TY - EJOU
AU - Saqib, Muhammad
AU - Hanif, a
AU - Abdeljawad, T.
AU - Khan, Ilyas
AU - Shafie, Sharidan
AU - Nisar, Kottakkaran Sooppy
TI - Heat Transfer in MHD Flow of Maxwell Fluid via Fractional Cattaneo-Friedrich Model: A Finite Difference Approach
T2 - Computers, Materials \& Continua
PY - 2020
VL - 65
IS - 3
SN - 1546-2226
AB - The idea of fractional derivatives is applied to several problems of viscoelastic
fluid. However, most of these problems (fluid problems), were studied analytically using
different integral transform techniques, as most of these problems are linear. The idea of
the above fractional derivatives is rarely applied to fluid problems governed by nonlinear
partial differential equations. Most importantly, in the nonlinear problems, either the
fractional models are developed by artificial replacement of the classical derivatives with
fractional derivatives or simple classical problems (without developing the fractional
model even using artificial replacement) are solved. These problems were mostly solved
for steady-state fluid problems. In the present article, studied unsteady nonlinear nonNewtonian fluid problem (Cattaneo-Friedrich Maxwell (CFM) model) and the fractional
model are developed starting from the fractional constitutive equations to the fractional
governing equations; in other words, the artificial replacement of the classical derivatives
with fractional derivatives is not done, but in details, the fractional problem is modeled
from the fractional constitutive equations. More exactly two-dimensional magnetic
resistive flow in a porous medium of fractional Maxwell fluid (FMF) over an inclined
plate with variable velocity and the temperature is studied. The Caputo time-fractional
derivative model (CFM) is used in the governing equations. The proposed model is
numerically solved via finite difference method (FDM) along with L1-scheme for
discretization. The numerical results are presented in various figures. These results
indicated that the fractional parameters significantly affect the temperature and velocity
fields. It is noticed that the temperature field increased with an increase in the fractional
parameter. Whereas, the effect of fractional parameters is opposite on the velocity field
near the plate. However, this trend became like that of the temperature profile, away from the plate. Moreover, the velocity field retarded with strengthening in the magnetic
parameter due to enhancement in Lorentz force. However, this effect reverses in the case
of the temperature profile.
KW - Viscoelastic fluid
KW - Cattaneo-Friedrich Maxwell model
KW - variable heating
KW - magnetohydrodynamic (MHD)
KW - porous medium
KW - fractional derivatives
DO - 10.32604/cmc.2020.011339