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Analytical solution to stagnation-point flow and heat transfer over a stretching sheet based on homotopy analysis

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Abstract

This paper is concerned with two-dimensional stagnation-point steady flow of an incompressible viscous fluid towards a stretching sheet whose velocity is proportional to the distance from the slit. The governing system of partial differential equations is first transformed into a system of dimensionless ordinary differential equations. Analytical solutions of the velocity distribution and dimensionless temperature profiles are obtained for different ratios of free stream velocity and stretching velocity, Prandtl number, Eckert number and dimensionality index in series forms using homotopy analysis method(HAM). It is shown that a boundary layer is formed when the free stream velocity exceeds the stretching velocity, and an inverted boundary layer is formed when the free stream velocity is less than the stretching velocity. Graphs are presented to show the effects of different parameters.

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Authors and Affiliations

  1. Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing, 100083, P. R. China

    Jing Zhu  (朱婧) & Lian-cun Zheng  (郑连存)

  2. Department of Thermal and Energy Engineering, University of Science and Technology Beijing, Beijing, 100083, P. R. China

    Xin-xin Zhang  (张欣欣)

Authors
  1. Jing Zhu  (朱婧)
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  2. Lian-cun Zheng  (郑连存)
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  3. Xin-xin Zhang  (张欣欣)
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Corresponding author

Correspondence to Lian-cun Zheng  (郑连存).

Additional information

(Communicated by Zhe-wei ZHOU)

Project supported by the National Natural Science Foundation of China (No. 50476083)

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Zhu, J., Zheng, Lc. & Zhang, Xx. Analytical solution to stagnation-point flow and heat transfer over a stretching sheet based on homotopy analysis. Appl. Math. Mech.-Engl. Ed. 30, 463–474 (2009). https://doi.org/10.1007/s10483-009-0407-2

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  • DOI: https://doi.org/10.1007/s10483-009-0407-2

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2000 Mathematics Subject Classification

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