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Unsteady mixed convection of a radiating and reacting nanofluid with variable properties in a porous medium microchannel

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Abstract

In this study we investigated unsteady mixed convection flow and heat transfer of radiating and reacting nanofluid with variable transport properties in a microchannel filed with a saturated porous medium by taking into account the convective boundary conditions. The Buongiorno’s nanofluid flow model is used to study the effects of the Brownian motion and the thermophoresis. The governing highly nonlinear partial differential equations corresponding to the momentum, energy and concentration profiles have been formulated and solved numerically by utilizing the semi-discretization finite difference method. The effect of each governing thermophysical parameters on the microchannel hydrodynamic and thermal behaviors is discussed with the usage of graphs. The numerical results indicate that the velocity and temperature profiles show an increasing behavior with the variable viscosity parameter, Eckert number, thermal Grashof number, solutal Grashof number, Prandtl number and chemical reaction parameter, whereas the concentration profile increases with increasing values of variable thermal conductivity parameter, porous medium shape parameter, Forchheimer number, Brownian motion parameter, Schmidt number, Biot number and radiation parameter. Moreover, the result reveals that the skin friction coefficient increases with suction/injection Reynolds number, porous medium shape parameter, thermal Grashof number, Schmidt number and Brownian motion parameter but decreases with Eckert number, thermophoresis parameter, Biot number and radiation parameter. Both the heat transfer and the mass transfer rates at both sides of the microchannel walls are higher for large values of suction/injection Reynolds number, porous medium shape parameter and variable viscosity parameter, while both are lower for large values of Eckert number, variable thermal conductivity parameter and radiation parameter. Besides, Grashof number, Schmidt number and Biot number indicate an increasing effect on both the heat transfer and mass transfer rates at the cold wall of the microchannel. The numerical simulation also reveals that Brownian motion parameter and thermophoresis parameter show an opposite effect on both heat transfer and mass transfer rates at both sides of the microchannel walls.

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Abbreviations

a :

Microchannel width

\(\sigma ^{*}\) :

Stefan Boltzmann constant

\(D_\mathrm{b}\) :

Brownian diffusion coefficient

\(k^{*}\) :

Rosseland mean absorption coefficient

\(D_\mathrm{T}\) :

Thermal diffusion coefficient

\(q_\mathrm{r}\) :

Thermal radiative heat flux

u :

Axial nanofluid velocity

\({ Ec}\) :

Eckert number

V :

Constant wall suction/injection velocity

A :

Dimensionless nanofluid pressure

g :

Acceleration due to gravity

Re :

Suction/injection Reynolds number

\(\mu \)(T):

Temperature-dependent nanofluid dynamic viscosity

\(\gamma \) :

Dimensionless variable viscosity parameter

\(\mu _{0}\) :

Initial nanofluid dynamic viscosity

\(\lambda \) :

Dimensionless variable thermal conductivity parameter

\(\gamma _{1}\) :

Viscosity variation parameter

Pr :

Prandtl number

\(\rho \) :

Density of nanofluid

Gt:

Thermal Grashof number

C :

Nanoparticles concentration

\({ Gt}\) :

Solutal Grashof number

\(C_{p}\) :

Specific heat at constant pressure

S :

Porous medium shape parameter

K :

Permeability parameter

F :

Forchheimer number

k(T):

Temperature-dependent thermal conductivity of nanofluid

Nb :

Brownian motion parameter

\(k_{0}\) :

Initial nanofluid thermal conductivity

Nt :

Thermophoresis parameter

\(\gamma _{2}\) :

Thermal conductivity variation parameter

R :

Radiation parameter

\(h_{f}\) :

Convective heat transfer coefficient

\(\alpha \) :

Chemical reaction parameter

\(\Gamma \) :

Heat capacity ratio

\({ Sc}\) :

Schmidt number

\(T_{0}\) :

Initial temperature

Bi :

Biot number

\(T_\mathrm{w}\) :

Right wall temperature

\(C_\mathrm{f}\) :

Coefficient of skin friction

\(T_\mathrm{f}\) :

Nanofluid temperature heating microchannel surface

\({ Nu}\) :

Nusselt number/heat transfer rate

T :

Temperature of nanofluid

\(\eta \) :

Dimensionless microchannel width

P :

Pressure of nanofluid

W :

Dimensionless axial nanofluid velocity

t :

Time

\(\tau \) :

Dimensionless time

b :

Porous inertial resistance coefficient

\(\theta \) :

Dimensionless nanofluid temperature

Da :

Darcy number

\(\phi \) :

Dimensionless nanoparticles concentration

\(\varepsilon \) :

Rate of reaction

Sh :

Sherwood number/mass transfer rate

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Acknowledgements

The authors are very much thankful for the constructive comments and suggestions of the editor as well as the anonymous reviewers, which led to improvement of the paper. The corresponding author is very grateful to the financial support of Adama Science and Technology University (Grant No. ASTU/SP-R/073/20).

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Authors and Affiliations

  1. Department of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia

    Bullo Hindebu Rikitu & Lemi Guta Enyadene

  2. Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha, 7395, South Africa

    O. D. Makinde

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  1. Bullo Hindebu Rikitu
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Correspondence to Bullo Hindebu Rikitu.

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Rikitu, B.H., Makinde, O.D. & Enyadene, L.G. Unsteady mixed convection of a radiating and reacting nanofluid with variable properties in a porous medium microchannel. Arch Appl Mech 92, 99–119 (2022). https://doi.org/10.1007/s00419-021-02043-8

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