Theoretical Study of Thermal and Mass Stratification Effects on MHD Nanofluid Past an Exponentially Accelerated Vertical Plate in a Porous Medium in Presence of Heat Source, Thermal Radiation and Chemical Reaction

Abstract

This research work investigates the impacts of thermal and mass stratification on unsteady magnetohydrodynamic nanofluid moving through a vertical plate that accelerates exponentially with variable temperature in a porous medium. The governing equations of the problem are solved numerically by using the implicit Crank Nicolson method. We compare the results obtained for the nanofluid with two distinct stratifications to those obtained with no stratification. The nanofluid's velocity decreases under both types of stratification, while temperature drops under thermal stratification and concentration reduces under mass stratification. We explored a wide range of factors using graphs, including the volume fraction of nanoparticles, thermal radiation, heat source/sink, and chemical reaction. The significant findings indicate that nanofluids exhibit higher thermal conductivity compared to conventional fluids. The current study has enormous significance in several domains, such as power generation, electronic component cooling, and vehicle construction.

Appendix

Nomenclature

${\left(\rho {C}_{p}\right)}_{f}$	Heat capacitance of ${{\text{H}}}_{2}\mathrm{O }({{\text{Jkg}}}^{-1}{{\text{K}}}^{-1})$	$Gc$	Mass Grashof number
${\left(\rho {C}_{p}\right)}_{nf}$	Heat capacitance of the nanofluid ${{\text{H}}}_{2}\mathrm{O }({{\text{Jkg}}}^{-1}{{\text{K}}}^{-1})$	$Gr$	Thermal Grashof number
${\left(\rho {C}_{p}\right)}_{s}$	Heat capacitance of nanoparticle Cu $({{\text{Jkg}}}^{-1}{{\text{K}}}^{-1})$	$K$	Non-dimensional porosity parameter
${\left({\beta }_{C}\right)}_{nf}$	Coefficient of expansion for species concentration of the nanofluid $({{\text{m}}}^{2}/{\text{h}})$	${k}_{p}^{\mathrm{^{\prime}}}$	Permeability of porous medium $({{\text{m}}}^{2})$
${\left({\beta }_{T}\right)}_{nf}$	Thermal expansion coefficient of the nanofluid $({{\text{K}}}^{-1})$	${k}_{1}$	Chemical reaction parameter
${\mu }_{f}$	Viscosity of the ${{\text{H}}}_{2}\mathrm{O }(\mathrm{m Pa})$	${k}_{f}$	Thermal conductivity of ${{\text{H}}}_{2}0$ $(\mathrm{W }{{\text{m}}}^{-1}{{\text{K}}}^{-1})$
${\mu }_{nf}$	Dynamic viscosity of the nanofluid $(\mathrm{m Pa})$	${k}_{nf}$	Thermal conductivity of the nanofluid $(\mathrm{W }{{\text{m}}}^{-1}{{\text{K}}}^{-1})$
${\rho }_{f}$	Density of the ${{\text{H}}}_{2}\mathrm{O }({\text{kg}}/{{\text{m}}}^{3})$	${k}_{s}$	Thermal conductivity of nanoparticle Cu $(\mathrm{W }{{\text{m}}}^{-1}{{\text{K}}}^{-1})$
${\rho }_{nf}$	Density of the nanofluid $({\text{kg}}/{{\text{m}}}^{3})$	$Kr$	Non-Dimensional Chemical Reaction Parameter
${\rho }_{s}$	Density of the nanoparticle Cu $({\text{kg}}/{{\text{m}}}^{3})$	$M$	Non-Dimensional Magnetic parameter
${\sigma }_{f}$	Electrical conductivity of ${{\text{H}}}_{2}\mathrm{O }({\text{s}}/{\text{m}})$	$Pr$	Prandtl Number
${\sigma }_{nf}$	Electrical conductivity of the nanofluid $({\text{s}}/{\text{m}})$	$Q$	Non-dimensional heat source/sink Parameter
${\sigma }_{s}$	Electrical conductivity of nanoparticle Cu $({\text{s}}/{\text{m}})$	${q}_{r}^{\mathrm{^{\prime}}}$	Radiative heat flux $(\mathrm{kW }{{\text{m}}}^{-2})$
$\phi$	Volume fraction of nanoparticle Cu	${Q}_{0}$	Heat source/sink $({{\text{JK}}}^{-1}{{\text{m}}}^{-3}{{\text{s}}}^{-1})$
$\gamma$	Thermal stratification parameter	$R$	Non-dimensional radiation
$\xi$	Mass stratification parameter	$S$	Non-dimensional thermal stratification parameter
$\tau$	Non-dimensional skin-friction	$Sc$	Schimdt number
$\theta$	Non-dimensional temperature	$t$	Non-dimensional time
$A, a, a\mathrm{^{\prime}}$	Constant	${t}^{\mathrm{^{\prime}}}$	Time $({\text{s}})$
${B}_{0}$	Magnetic field strength $(\mathrm{N m}{\mathrm{ A}}^{-1})$	${T}^{\mathrm{^{\prime}}}$	Temperature of the fluid $({\text{K}})$
$C$	Non-dimensional concentration	${T}_{\infty }^{\mathrm{^{\prime}}}$	Temperature of the fluid far away from the plate $({\text{K}})$
${C}^{\mathrm{^{\prime}}}$	Species concentration in the fluid $({\text{mol}}/{{\text{m}}}^{3})$	${T}_{\omega }^{\mathrm{^{\prime}}}$	Temperature of the plate $({\text{K}})$
${C}_{\infty }^{\mathrm{^{\prime}}}$	Concentration of the fluid far away from the plate $({\text{mol}}/{{\text{m}}}^{3})$	$U$	Non-dimensional velocity
${C}_{\omega }^{\mathrm{^{\prime}}}$	Concentration of the plate $({\text{mol}}/{{\text{m}}}^{3})$	${u}^{\mathrm{^{\prime}}}$	Velocity of the fluid in $\mathrm{x{\prime}}$ direction $({\text{m}}/{\text{s}})$
${D}_{nf}$	Mass diffusion coefficient $({\text{m}}/{\text{s}})$	${u}_{0}$	Velocity of the plate $({\text{m}}/{\text{s}})$
$F$	Non-dimensional mass stratification parameter	$y$	Non-dimensional coordinate normal to the plate
$g$	Acceleration due to gravity $({\text{m}}/{{\text{s}}}^{2})$	${y}^{\mathrm{^{\prime}}}$	Coordinate normal to the plate $({\text{m}})$