Numerical Simulation of unsteady MHD Flow and Heat Transfer of a Second Grade Fluid with Viscous Dissipation and Joule Heating using Meshfree Approach

Authors: R. Bhargava, Sonam Singh

Abstract:

In the present study, a numerical analysis is carried out to investigate unsteady MHD (magneto-hydrodynamic) flow and heat transfer of a non-Newtonian second grade viscoelastic fluid over an oscillatory stretching sheet. The flow is induced due to an infinite elastic sheet which is stretched oscillatory (back and forth) in its own plane. Effect of viscous dissipation and joule heating are taken into account. The non-linear differential equations governing the problem are transformed into system of non-dimensional differential equations using similarity transformations. A newly developed meshfree numerical technique Element free Galerkin method (EFGM) is employed to solve the coupled non linear differential equations. The results illustrating the effect of various parameters like viscoelastic parameter, Hartman number, relative frequency amplitude of the oscillatory sheet to the stretching rate and Eckert number on velocity and temperature field are reported in terms of graphs and tables. The present model finds its application in polymer extrusion, drawing of plastic films and wires, glass, fiber and paper production etc.

Keywords: EFGM, MHD, Oscillatory stretching sheet, Unsteady, Viscoelastic

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1070219

References:

[1] J.E. Dunn, K.R. Rajagopal, "Fluids of differential type - critical review and thermodynamic analysis", Int. J. Eng. Sci., vol. 33 (1995) 689-729.
[2] B. C. Sakiadis, "Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow", AIChE Journal, vol. 7 (1961) 26-28.
[3] L.J Crane, "Flow past a stretching plate", J. App. Math. And Phys., vol. 21 (1970) 645-647.
[4] C.Y. Wang, "Nonlinear streaming due to the oscillatory stretching of a sheet in a viscous fluid", Acta Mech., vol. 72 (1988) 261--268.
[5] V. Ambethkar, "A numerical study of heat and mass transfer effects on an oscillatory flow of a viscoelastic fluid with thermal relaxation", Adv. Theor. Appl. Mech., vol. 3 (2010) 397-407.
[6] V.M. Soundalgekar, S.K. Gupta, "Free convection effects on the oscillatory flow of a viscous, incompressible fluid past a steadily moving vertical plate with constant suction", Int. J. Heat Mass Transfer, vol. 18 (1975) 1083--1093.
[7] Z. Abbas, Y. Wang, T. Hayat, M. Oberlack, " Hydromagnetic flow in a viscoelastic fluid due to the oscillatory stretching surface", Int. J. Non- Linear Mech., vol. 43 (2008) 783-793.
[8] R. Sharma , R. Bhargava and P. Bhargava , "A numerical solution of unsteady MHD convection heat and mass transfer past a semi-infinite vertical porous moving plate using element free galerkin method", Comput. Mater. Sci.,vol. 48 (2010) 537-543.
[9] T. Belytscho , L. Gu , Y.Y. Lu , "Fracture and crack growth by element free Galerkin method", Model. Simulat. Mater. Sci. and Engg., vol. 2 (1994) 519-534.
[10] S. Singh, R. Bhargava, " Element free Galerkin simulation of micropolar squeeze film flow of a biological lubricant", J. Info. And Oper. Management, vol. 3, (2012) 149-152.
[11] C. H. Chen, "Laminar mixed convection adjacent to vertical continuously stretching sheets", Int. J. Heat Mass Transfer, vol. 33 (1998) 471-476.
[12] L.T. Grubka and K.M. Bobba, "Heat transfer characteristic of a continuous stretching surface with variable temperature", ASME J. heat transfer, vol. 107 (1985b) 248-250.
[13] R.L. Fosdick K.R. Rajagopal, "Thermodynamics and stability of fluids of third grade", Proc R Soc A, vol. 369 (1980) 351-377.
[14] G.R. Liu, "Mesh free method-Moving beyond the Finite element method", CRC Press,2003, Ch. 5-6.
[15] A. Singh, I.V. Singh, R. Prakash, "Numerical analysis of fluid squeezed between two parallel plates by meshless method", Comp. & fluids, vol. 36 (2007) 1460-1480.
[16] I.V. Singh, "A numerical solution of composite heat transfer problems using meshless method", Int. J. Heat Mass transfer, vol. 47 (2004) 2123-2138.