@Article{cmc.2020.011339,
AUTHOR = {Muhammad Saqib, Hanifa Hanif, T. Abdeljawad, Ilyas Khan, Sharidan Shafie, Kottakkaran Sooppy Nisar},
TITLE = {Heat Transfer in MHD Flow of Maxwell Fluid via Fractional  Cattaneo-Friedrich Model: A Finite Difference Approach},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {65},
YEAR = {2020},
NUMBER = {3},
PAGES = {1959--1973},
URL = {http://www.techscience.com/cmc/v65n3/40149},
ISSN = {1546-2226},
ABSTRACT = {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.},
DOI = {10.32604/cmc.2020.011339}
}