Positive and negative soret and dufour mechanism on unsteady heat and mass transfer flow in the presence of viscous dissipation, thermal and mass buoyancy

ABSTRACT

The combined effects of positive and negative Soret and Dufour on unsteady heat and mass transfer flow in the presence of viscous dissipation, thermal and mass buoyancy is considered. The governing boundary layer equations are formulated to be coupled, nonlinear partial differential equations and are non-dimensionalised. A robust, efficient and accurate spectral relaxation method is used to solve the dimensionless, unsteady, nonlinear and coupled partial differential equations. All pertinent flow parameters are analysed and presented graphically. The effect of flow parameters on the physical quantities of engineering interest is also tabulated. It was found out that the negative Soret reversed the concentration profile while negative Dufour reversed the temperature profile. The present results are compared with previous works and were found to be in good agreement.

KEYWORDS:

• Soret-Dufour
• free convection
• spectral relaxation method
• semi-infinite
• double-diffusion
• magnetohydrodynamics (Mhd)

Nomenclature

C=Dimensional concentration [-]

D=Mass diffusivity [$kg/m^2/s$]

T=Fluid temperature [K]

g=Acceleration due to gravity [$m/s^2$]

$u^{\prime }$= velocity component in $x^{\prime }$direction[$m/s$]

$t^{\prime }=time\left[s\right]$

$\nu$= viscosity [$m^2/s$]

${\beta }_t$= thermal expansion coefficient [$K^{-1}$]

${\beta }_c$=concentration expansion coefficient [$mol.$]

$T_{\mathrm{\infty }}$=free stream dimensional temperature [K]

$C_{\mathrm{\infty }}$= free stream dimensional concentration [mol.]

$\sigma$=electrical conductivity [$s/m$]

${\beta }_0$=external imposed magnetic field [$Weber/m^2$]

$\rho$=fluid density [$c_p$]

$v^{\prime }$=velocity component in $y^{\prime }$-direction [$m/s$]

$\alpha$=Fluid thermal diffusivity [$m^2/s$]

$c_p$=specific heat at constant pressure

$\mu$=coefficient of viscosity [$m^2/s$]

$k_T$=thermal diffusion ratio [K]

$c_s$=concentration susceptivity [mol]

$T_m$=mean fluid temperature [K]

$T_w$=wall dimensional temperature [K]

$U_0$=scale of free stream velocity [mol]

$C_w$=wall dimensional concentration

$n^{\prime },v_0,A$=Constants

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data Availability Statement

The data used in the numerical computations of this study is available upon request https://www.sciencedirect.com/science/article/pii/S0189896516000068.

Additional information

Notes on contributors

B.O. Falodun

Dr. B.O. Falodun is an expert in the field of fluid mechanics, his area of interest is the numerical simulations of fluid flow. He is a research assistant in the department of mathematics, University of Ilorin, Ilorin, Nigeria

A.A. Ayoade

Dr. Ayoade is a lecturer in the department of mathematics, University of Lagos, Lagos, Nigeria. His area of interest is modelling of real life problem.

O. Odetunde

Dr. O. Odetunde is a lecturer in the department of mathematics, University of Ilorin, Ilorin, Nigeria. His area of interest is modelling of real life problem.