Abstract
A study of Darcy flow of magnetized Oldroyd-B fluid over a rotating porous disk is analyzed. The heat and mass transport mechanism are analyzed with the significant features of thermal diffusion (Soret) and diffusion thermo (Dufour). Additionally the influence of chemical reaction is also considered on solutal field. The Von Karman transformations are used and in order to obtain the similarity equations which are then integrated numerically on \(\left[ 0,\infty \right) \) through BVP Midrich technique in Maple. The results are given through graphical structure and tabular form. A brief parametric survey is conducted against velocity fields, temperature and concentration distributions in the form of graphs. The corresponding heat transfer rate and wall concentration gradient are displayed through tables with different physical effects. The comparison tables are presented to assure the validity of our numerical scheme with the past outcomes. It is revealed that the velocity fields decline with the effect of porosity parameter. The heat transfer rate rises significantly with diminishing value of Soret number.
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Abbreviations
- \(r,\varphi ,z\) :
-
Cylindrical coordinate
- u, v, w :
-
Components of velocity
- T :
-
Fluid temperature
- \(T_\mathrm{w}\) :
-
Wall temperature
- \(T_\mathrm{m}\) :
-
Fluid mean temperature
- \(\nu \) :
-
Kinematic viscosity
- C :
-
Fluid concentration
- \(\phi _{1}\) :
-
Porosity of the medium
- D :
-
Molecular diffusion coefficient
- \(\lambda _{1}\) :
-
Time relaxation
- M :
-
Magnetic field
- \(\beta _{1}\) :
-
Relaxation time parameter
- \(\Pr \) :
-
Prandtl number
- \(k_\mathrm{T}\) :
-
The thermal–diffusion ratio
- \(\varOmega \) :
-
Angular velocity rate
- \(c_{s}\) :
-
The concentration susceptibility
- \(\delta \) :
-
Ratio of diffusion coefficients
- F :
-
Radial velocity
- H :
-
Axial velocity
- \(\theta \) :
-
Dimensionless temperature
- \(\alpha \) :
-
Thermal diffusivity
- \(c_{p}\) :
-
Specific heat capacity
- \(T_{\infty }\) :
-
Ambient temperature
- \(C_\mathrm{w}\) :
-
Wall concentration
- \(\mu \) :
-
Dynamic viscosity
- \(\rho \) :
-
Fluid density
- \(C_{\infty }\) :
-
Ambient concentration
- K :
-
Permeability of the medium
- \(K_{1}\) :
-
The chemical reaction rate
- \(\lambda _{2}\) :
-
Time retardation
- R :
-
Stretching parameter
- \(\beta _{2}\) :
-
Retardation time parameter
- Sc:
-
Schmidt number
- \(\eta \) :
-
Dimensionless variable
- \(\theta \) :
-
Dimensionless temperature
- \(B_{0}\) :
-
Strength of magnetic field
- \(\mu \) :
-
Dynamic viscosity
- G :
-
Azimuthal velocity
- c :
-
Stretching rate
- \(\phi \) :
-
Dimensionless concentration
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Hafeez, A., Khan, M., Ahmed, J. et al. Flow of Oldroyd-B Fluid over a Rotating Disk Through Porous Medium with Soret–Dufour Effects. Arab J Sci Eng 45, 5949–5957 (2020). https://doi.org/10.1007/s13369-020-04575-7
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DOI: https://doi.org/10.1007/s13369-020-04575-7