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Group method analysis of unsteady free-convective laminar boundary-layer flow on a nonisothermal vertical circular cylinder

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Summary

The transformation group theoretic approach is applied to present an analysis of the problem of unsteady free convection from the outer surface of a vertical circular cylinder. The application of two-parameter group reduces the number of independent variables by two, and consequently the system of the governing partial differential equations with the boundary conditions reduces to a system of ordinary differential equations with the appropriate boundary conditions. The ordinary differential equations are solved numerically using a fourth-order Runge-Kutta scheme and the gradient method. Numerical results are obtained for the study of the boundary-layer characteristics. The general analysis developed in this study corresponds to the case of surface temperature that varies exponentially with time and uniform with respect to the axial coordinate, i.e., in the formT w =ae bt, wherea andb are constants. The effect of Prandtl number,Pr, andb on the boundary layer characteristics and the maximum value of the vertical component of the velocity are studied.

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Author notes

  1. M. B. Abd-el-Malek

    Present address: Science Department, Mathematics Unit, The American University in Cairo, Cairo, Egypt

  2. N. A. Badran

    Present address: Department of Engineering, Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria, Egypt

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    1. M. B. Abd-el-Malek
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    2. N. A. Badran
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    Abd-el-Malek, M.B., Badran, N.A. Group method analysis of unsteady free-convective laminar boundary-layer flow on a nonisothermal vertical circular cylinder. Acta Mechanica 85, 193–206 (1990). https://doi.org/10.1007/BF01181517

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    • DOI: https://doi.org/10.1007/BF01181517

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