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Mixed convection flow of Newtonian fluids over an upper horizontal thermally stratified melting surface of a paraboloid of revolution

  • I. L. AnimasaunEmail author
  • O. D. Makinde
  • S. Saleem
Technical Paper
  • 24 Downloads

Abstract

This article presents the combined effects of melting heat transfer and linear stratification of not only the heat energy, but also stratified concentration on the motion of an electrically conducting fluid over an object with a non-uniform thickness. Owing to the melting heat transfer and stretching of fluid layers at the free stream, the case of mixed convection is considered to be more appropriate than neither free nor forced convection. Consequently, the energy and concentration equations which model the flow and satisfy the free stream conditions are presented. Suitable thermophoresis model and Boussinesq approximation for the case \(T_m(x)<T_\infty (x)\) and \(C_m(x)<C_\infty (x)\) were adopted. A suitable similarity transformation is applied to reduce the governing equations to coupled ordinary differential equations. These equations along with the boundary conditions were solved numerically using Runge–Kutta technique along with shooting technique. Maximum variations in the local skin friction coefficients \(Re_{x}^{1/2}C_{fx}\) with thermal stratification occur at larger values of temperature-dependent viscosity parameter. Temperature distribution, local skin friction coefficients \(Re_{x}^{1/2}C_{fx}\) and mass transfer rate \(S_{hx}Re_{x}^{-1/2}\) are decreasing properties of thermal stratification and thermophoresis parameter.

Keywords

Melting surface Thermal stratification Thermophoresis Magnetohydrodynamic Paraboloid of revolution 

Notes

Acknowledgements

The authors would like to appreciate the support of the Editor-in-Chief, all the reviewers of BMSE-D-17-01017, BMSE-D-17-01593, and BMSE-D-18-01535 for their valuable comments and useful suggestions. Also, the authors would like to express their gratitude to King Khalid University, Abha 61413, Saudi Arabia, for providing administrative and technical support.

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesFederal University of TechnologyAkureNigeria
  2. 2.Faculty of Military ScienceStellenbosch UniversitySaldanhaSouth Africa
  3. 3.Department of Mathematics, College of SciencesKing Khalid UniversityAbhaSaudi Arabia

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