2011; 38: 917-922.
- 44Turkyilmazoglu M. Multiple solutions of hydromagnetic permeable flow and heat for viscoelastic fluid. J Thermophys Heat Transfer. 2011; 25: 595-605.
- 45Turkyilmazoglu M. Multiple solutions of heat and mass transfer of MHD slip flow for the viscoelastic fluid over a stretching sheet. Int J Therm Sci. 2011; 50: 2264-2276.
- 46Kameswaran PK, Shaw S, Sibanda P. Dual solutions of Casson fluid flow over a stretching or shrinking sheet. Sadhana. 2014; 39: 1573-1583.
- 47Akbar NS, Khan ZH, Haq RU, Nadeem S. Dual solutions in MHD stagnation-point flow of Prandtl fluid impinging on shrinking sheet. Applied Mathematics and Mechanics. 2014; 35: 813-820.
10.1007/s10483-014-1836-9 Google Scholar
- 48Subhashini SV, Sumathi R. Dual solutions of a mixed convection flow of nano fluids over a moving vertical plate. Int J Heat Mass Transfer. 2014; 71: 117-124.
- 49Abd El-Aziz M. Dual solutions in hydromagnetic stagnation point flow and heat transfer towards a stretching/shrinking sheet with non-uniform heat source/sink and variable surface heat flux. J Egyptian Math Soc. 2016; 24: 479-486.
10.1016/j.joems.2015.09.004 Google Scholar
- 50Freidoonimehr N, Rahimi AB. Exact-solution of entropy generation for MHD nano fluid flow induced by a stretching/shrinking sheet with transpiration: dual solution. AdvanPowder Techn. 2017; 28: 671-685.
- 51Raju CS, Sandeep N. Dual solutions for unsteady heat and mass transfer in bio-convection flow towards a rotating cone/plate in a rotating fluid. Int J Eng Res Africa. 2016; 20: 161-176.
10.4028/www.scientific.net/JERA.20.161 Google Scholar
- 52Turkyilmazoglu M. Multiple exact solutions of free convection flow in saturated porous media with variable heat flux. J Porous Media. 2022; 25. doi:10.2139/ssrn.3973368
- 53Khan ZH, Qasim M, Haq RU, Al-Mdallal QM. Closed form dual nature solutions of fluid flow and heat transfer over a stretching/shrinking sheet in a porous medium. Chin J Phys. 2017; 55: 1284-1293.
- 54Khan ZH, Qasim M, Ishfaq N, Khan WA. Dual solutions of MHD boundary layer flow of a micropolar fluid with weak concentration over a stretching/shrinking sheet. Commun Theor Phys. 2017; 67: 449.
- 55Turkyilmazoglu M. Exact solutions for two-dimensional laminar flow over a continuously stretching or shrinking sheet in an electrically conducting quiescent couple stress fluid. Int J Heat Mass Transfer. 2014; 72: 1-8.
- 56Wang CY. Analysis of viscous flow due to a stretching sheet with surface slip and suction. Nonlin Anal Real World Appl. 2009; 10: 375-380.
