Applications of Bernoulli wavelet collocation method in the analysis of Jeffery–Hamel flow and heat transfer in Eyring–Powell fluid

• Published in: Journal of thermal analysis and calorimetry 2023-02, Vol.148 (3), p.1173-1189
• Main Authors: Kumbinarasaiah, S., Raghunatha, K. R., Preetham, M. P.
• Format: Article
• Language: English
• Subjects: Analytical Chemistry; Boundary layers; Chemistry; Chemistry and Materials Science; Collocation methods; Differential equations; Flow characteristics; Fluid flow; Heat transfer; Inorganic Chemistry; Measurement Science and Instrumentation; Methods; Nonlinear differential equations; Numerical differentiation; Ordinary differential equations; Parameters; Partial differential equations; Physical Chemistry; Polymer Sciences; Reynolds number; Roundoff error; Technology application; Wavelet analysis
• ISSN: 1388-6150; 1588-2926
• DOI: 10.1007/s10973-022-11706-9

In this article, we developed the new functional matrix of integration using the Bernoulli wavelet and proposed a novel technique called the Bernoulli wavelet collocation method (BWCM). The main intention of this study is to present a consistent methodology to compute an imprecise solution of Jeffery–Hamel flow and heat transfer in Eyring–Powell fluid in the presence of a magnetic field by using the BWCM. Jeffery–Hamel flows occur in different realistic situations connecting flow between two non-parallel walls. Applications of such fluids in biological and industrial sciences brought great concern to the investigation of flow characteristics in converging and diverging channels. Here, we transform the nonlinear partial differential equations into coupled ordinary differential equations (ODEs) via similarity transformation. Using the BWCM, coupled ODEs are converted into a system of a nonlinear algebraic equation. This technique finds the numerical solution without any restrictive assumptions and avoids round-off errors. The numerical solutions attained by the proposed scheme point out that the approach is easy to implement and computationally very beautiful. The validity of the BWCM is ascertained by comparing our results with the Haar wavelet method and numerical differentiation Solver in Mathematica results. The influence of several emerging dimensionless parameters, namely the Eyring–Powell parameter, Hartman number, Eckert number, local Reynolds number, and the angle between the two walls on velocity and temperature evolution in the boundary layer regime, is examined in detail.