Ali Belhocine

Exact Analytical Solution of Boundary Value Problem in a Form of an Infinite Hypergeometric Series

Full Text (PDF, 284KB), PP.28-37

Views: 0 Downloads: 0

Author(s)

1. Faculty of Mechanical Engineering, University of Sciences and the Technology of Oran L.P 1505 El - MNAOUER, USTO 31000 Oran Algeria

* Corresponding author.

DOI: https://doi.org/10.5815/ijmsc.2017.01.03

Received: 8 Oct. 2016 / Revised: 5 Nov. 2016 / Accepted: 3 Dec. 2016 / Published: 8 Jan. 2017

Index Terms

Graetz problem, Sturm-Liouville problem, Dimensionless variable, Partial differential equation

Abstract

This paper proposes an exact solution of the classical Graetz problem in terms of an infinite series represented by a nonlinear partial differential equation considering two space variables, two boundary conditions and one initial condition. The mathematical derivation is based on the method of separation of variables whose several stages were illustrated to reach the solution of the Graetz problem.

Cite This Paper

Ali Belhocine,"Exact Analytical Solution of Boundary Value Problem in a Form of an Infinite Hypergeometric Series", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.3, No.1, pp.28-37, 2017.DOI: 10.5815/ijmsc.2017.01.03

Reference

[1]Shah RK, London AL, Laminar Flow Forced Convection in Ducts, Chap.V, Academic Press, New York, 1978.

[2]Khashei M, Montazeri MA, Bijari M., "Comparison of Four Interval ARIMA-base Time Series Methods for Exchange Rate Forecasting", International Journal of Mathematical Sciences and Computing, Vol. 1, No. 1, Pages 21-34, 2015.

[3]Younis A. Shah, Irshad.A. Mir, Uzair M. Rathea, "Quantum Mechanics Analysis: Modeling and Simulation of some simple systems", International Journal of Mathematical Sciences and Computing, Vol.2, No. 1, Pages 23-40, 2016.

[4]Braga, N. R.., de Barros, L. S., Sphaier, L. A.: Generalized Integral Transform Solution of Extended Graetz Problems with Axial Diffusion ICCM2014 28-30th July, Cambridge, England pp.1-14 (2014)

[5]Min, T., Yoo, J. Y., Choi, H.: Laminar convective heat transfer of a bingham plastic in a circular pipei. Analytical approach—thermally fully developed flow and thermally developing flow (the Graetz problem extended). International Journal of Heat and Mass Transfer, 40(13):3025–3037, (1997).

[6]Brown, G.M.: Heat or mass transfer in a fluid in laminar flow in a circular or flat conduit, AIChE J. 6 179–183 (1960).

[7]Ebadian MA, Zhang HY, An exact solution of extended Graetz problem with axial heat conduction International Journal of Heat and Mass Transfer 32(9):1709-1717 1989.

[8]J. Lahjomri , A. Oubarra, Analytical Solution of the Graetz Problem With Axial Conduction Journal of Heat Transfer, 1, (1999) ,1078 -1083.

[9]Papoutsakis, E., Damkrishna, D., Lim, H. C, "The Extended Graetz. Problem with Dirichlet Wall Boundary Conditions," Appl. Sci. Research, Vol. 36, pp.13-34, 1980.

[10]Liou, C. T., Wang, F. S., "A Computation for the Boundary Value Problem of a Double Tube Heat Exchanger," Numerical Heat Transfer, Part A., Vol.17, pp. 109-125, 1990.

[11]Lahjomri, .J., Oubarra, A., and Alemany, A., "Heat transfer by laminar Hartmann flow in thermal entrance eregion with a step change in wall temperatures: The Graetz problem extended," International Journal of Heat and Mass Transfer 45(5):1127-1148,2002.

[12]Fithen, R. M" Anand, N. K., "Finite Element Analysis of Conjugate Heat Transfer in Axisymmetric Pipe Flows," Numerical Heat Transfer, Vol. 13, pp.189-203,1988.

[13]Belhocine.A. Numerical study of heat transfer in fully developed laminar flow inside a circular tube, International Journal of Advanced Manufacturing Technology, pp.1-12 (2015).

[14]Huang C. R., M. Matloz, Wen Dow-Pan and William Snyder, "Heat Transfer to a Laminar Flow in a Circular Tube", AIChE Journal, 5, 833, 1984.

[15]Slater L. J., "Confluent Hypergeometric Functions", Cambridge University Press, 1960.

International Journal of Mathematical Sciences and Computing (IJMSC)