ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2022 · 12 citations · 12 references
EngineeringMechanical EngineeringPhysicsComputational Fluid DynamicsFluid DynamicsHeat TransferHeat Transfer AnalysisHeat Transfer In FluidsHeat Transfer ModelingNumerical AnalysisNumerical Methods For Differential EquationsPerturbation MethodsAccuracyComputational Fluid Dynamics Of Cooling SystemsReynolds NumberTurbine CoolingTurbine TechnologyTurbinesViscoelastic FlowViscoelastic Fluid Flow
Abstract In this paper, a new method is suggested and implemented to find an analytical approximate solution for a non‐Newtonian viscoelastic fluid flow on the turbine disk, used to cool the axisymmetric channel that has a porous wall. The new method depends on combining the algorithms of Yang transform and the homotopy perturbation method (HPM) named Yang transformation–homotopy perturbation method (YTHPM). To ensure the correctness of the method, we compared the results of YTHPM with the ones obtained by the numerical method (Runge–Kutta 4th order) and by other methods as reported in the literature; a good agreement was observed. Additionally, the effect of the power‐law index, Prandtl and Reynolds numbers on the velocity, and heat transfer was studied. The results that we obtained by using the new method confirm that this method has high accuracy and efficiency compared with other methods, used to find the analytical approximate solution for the current problem. Furthermore, the graphs and tables of error show the validity, utility, and necessity of this method.
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