Application of Hermite wavelet method for heat transfer in a porous media

Abstract

In this article, the flow and heat transfer for non‐Newtonian viscoelastic fluid in an axisymmetric channel with a porous wall is investigated. Convective boundary conditions have been used in the problem formulation. We obtain coupled, highly nonlinear ordinary differential equations from the fundamental governing equations via appropriate similarity variables. The solution for velocity and temperature are computed by applying the Hermite wavelet method (HWM). The comparison between the results from the HWM, differential transform method, and numerical method are well in agreement which proves the capacity of HWM for solving such problems. The effects of Reynolds number and Prandtl number on the velocity and temperature are illustrated through graphs and tables for different values of an independent variable.

Effects of heat transfer on MHD suction–injection model of viscous fluid flow through Differential transformation and Hermite wavelet techniques

“…Given the effectiveness of numerical wavelet techniques, developing a parametric Hermite wavelet approach for nonlinear problems is important. With the availability of powerful computational software, HWM has been successfully employed by researchers to solve various nonlinear boundary value problems, including different fluid flow models [14][15][16][17][18][19][20][21]. This study aims to apply the HWM to analyze the present magnetohydrodynamic flow problem.…”

Effects of heat transfer on MHD suction–injection model of viscous fluid flow through differential transformation and Bernoulli wavelet techniques

“…Many mathematician's contributions towards wavelets based numerical methods are as follows: Hermite wavelet, 11 Hermite wavelet matrix, 12 Morlet continuous wavelet, 13 new generalized operational matrix, 14 Laguerre wavelet, 15 continuous polynomial wavelet, 16 Bernoulli wavelet, 17 and Haar wavelet methods 18 . Many fluid flow problems have been solved in recent years by using different wavelet techniques 19–26 …”

“…18 Many fluid flow problems have been solved in recent years by using different wavelet techniques. [19][20][21][22][23][24][25][26] The differential transformation method (DTM) is also another numerical method that requires only a few minor parameters and is semiexact. A polynomial-shaped analytical solution is produced by this method.…”

Application of Bernoulli wavelet method on triple‐diffusive convection in Jeffery–Hamel flow

“…Many mathematician's contributions towards wavelet‐based numerical methods are as follows: Laguerre wavelets method for Lane–Emden equation, 1 Hermite wavelet method, 2 cardinal B‐spline, 3 Laguerre wavelets collocation method, 4 new generalized Hermite wavelet method, 5 Bernoulli wavelet method (BWM), 6 and so forth. Many fluid flow problems are solved by using different wavelet methods 7–14 . The Bernoulli wavelet has been widely utilized in recent years to solve a variety of fluid flow problems 15,16 …”

“…Many fluid flow problems are solved by using different wavelet methods. [7][8][9][10][11][12][13][14] The Bernoulli wavelet has been widely utilized in recent years to solve a variety of fluid flow problems. 15,16 Double-diffusive convection in flow has tremendous application, whereas it is extensively used in many natural and scientific systems, in which the diffusion of heat and mass occur all together.…”