Application of Differential Transformation Method for Nanofluid Flow in a Semi-Permeable Channel Considering Magnetic Field Effect

Abstract

In this study, we propose a reliable algorithm to develop an analytical solution for the problem of laminar steady magnetohydrodymanics (MHD) nanofluid flow in a semi-permeable channel using the differential transformation method (DTM). The working fluid is water with copper nanoparticles. The effects of Hartmann number and Reynolds number on velocity profiles have been also considered for various numerical cases. The effective thermal conductivity and viscosity of nanofluid are calculated by the Maxwell and Brinkman models, respectively. A close agreement between the obtained solution and some well-known results has been established.

Steady natural convection heat and mass transfer flow through a vertical porous channel with variable viscosity and thermal conductivity

“…A result obtained from their work indicates that increasing Hartmann number lead to backflow reduction. Sheikholeslami and Azimi 20 applied DTM on a Nanofluid flow with magnetic field effect. Results obtained from DTM matched with results carried out using fourth‐order Runge‐Kutta method.…”

“…where a, b, and c are constants which are computed from the boundary conditions in Equation(20). The above equations for temperature, velocity, and concentration are solved and the results obtained are presented graphically fromFigures 2 to 15, and numerically from Tables 2 and 7 for different governing parameters F I G U R E 2 Temperature profile for binary mixture of carbon dioxide in air for different values of Suction/Injection parameter S [Q = − 10, N = 1, Ec = 0.2, Kc = 0.7, = − 0.1 and = 0.5] Concentration profile for binary mixture of carbon dioxide in air for different values of Suction/Injection parameter S [Q = − 10, N = 1, Ec = 0.2, Kc = 0.7, = − 0.1 and = 0.5] Velocity profile for binary mixture of carbon dioxide in air for different values of Suction/Injection parameter S [Q = − 10, N = 1, Ec = 0.2, Kc = 0.7, = − 0.1, and = 0.5] F I G U R E 5 Temperature profile for binary mixture of carbon dioxide in air for different values of Eckert number [Q = − 10, N = 1, Kc = 0.7, S = − 0.4, = − 0.1, and = 0.5] Velocity profile for binary mixture of carbon dioxide in air for different values of Eckert number [Q = − 10, N = 1, Kc = 0.7, S = − 0.4, = − 0.1 and = 0.5] Temperature profile for binary mixture of carbon dioxide in air for different values of Viscosity parameter [Q = − 10, N = 1, Kc = 0.7, S = − 0.4, = − 0.2, and = 0.5] F I G U R E 8 Velocity profile for binary mixture of carbon dioxide in air for different values of Viscosity parameter [Q = − 10, N = 1, Kc = 0.7, S = − 0.4, = − 0.2 and = 0.5] Temperature profile for binary mixture of carbon dioxide in air for different values of Thermal conductivity parameter [Q = − 10, N = 1, Kc = 0.7, S = − 0.4, = − 0.2 and = 0.5] Velocity profile for binary mixture of carbon dioxide in air for different values of Thermal conductivity parameter [Q = − 10, N = 1, Kc = 0.7, S = − 0.4, = − 0.1 and = 0.5] F I G U R E 11 Temperature profile for binary mixture of carbon dioxide in air for different values of heat source/sink parameter [ = 0.5, N = 1, Kc = 0.7, S = − 0.4, Ec = 0.2 and = − 0.1] Velocity profile for binary mixture of carbon dioxide in air for different values of heat source/sink parameter [ = 0.5, N = 1, Kc = 0.7, S = − 0.4, Ec = 0.2 and = − 0.1] F I G U R E 13 Velocity profile for binary mixture of carbon dioxide in air for different values of Buoyancy parameter [ = 0.5, Q = − 10, Kc = 0.7, S = − 0.4, Ec = 0.2 and = − 0.1] F I G U R E 14 Concentration profile for binary mixture of carbon dioxide in air for different values of chemical reaction parameter [Q = − 10, N = 1, Ec = 0.2, = − 0.1, and = 0.5]…”

Magnetohydrodynamic go-water nanofluid flow and heat transfer between two parallel moving disks

“…In most cases, scientific problems are inherently of non-linearity that does not admit analytical solution, so these equations should be solved using special techniques. Some of these methods are reconstruction of variational iteration method [7], differential transformation method [8,9], homotopy perturbation method [10], and optimal homotopy asymptotic method (OHAM) [11], and others [12][13][14][15][16].…”

A numerical scheme for solutions of a class of nonlinear differential equations

“…Recently, the Taylor, Chebyshev, Legendre, Bernstein and Bessel matrixcollocation methods have been used [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] to solve some types of differential, integral, integro-differential-difference equations. Additionally, Sheikholeslami et al [48][49][50][51][52][53][54][55][56][57][58] studied on solutions to various differential equations and model problems.…”