SECOND GRADE MHD FLOW AND HEAT TRANSFER OVER A STRETCHING SHEET WITH VISCOUS AND OHMIC DISSIPATIONS

Emmanuel Sanjayanand

doi:10.29121/shodhkosh.v4.i1.2023.4042

Authors

Emmanuel Sanjayanand Assoiate Professor, Department of Mathematics, SKNG Govt First College, Gangavati, Karnataka, INDIA.

DOI:

https://doi.org/10.29121/shodhkosh.v4.i1.2023.4042

Keywords:

Viscoelastic Stretching Surface, Viscous Dissipation, Ohmic Dissipation, Magnetic Field and Normal Electric Field

Abstract [English]

Two dimensional second grade fluid has been considered for analysis. Basic governing equation of velocity and temperature are partial differential equation which is converted to ordinary differential equation by using transformation variable. Employing fifth order Runge-Kutta-Fehlberg method with shooting to solve momentum equation. The results are analysed for the situation when stretching boundary sheet is prescribed by non-isothermal temperature and variable heat flux, varying quadratically with the flow directional coordinate x..

References

RAJAGOPAL. K. R.; NA, T. Y.; GUPTA. A. S.; Flow of a viscoelastic fluid over a stretching sheet. Rheol. Acta. 23 (1984), 213-215. DOI: https://doi.org/10.1007/BF01332078

DANDAPAT B.S.; SINGH. S.N.; SING. R.P.; Heat transfer due to permeable stretching wall in presence of transverse magnetic field. Arch. Mech., 56,2. (2004), 127-141.

CORTELL. R.; Similarity solutions for flow and heat transfer of a viscoelastic fluid over a stretching sheet; Int. J. Non-Linear Mechanics. 29, 2 (1994), 155-161. DOI: https://doi.org/10.1016/0020-7462(94)90034-5

VAJRAVELU. K.; ROLLINS. D.; Heat transfer in an electrically conducting fluid over a stretching surface. Int. J. Non-Linear Mech., 27,2 (1992), 265-277. DOI: https://doi.org/10.1016/0020-7462(92)90085-L

MAHAPARTA. T. R.; GUPTA A. S.; Stagnation-point flow of a viscoelastic fluid towards a stretching surface. Inter. J. of Non-Linear Mech. 39 (2004) 811-820. DOI: https://doi.org/10.1016/S0020-7462(03)00044-1

POP. I.; SOUNDALGEKAR. V. M.; On thermal boundary layer of a viscoelastic fluid. ZAMM 57 (1997), 193-194.

SUBSHAS ABEL M.; JOSHI. A.; SONTH. R. M.; Heat transfer in MHD viscoelastic fluid over a stretching sheet ZAMM . Z. Angew. Math. Mech. 81 (2001) 10, 691-698 DOI: https://doi.org/10.1002/1521-4001(200110)81:10<691::AID-ZAMM691>3.0.CO;2-Z

DANDAPAT. B. S.; HOLMEDAL. L. E.; ANDERSSON. H. I; Stability of flow of a viscoelastic fluid over a stretching sheet. Arch. Mech. 46,6 (1994 ), 829-838.

ANDERSSON. H. I.; MHD flow of a viscoelastic fluid past a stretching surface. Acta Mech. 95 (1992), 227-230. DOI: https://doi.org/10.1007/BF01170814

CHAR. M. I.; Heat and mass transfer in a hydromagnetic flow of viscoelastic fluid over a stretching sheet. J. of Math. Anal. Appl. 186 (1994), 674-689. DOI: https://doi.org/10.1006/jmaa.1994.1326

LAWRENCE P.S.; RAO. B.N.; The non-uniqueness of the MHD flow of a viscoelastic fluid s stretching sheet. Acta. Mech., 112 (1995), 223-228. DOI: https://doi.org/10.1007/BF01177490

CHAMKHA. A. J.; Unsteady hydromagnetic flow and heat transfer from a non-isothermal stretching sheet immersed in a porous medium Int. Comm.. Heat Mass Transfer. 25,6 (1998), 899-906. DOI: https://doi.org/10.1016/S0735-1933(98)00075-X

HELMY. K.A.; MHD Unsteady free convection flow past a vertical porous plate. ZAMM . Z. Angew. Math. Mech. 78 (1998) 4, 255-270 DOI: https://doi.org/10.1002/(SICI)1521-4001(199804)78:4<255::AID-ZAMM255>3.0.CO;2-V

RAJAGOPAL. K. R.; NA. T. Y.; GUPTA. A. S.; A non-similar boundary layer on a stretching sheet in non-Newtonian fluid with uniform free stream. J. Math. Phy. Sc. 21, 2 (1987), 189-200.

COLEMAN. B. D. ; NOLL. W.; An approximation theorem for functionals with applications in continuum mechanics. Arch. Rat. Mech. Anal. 6 (1960), 355-370. DOI: https://doi.org/10.1007/BF00276168

FOSDICK. R. L.; RAJAGOPAL. K. R.; Anomalous features in the model of second order fluids. Arch. Ration. Mech. Anal 70 (1979), 145-152. DOI: https://doi.org/10.1007/BF00250351

BEARD. D. W.; WALTERS. K.; Elastico – viscous boundary layer flows. 1. Two dimensional flow near a stagnation point. Proc. Comb. Phil. Soc. 60 (1964), 667-674. DOI: https://doi.org/10.1017/S0305004100038147

TEMITOPE E. AKINBOBOLA, SAMUEL S. OKOYA1 The flow of second grade fluid over a stretching sheet with variable thermal conductivity and viscosity in the presence of heat source/sink journal of Nigerian mathematic society 34(2015) 331-342 DOI: https://doi.org/10.1016/j.jnnms.2015.10.002