Analytical solution and operation of Homotopy Perterbation Method for thermal boundary layer over a flat plate with a convection surface boundary condition

Document Type : Original Article


1 Mechanical Engineering Department, Islamic Azad University, South Tehran Branch, Tehran, Iran

2 Civil Engineering Department, Islamic Azad University, South Tehran Branch, Tehran, Iran


In this paper, an analytical solution of the energy equation and momentum (Navier-Stokes) equation in the convection heat transfer over a flat plate has been carried out for an incompressible flow. The equations governing the problem are with multivariate partial derivatives which have been initially converted to non-dimensional equations by applying dimensionless parameters. Considering the linearity of the dimensionless energy equation and the nonlinearity of the dimensionless momentum equation, two solving methods have been considered for solving the two equations. The energy equation has been solved by direct method and applying the conditions governing the problem, and the momentum (Navier-Stokes) equation has also been solved by the Homotopy Perturbation Method (HPM) using the initial guess based on the boundary conditions governing the problem. Finally, the results of the analytic solution of the governing equations have been presented in the form of tables and graphs including temperature profiles, flow function, velocity and skin friction coefficient and then it has been investigated the effects of changing the non-dimensional values such as η, 𝑎 and  on the temperature and heat transfer profiles.


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Volume 2, Issue 2 - Serial Number 4
September 2023
Pages 115-129
  • Receive Date: 09 March 2023
  • Revise Date: 15 March 2023
  • Accept Date: 17 March 2023