Perturbation Solutions For Magnetohydrodynamics (Mhd) Flow of in a Non-Newtonian Fluid Between Concentric Cylinders

The steady-state magnetohydrodynamics (MHD) flow of a third-grade fluid with a variable viscosity parameter between concentric cylinders (annular pipe) with heat transfer is examined. The temperature of annular pipes is assumed to be higher than the temperature of the fluid. Three types of viscosity models were used, i.e., the constant viscosity model, space dependent viscosity model and the Reynolds viscosity model which is dependent on temperature in an exponential manner. Approximate analytical solutions are presented by using the perturbation technique. The variation of velocity and temperature profile in the fluid is analytically calculated. In addition, equations of motion are solved numerically. The numerical solutions obtained are compared with analytical solutions. Thus, the validity intervals of the analytical solutions are determined.

REFERENCES (13)

Yürüsoy M. and Pakdemirli M. (1999): Exact solutions of boundary layer equations of a special non-Newtonian fluid over a stretching sheet. – Mechanics Research Communications, vol.26, No.2, pp.171-175.

Google Scholar

Pakdemirli M. (1994): Conventional and multiple deck boundary layer approach to second and third grade fluids. – Int. J. Engng Sci., vol.32, 141.

Google Scholar

Hayat T. and Kara A.H. (2006): Couette flow of a third-grade fluid with variable magnetic field. – Mathematical and Computer Modelling, vol.43, pp.132-137.

Google Scholar

Hayat T., Shahzad F. and Ayub M. (2007): Analytical solution for the steady flow of the third grade fluid in a porous half space. – Applied Mathematical Modelling, vol.31, pp.2424-2432.

Google Scholar

Pakdemirli M., Hayat T., Yürüsoy M., Abbasbandy S. and Asghar S. (2011): Perturbation analysis of a modified second grade fluid over a porous plate. – Nonlinear Analysis: Real World Applications, vol.12, pp.1774-785.

Google Scholar

Pakdemirli M.,·Aksoy Y., Yürüsoy M. and Khalique C.M. (2008): Symmetries of boundary layer equations of power-law fluids of second grade. – Acta Mech Sin., vol.24, pp.661-670.

Google Scholar

Ali J. Chamkha (1997): Similarity solution for thermal boundary layer on a stretched surface of a non-Newtonian fluid. – Int. Comm. Heat Mass Transfer, vol.24, No.5, pp.643-652.

Google Scholar

Kecebas A. and Yürüsoy M. (2006): Similarity solutions of unsteady boundary layer equations of a special third grade fluid. – International Journal of Engineering Science, vol.44, pp.721-729.

Google Scholar

Massoudi M. and Christie I. (1995): Effects of variable viscosity and viscous dissipation on the flow of a thirdgrade fluid in a pipe. – Int. J. Non-Linear Mech., vol.30, pp.687-699.

Google Scholar

10.

Yürüsoy M. and Pakdemirli M. (2002): Approximate analytical solutions for the flow of a third-grade fluid in a pipe. – International Journal of Non-Linear Mechanics, vol.37, pp.187-195.

Google Scholar

11.

Ellahi R. and Riaz A. (2010): Analytical solutions for MHD flow in a third-grade fluid with variable viscosity. – Mathematical and Computer Modelling, vol.52, pp.1783-1793.

Google Scholar

12.

Akinshilo A.T. and Olaye O.: On the analysis of the Erying Powell model based fluid flow in a pipe with temperature dependent viscosity and internal heat generation. – Journal of King Saud University – Engineering Sciences, (to be published).

Google Scholar

13.

Jayeoba O.J. and Okoya S.S. (2012): Approximate analytical solutions for pipe flow of a third grade fluid with variable models of viscosities and heat generation/absorption. – Journal of the Nigerian Mathematical Society, vol.31, pp.207-227.

Google Scholar

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