FLOW BEHAVIOUR OF NON-DARCIAN MAGNETOHYDRODYNAMIC CASSON NANOFLUID OVER A STRETCHING OR SHRINKING SHEET WITH SLIPS AND CONVECTIVE HEATING
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Date
2021-04
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
UNIVERSITY OF ILORIN
Abstract
Investigations of electrically conducting Magnetohydrodynamic (MHD) Casson nanofluid
flow are important areas of research due to their applications in industries and engineering
for industrial coolant, brake fluid, MHD generator, nanodrug delivery, and others. Several studies
concerning heat and mass transfer of MHD nanofluids have been reported in literature. However,
most of the existing related works do not consider the combined effects of nonlinear radiation and
non-Darcian porous medium. If the fluid velocity is high and the temperature differences within
the fluid are sufficiently large, both Darcy and linearized radiative heat flux models may not
accurately determine the fluid flow and thermal structure. Therefore, this study was aimed at
analysing the effect of nonlinear radiation, binary chemical reaction, Arrhenius activation energy,
variable viscosity and thermal conductivity on convective non-Darcian MHD dissipative Casson
nanofluid flow past a stretching or shrinking sheet with slip and convective heating. The objectives
of the study were to: (i) determine the flow behaviour of a non-Darcian MHD dissipative Casson
nanofluid over a stretching or shrinking sheet with multiple slip boundary conditions; (ii) examine
the influence of variable viscosity and variable thermal conductivity on natural convective flow of
non-Darcian MHD Casson nanofluid flow with velocity slip and convective heating; and (iii)
analyse the effect of binary chemical reaction and Arrhenius activation energy on forced
convective flow of non-Darcian MHD Casson nanofluid in the presence of non-Navier velocity
slip condition.
The mathematical equations governing the flow, heat and mass transfer of Casson
nanofluid in a non-Darcian porous medium are:
= 0,
u v
x y
+
2 2 *
2
0
2
1 ( ) 1
= 1 1 , B B
f f f p p
u u u B x b
u v u u u
x y y k k
+ + − − + −
2 2
2
2
1
= 1
( )
T B
B
p f
T T T C T D T u
u v D and
x y y y y T y C y
+ + + + +
2 2
2 2 = . T
B
C C C D T
u v D
x y y T y
+ +
Where 0 ( , ) , , , , , , , , , , , , , , B f p B p T u v B k b T D C C D are respectively velocity
components in x and y directions, dynamic viscosity, fluid density, Casson parameter, electric
conductivity, magnetic field, porous medium permeability, Forchhiemer inertial coefficient, fluid
temperature, fluid thermal diffusivity, heat capacity ratio, Brownian diffusion coefficient,
nanoparticle concentration, heat capacity and thermophoretic diffusion coefficient. The above
governing equations were reduced to nonlinear ordinary differential equations using similarity
transformation and then solved by employing weighted residual method. The computational procedure was implemented by writing codes in MATHEMATICA Software.
The findings of the study were that: [label=()]
1. an increase in non-Darcian porous medium parameter resulted into a reduction in velocity, while it enhanced both temperature and nanoparticle volume fraction;
2. a hike in temperature dependent viscosity and thermal conductivity parameters contributed to a decrease in both temperature and nanoparticle volume fraction profiles and a rise in velocity profile;
3. nanoparticle volume fraction profile was reduced as a result of an increase in chemical reaction parameter, while increasing activation energy parameter led to an increase in nanoparticle volume fraction profile; and
4. an increase in radiation parameter resulted into a decrease in temperature profile.
The study concluded that the thermal radiation, Forchheimer, variable viscosity, variable thermal conductivity, chemical reaction and activation energy parameters have significant effects on the velocity, temperature, nanoparticle volume fraction, Nusselt number and the Sherwood number of Casson nanofluid. It is therefore recommended that those parameters are necessary and should be considered when carrying out a design involving Casson nanofluid flow.
Description
Keywords
FLOW BEHAVIOUR, NON-DARCIAN MAGNETOHYDRODYNAMIC, CASSON NANOFLUID, STRETCHING SHEET, SHRINKING SHEET, SLIPS, CONVECTIVE HEATING