Abstract.
The present paper deals with the study of momentum, heat and mass transfer characteristics in a viso-elastic fluid flow over a porous sheet, where the flow is generated due to linear stretching of the sheet and influenced by a uniform magnetic field applied vertically and a continuous injection of the fluid through porous boundary. In the flow region, heat balance is maintained with a temperature dependent heat source/sink, viscous dissipation, dissipation due to elastic deformation and stress work produced as the result of magnetic field on the non-Newtonian fluid. In mass transfer analysis we have taken into account the loss of mass of the chemically reactive diffusive species by means of first order chemical conversion rate. Using suitable similarity transformations on the highly non-linear partial differential equations we derive several closed form analytical solutions for non-dimensional temperature, concentration, heat flux, mass flux profiles in the form of confluent hyper geometric (Kummer's) functions and some other elementary functions as its special form, for two different cases of the boundary conditions, namely, (i) wall with prescribed second order power law temperature (PST) and prescribed second order power law concentration (ii) wall with prescribed second order power law heat flux (PHF) and prescribed second order power law mass flux. The effect of the non-dimensional magnetic parameter on momentum, heat and mass transfer characteristics for non-isothermal boundary condition and different physical situations of the fluid, having various degrees of visco-elasticity, Prandtl number, heat source/sink strength and Schmidt number, are discussed in detail. Some of the several important findings reported in this paper are: (i) The combined effect of magnetic field, visco-elasticity and impermeability of the wall is to increase skin-friction largely at the wall; (ii) maximum enhancement of wall-temperature profile due to the application of transverse magnetic field occurs when the boundary heating is maintained with prescribed heat flux, boundary wall is porous and Prandtl number of the fluid is low; (iii) the effect of transverse uniform magnetic field is to increase concentration in the flow region, however, enhancement of concentration is higher when the stretching wall is porous and subjected to injection and (iv) the reduction of concentration due to chemical conversion is of significant order near the wall in PHF case when the wall is maintained with prescribed power low mass flux, in comparison with the PST case when the wall is maintained with prescribed power law surface concentration.
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Rajagopal KR; Na TY; Gupta AS (1984) Flow of a visco-elastic fluid over a stretching sheet. Rheol Acta 23: 213–215
Siddappa B; Abel MS (1985) Non-Newtonian flow past a stretching plate. Z Angew Math Phys 36: 890–892
Gupta RK; Sridhar T (1985) Visco-elastic effects in non-Newtonian flow through porous media. Rheol Acta 24: 148–151
Siddappa B; Abel MS (1986) Visco-elastic boundary layer flow past a stretching plate with suction and heat transfer. Rheol Acta 25: 319–230
Rajagopal KR; Na TY; Gupta AS (1987) A non-similar boundary layer on a stretching sheet in a non-Newtonian fluid with uniform free stream. J Math Phys Sci 21(2): 189–200
Bujurke NM; Birader SN; Hiremath PS (1987) Second order fluid flow past a stretching sheet with heat transfer. Z Angew Math Phys 38: 653–657
Dandapat BS; Gupta AS (1989) Flow and heat transfer in a visco-elastic fluid flow over a stretching sheet. Int J Non-Linear Mech 24(3): 215–219
Rollins D; Vajravelu K(1991) Heat transfer in a second-order fluid over a continuous stretching surface. Acta Mech 89: 167–178
Lawrence PS; Rao BN (1992) Heat transfer in the flow of a visco-elastic fluid over a stretching sheet. Acta Mech 93: 53–61
Siddappa B; Abel S; Veena H (1995) Oscillatory motion of a visco-elastic fluid past a stretching sheet. IL Nuovocimento 17D (1): 53–60
Abel S; Veena P (1998) Visco-elastic fluid flow and heat transfer in a porous medium over a stretching sheet. Int J Non-Linear Mech 33(3): 531–540
Prasad KV; Abel S; Joshi A (2000) Oscillatory motion of a visco-elastic fluid over a stretching sheet in porous media. J Porous Media 3(1): 61–68
Abel MS; Khan SK; Prasad KV (2002) Study of visco-elastic fluid flow and heat transfer over a stretching sheet with variable viscosity. Int J Non-Linear Mech 37: 81–88
Andersson HI (1992) MHD flow of a visco-elastic fluid past a stretching surface. Acta Mech 95: 227–230
Char MI (1994) Heat and mass transfer in a hydromagnetic flow of the visco-elastic fluid over a stretching sheet. J Math Anal Appl 186: 674–689
Lawrence PS; Rao BN (1995) The non-uniqueness of the MHD flow of a visco-elastic fluid past a stretching sheet. Acta Mech 112: 223–228
Abel MS; Joshi A; Sonth RM (2001) Heat transfer in MHD visco-elastic fluid flow over a stretching surface. Z Angew Math Mech 81(10): 691–698
Sonth RM; Khan SK; Abel MS; Prasad KV (2002) heat and mass transfer in a visco-elastic fluid flow over an accelerating surface with heat source/sink and viscous dissipation. Heat Mass Transfer 38: 213–220
Soundalgekar VM; Ramana Murty TV (1980) Heat Transfer in flow of past a continuous moving plate with variable temperature. Warme-und Stoffubertragung 14: 91–93
Vajravelu K; Rollins D (1992) Heat transfer in an electrically conducting fluid over a stretching surface. Int J Non-Linear Mech 27(2): 265–277
Vajravelu K; Nayfeh J (1993) Convective heat transfer at a stretching sheet. Acta Mech 96: 47–54
Vajravelu K (1994) Flow and heat transfer in a saturated porous medium over a stretching surface. Z Angew Math Mech 74(12): 605–614
Chamkha AJ; Issa C (1999) Mixed convection effects on unsteady flow and heat transfer over a stretched surface. Int Comm Heat Mass Transfer 26(5): 717–727
Acharya M; Singh LP; Dash GC (1999) Heat and mass transfer over an accelerating surface with heat source in presence of suction and blowing. Int J Eng Sci 37: 189–211
Abramowitz M; Stegun LA (1972) Hand book of mathematical functions. National Bureau of Standards/Amer Math Soc 55, Providence, RI
Acknowledgements.
Authors express their sincere thanks to the referee for giving valuable suggestions in the review process of the paper. One of the authors (RMS) is thankful to Sri. Qamar-ul-Islam, President, H.S.M.A Kallerawan Charitable Trust, Gulbarga and Dr. M. Basavaraja, Principal, K.C.T. Engineering College, Gulbarga for inculcating invaluable inspirations in pursuing this research work.
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Khan, S.K., Abel, M.S. & Sonth, R.M. Visco-elastic MHD flow, heat and mass transfer over a porous stretching sheet with dissipation of energy and stress work. Heat and Mass Transfer 40, 47–57 (2003). https://doi.org/10.1007/s00231-003-0428-x
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DOI: https://doi.org/10.1007/s00231-003-0428-x