A Numerical study of the flow with heat Transfer of a Pseudoplastic fluid Between Parallel Plates

S. Iqbal, A Zeb, A. M Siddiqui, T Haroon

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DOI: 10.4236/jqis.2011.11003                

Abstract

One dimensional flow with heat transfer of a pseudoplastic fluid between two infinite horizontal parallel plates is investigated. The thermophysical properties of the fluid are assumed to be constant and numerical solution using the finite element method, along with the corresponding exact solution for the fluid velocity and the fluid temperature is obtained. The effect of variation of the governing parameters is studied using figures and tables. It is found that the numerical solution agrees well with the corresponding exact solution and that the fluid velocity, together with the fluid temperature, increases with increasing values of the governing parameters.

Keywords

Pseudoplastic Fluids, Heat Transfer, Finite Element Method, Exact Solution

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	G. Astarita and G. Marrucci, “Principles of Non- Newtonian Fluid Mechanics,” McGraw Hill, London, 1974.
[2]	R. B. Bird, R. C. Armstrong and O. Hassager, “Dynamics of Polymeric Liquids, Fluid Mechanics,” Wiley, New York, 1987.
[3]	M. Moradi, “Laminar Flow Heat Transfer of a Pseudoplastic Fluid through a Double Pipe Heat Exchanger,” Iranian Journal of Chemical Engineering, Vol. 3, No. 2, 2006, pp. 13-19.
[4]	M. Massoudi and I. Christie, “Effects of Variable Viscosity and Viscous Dissipation on the Flow of a Third Grade Fluid in a Pipe,” International Journal of Non-Linear Mechanics, Vol. 30, No. 5, 1995, pp. 687-699.
[5]	doi:10.1016/0020-7462(95)00031-I
[6]	A. M. Siddiqui, A. Zeb, Q. K. Ghori and A. M. Benharbit, “Homotopy Perturbation Method for Heat Transfer Flow of a Third Grade Fluid between Parallel Plates,” Chaos Solitons and Fractals, Vol. 36, No. 1, 2008, pp. 182-192.
[7]	T. Hayat, K. Maqbool and M. Khan, “Hall and Heat Transfer Effects on the Steady Flow of a Generalized Burger's Fluid Induced by Sudden Pull of Eccentric Rotating Disks,” Nonlinear Dynamics, Vol. 51, No. 1-2, 2008, pp. 267-276. doi:10.1007/s11071-007-9209-2
[8]	F. L. Stasa, “Applied Finite Element Analysis for Engineers, ” CBS Publishing, 1985.
[9]	O. C. Zienkiewicz, “The Finite Element Method,” McGraw Hill, London, 1977.
[10]	S. Iqbal, A. M. Mirza and I. A. Tirmizi, “Galerkin’s Finite Element Formulation of the Second-Order Boundary-Value Problems,” International Journal of Computer Mathematics, Vol. 87, No. 9, 2010, pp. 2032-2042.
[11]	doi:10.1080/00207160802562580
[12]	S. Iqbal and N. A. Memon, “Numerical Solution of Singular Two-Point Boundary Value Problems Using Galerkin's Finite Element Method,” Quaid-e-Awam University Research Journal of Engineering, Science and Technology (QUEST-RJ), Vol. 9, No. 1, 2010, pp. 14-19.
[13]	J. A. Deiber and A. S. M. Santa Cruz, “On Non-Newtonian Fluid Flow through a Tube of Circular Cross Section,” Latin American. Journal of Chemistry Engineering and Applied Chemistry, Vol. 14, 1984, pp. 19-38.
[14]	R. E. Bellman and R. E. Kalaba, “Quasilinearizalion and Nonlinear Boundary-Value Problems,” American Elsevier, New York, 1965.