Numerical Simulation of MHD Peristaltic Flow with Variable Electrical Conductivity and Joule Dissipation Using Generalized Differential Quadrature Method

Abstract

In this paper, the MHD peristaltic flow inside wavy walls of an asymmetric channel is investigated, where the walls of the channel are moving with peristaltic wave velocity along the channel length. During this investigation, the electrical conductivity both in Lorentz force and Joule heating is taken to be temperature dependent. Also, the long wavelength and low Reynolds number assumptions are utilized to reduce the governing partial differential equations into a set of coupled nonlinear ordinary differential equations. The new set of obtained equations is then numerically solved using the generalized differential quadrature method (GDQM). This is the first attempt to solve the nonlinear equations arising in the peristaltic flows using this method in combination with the Newton-Raphson technique. Moreover, in order to check the accuracy of the proposed numerical method, our results are compared with the results of built-in Mathematica command NDSolve. Taking Joule heating and viscous dissipation into account, the effects of various parameters appearing in the problem are used to discuss the fluid flow characteristics and heat transfer in the electrically conducting fluids graphically. In presence of variable electrical conductivity, velocity and temperature profiles are highly decreasing in nature when the intensity of the electrical conductivity parameter is strengthened.

Magneto-Convection of Alumina - Water Nanofluid Within Thin Horizontal Layers Using the Revised Generalized Buongiorno's Model

“…Later, Amanulla et al (2018) performed a thorough numerical investigation to simulate the steady MHD convective flow of Carreau non-Newtonian fluid past an isothermal sphere by applying Keller-Box Method (KBM). Qasim et al (2018) conducted an innovative numerical simulation of MHD peristaltic flow with variable electrical conductivity and joule dissipation by utilizing Generalized Differential Quadrature Method (GDQM). On the other hand, a comprehensive survey was done by Wakif et al (2017a) on the thermo-magneto-hydrodynamic stability of nanofluids saturating porous mediums by means of Chebyshev-Gauss-Lobatto Spectral Method (CGLSM).…”

“…Hence, in order to provide extensive details about this numerical method, the readers can refer to the book of Shu (2012). Also, the interested researchers can see the innovative works of Fidanoglu et al (2014) , Qasim et al (2018) and the references therein, in which GDQM is explained more fully through two different practical situations. Based on our CGLSM and GDQM codes, the results are presented in tabular and graphical forms to discuss the significant effects of the emerging parameters , 0 and on the thermo-magnetohydrodynamic stability of 2 3 -water nanofluids as well as to quantify the agreement between the results of these numerical methods.…”

On the Cattaneo–Christov Heat Flux Model and OHAM Analysis for Three Different Types of Nanofluids

“…Liao [36,37] suggested the homotopy analysis method and optimal HAM approach to get analytical solutions for non-linear differential equations. Other interesting related numerical investigations can be found in [38][39][40][41][42][43][44][45][46][47][48][49].…”

Comments on the paper “The effects of Joule heating and variable thermal conductivity on peristaltic pumping of Jeffrey nanofluid in the presence of heat transfer” by Hanaa Abdel‐Hameed Asfour

“…3 as given by Abdel‐Hameed Asfour 1 is wrong as it can not guarantee the channel nonclogging due to possible clashing between the channel walls. The correct condition is that satisfies 3 Now, from fig. 1 as given by Abdel‐Hameed Asfour 1 since and implies that and to contain the phase angle in a relation that guarantees no collision will occur between the channel walls, we can write hence by adding, we get, So the correct condition for the channel walls can be written as in Equation (5).…”

“…3 as given by Abdel‐Hameed Asfour 1 is wrong as it can not guarantee the channel nonclogging due to possible clashing between the channel walls. The correct condition is that satisfies 3 …”