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A study on the mixed convection boundary layer flow and heat transfer over a vertical slender cylinder

Ellahi Rahmat (Department of Mechanical Engineering Bourns Hall Riverside, CA USA + Department of Mathematics & Statistics, FBAS, IIU, Islamabad, Pakistan)
Riaz Arshad (Department of Mathematics & Statistics, FBAS, IIU, Islamabad, Pakistan)
Abbasbandy Saeid (Department of Mathematics, SRB, Islamic Azad University, Tehran, Iran)
Hayat Tasawar (Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan + Department of Mathematics, College of Science, KSU, Riyadh, Saudi Arabia)
Vafai Kambiz (Department of Mechanical Engineering Bourns Hall Riverside, CA USA)

In this investigation, the series solutions of mixed convection boundary layer flow over a vertical permeable cylinder are constructed. Two types of series as well numerical solutions are presented by choosing exponential and rational bases. The resulting differential system are solved by employing homotopy analysis method (HAM) and Pade technique which have been proven to be successful in tackling nonlinear problems. We offer various verifications of the solutions by comparing to existing, documented results and also mathematically, through reduction of sundry parameters. The convergence of the series solutions have been discussed explicitly. Comparison with existing results reveal that the series solutions are not only valid for large (aiding flow) but also for small values (opposing flow) of λ and the dual solutions do not obtain in both cases.

Keywords: mixed convection, series solutions, homotopy analysis method, pade technique, porous cylinder, steady flow