Numerical Simulation of unsteady MHD Flow and Heat Transfer of a Second Grade Fluid with Viscous Dissipation and Joule Heating using Meshfree Approach
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:57161", author = "R. Bhargava and Sonam Singh", title = "Numerical Simulation of unsteady MHD Flow and Heat Transfer of a Second Grade Fluid with Viscous Dissipation and Joule Heating using Meshfree Approach", 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", volume = "6", number = "6", pages = "664-7", }