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Heat and Mass Transfer on the Mixed Convection of Non-Newtonian Fluids Over a Vertical Wedge with Soret/Dufour Effects and Internal Heat Generation: Variable Wall Temperature/Concentration

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Abstract

This numerical analysis investigated the effects of heat and mass transfer characteristics on the mixed convection flow of non-Newtonian fluids over the vertical wedge in a saturated porous medium with Soret/Dufour effects and internal heat generation. The numerical modeling of this problem has attracted considerable attention from researchers because it has practical applications in biological sciences, electronic cooling, advanced nuclear systems, etc. The internal heat generation is assumed to be an exponential decaying form. The power-law model of Ostwald–de Waele for non-Newtonian fluids is considered. The surface of the vertical wedge is kept at variable wall temperature and concentration. In the analysis of mixed convection, which included free convection and forced convection, parameter varies from 0 (pure free convection) to 1 (pure forced convection). The transformed equations are obtained by using a suitable coordinate transformation, and then, Keller box method is utilized to solve the non-similar equations. Comparisons with data published previously showed good agreement. Both the local Nusselt number and the local Sherwood number increase with increasing the exponent of variable wall temperature/concentration. Increasing the internal heat generation coefficient decreases (increases) the local Nusselt (Sherwood) number. As the power-law index is increased, the local Nusselt and Sherwood numbers are decreased.

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Abbreviations

\(A^{ * }\) :

Internal heat generation coefficient

B :

Constant

C :

Concentration

\(C_{\text{P}}\) :

Specific heat at constant pressure

c 1 :

Constant

c 2 :

Constant

D :

Dufour parameter

d :

Particle diameter

\(\bar{D}\) :

Dufour coefficient

\(D_{\text{m}}\) :

Mass diffusivity

\(f\) :

Dimensionless stream function

\(g\) :

Gravitational acceleration

\(K\) :

Permeability of the porous medium

\(k\) :

Equivalent thermal conductivity

\(Le\) :

Lewis number

\(m\) :

Wedge angle parameter

\(N\) :

Buoyancy ratio

\(n\) :

Power-law index of the non-Newtonian fluid

\(Nu_{x}\) :

Local Nusselt number

\(Pe_{x}\) :

Local Peclet number

\(q^{\prime \prime \prime }\) :

Internal heat generation rate per unit volume

\(Ra_{x}\) :

Modified local Rayleigh number

\(S\) :

Soret parameter

\(\bar{S}\) :

Soret coefficient

Sh x :

Local Sherwood number

T :

Temperature

u :

Darcy velocity component in the x-direction

\(U_{\infty }\) :

Velocity of the potential flow outside the boundary layer

\(v\) :

Darcy velocity component in the y-direction

x :

Streamwise coordinate

y :

Transverse coordinate

\(\alpha_{\text{m}}\) :

Equivalent thermal diffusivity

\(\beta_{\text{C}}\) :

Coefficient of concentration expansion

\(\beta_{\text{T}}\) :

Coefficient of thermal expansion

\(\delta_{\text{C}}\) :

Concentration boundary layer thickness

\(\delta_{\text{T}}\) :

Thermal boundary layer thickness

\(\eta\) :

Pseudo-similarity variable

\(\theta\) :

Dimensionless temperature

\(\phi\) :

Dimensionless concentration

\(\lambda\) :

Exponent of VWT/VWC

\(\mu\) :

Absolute viscosity of fluid

\(\rho\) :

Density of fluid

\(\psi\) :

Stream function

\(\chi\) :

Combined convection parameter

\(\varOmega\) :

Half angle of the wedge

\({\text{w}}\) :

Condition at the wall

\(\infty\) :

Condition at infinity

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  1. Department of Aircraft Engineering, Air Force Institute of Technology, Kaohsiung, Taiwan, ROC

    Chuo-Jeng Huang & Kuo-Ann Yih

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  1. Chuo-Jeng Huang
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Huang, CJ., Yih, KA. Heat and Mass Transfer on the Mixed Convection of Non-Newtonian Fluids Over a Vertical Wedge with Soret/Dufour Effects and Internal Heat Generation: Variable Wall Temperature/Concentration. Transp Porous Med 130, 559–576 (2019). https://doi.org/10.1007/s11242-019-01325-8

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