Barycentric rational interpolation method for numerical investigation of magnetohydrodynamics nanofluid flow and heat transfer in nonparallel plates with thermal radiation

Abstract

In this study, the problem of heat transfer in the steady two-dimensional flow of an incompressible viscous magnetohydrodynamics nanofluid from a sink or source between two shrinkable or stretchable plates under the effect of thermal radiation has been studied. The governing differential equations have been solved numerically using a collocation method based on the barycentric rational basis functions. This method employs the derivative operational matrix of the barycentric rational bases and the weights that were introduced by Floater and Hormann. The influence of some embedding parameters, such as the solid volume fraction ϕ, the Reynolds number Re, the Hartmann number Ha, the Prandtl number Pr, the radiation parameter N , the stretching-shrinking parameter, C, and the angle of the channel α on the temperature distribution and velocity profile has been illustrated by graphs and tables. Numerical results reveal the efficiency and high accuracy of the proposed scheme compared to the previously existing solutions.Furthermore, the implementation of the proposed method is fast and the run time is short.linear barycentric rational interpolant, magnetohydrodynamic flow, nanofluid, operational matrix of derivative, stretchable or shrinkable walls, thermal radiation | INTRODUCTIONThe study of fluid flow between nonparallel plates is the focus of many research studies in the fields of engineering and science. This type of fluid flow is widely used in fluid mechanics, biomechanics, and electrical engineering. In the early 19th century, this kind of fluid flow, which is known as the Jeffrey-Hamel flow, was investigated by Jeffery 1 and Hamel. 2 The basic concept of magnetohydrodynamics (MHD) was first provided by Alfvén 3 in 1942, and it has important applications in engineering sciences, such as pumps, flow meters, MHD power generation, modeling of cooling systems based on liquid metals, and so on. [4][5][6][7] Most of the governing differential equations arising in engineering and physics are nonlinear, and, in most cases, it is not possible to obtain accurate and analytical solutions. Therefore, numerical or semianalytical techniques are utilized to solve such problems. Various numerical and semianalytical methods have been proposed for solving nonlinear problems arising in MHD nanofluid flow and heat transfer. In Esmaili et al, 8,9 the Adomian decomposition method is applied to obtain an approximate solution of the Jeffery-Hamel flow problem. Moghimi et al 10 used the homotopy perturbation method to solve the MHD Jeffery-Hamel flow problem. Also, Moghimi et al 11 employed the homotopy analysis method for the numerical solution of nonlinear MHD Jeffery-Hamel flows in nonparallel plates. Comparison between the HAM solutions and the numerical results based on fourth-fifth order Runge-Kutta (RKF45) method revealed the accuracy of this scheme. In Gerdroodbary et al, 12 the effect of thermal radiation on the classical Jeffery-Hamel flow has been studied numerically by using the collocation method (CM) and the least-square me...

Piecewise barycentric interpolating functions for the numerical solution of Volterra integro‐differential equations

“…So in this case, the FH family of interpolants is a better choice. During the last few years, some numerical methods based on the LBRIs with Floater-Hormann weights have been introduced to approximate the solutions of the nonlinear differential equations, [55][56][57][58] the Volterra integral equations (VIEs), 59 stiff VIEs, 60 weakly singular VIEs, 61,62 VIDEs, 63,64 delay VIDEs, 65 and high-dimensional Fredholm integral equations (FIEs). 66 The main purpose of this work is to develop a computational method based on an extended form of the interpolating scaling functions (ISFs), named the piecewise barycentric interpolating functions (PBIFs), with the associated operational matrices of integral and product for the VIDE (1).…”

“…So in this case, the FH family of interpolants is a better choice. During the last few years, some numerical methods based on the LBRIs with Floater–Hormann weights have been introduced to approximate the solutions of the nonlinear differential equations, 55–58 the Volterra integral equations (VIEs), 59 stiff VIEs, 60 weakly singular VIEs, 61,62 VIDEs, 63,64 delay VIDEs, 65 and high‐dimensional Fredholm integral equations (FIEs) 66 …”