The steady boundary layer problems with buoyancy effect over a moving and permeable plate are studied in the present paper. By using the boundary layer approximations with similarity variables, we obtain coupled nonlinear velocity and temperature equations. Then, we derive boundary shape functions for velocity and temperature, which automatically satisfy the specified boundary conditions, including a convective boundary condition. Generally, numerical method is difficult to keep all the specific boundary conditions exactly and accurately. Because this will lead to the decline of the accuracy of numerical solution, we are motivated to develop a novel iterative algorithm which is based on the boundary shape functions. It transforms the nonlinear boundary layer problems into the initial value problems for new variables. The unknown terminal values of these variables can be determined by iteration, while the initial values of them can be arbitrarily given. The high-performance of the iterative boundary shape functions method (BSFM), which is convergent very fast, can be confirmed by numerical examples. The parametric studies in terms of the Grashof number, Prandtl number and Biot number with different suction/injection and velocity ratio values, as well as the flow instability area in terms of the Biot number and velocity ratio are carried out by the BSFM.
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The work of B. Li is supported by the Fundamental Research Funds for the Central Universities.
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On behalf of all authors, the corresponding author states that there is no conflict of interest.
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Liu, CS., Qiu, L., Li, B. et al. Solving the boundary layer problems with buoyancy effect over a moving and permeable plate by a boundary shape function method. Eur. Phys. J. Plus 136, 216 (2021). https://doi.org/10.1140/epjp/s13360-021-01210-8