Abstract
The current paper studies the swirling flow caused by rotating disk in an electrically conducting upper-convected Maxwell fluid with the novel thermal diffusion and diffusion-thermo features. The analysis is performed for the porous disk surface which contributes to the uniform suction/blowing effects. The computations are carried out to understand heat and mass transfer in the occurrence of non-linear radiation. Furthermore, the Rosseland approximation model is used to scrutinize the impact of thermal radiations on heat transfer traits of Maxwell fluid. The effects of Joule heating are also captured on fluid thermal behavior. The governing partial differential equations representing the flow motion, energy, and concentration are reduced into ordinary differential equations within the framework of similarity transformations. A well-known bvp4c scheme in Matlab is utilized for the solution of governing non-linear problem. The outcomes divulge that increasing Deborah number creates a decline in radial and angular motion while axial flow decreases in magnitude. Moreover, the strength of thermal radiation parameter and temperature ratio parameter is extremely useful to increase the temperature of the fluid. Further, the increase in Soret number (or decreasing Dufour number) results in an increase in the mass transfer rate.
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Abbreviations
- \(r,\varphi ,z\) :
-
Cylindrical coordinate system
- \(v_{r},v_{\theta },v_{z}\) :
-
Velocity components
- \(\mathbf {V}\) :
-
Velocity vector
- \(\mathbf {\nabla }\) :
-
Nabla
- p, T :
-
Fluid pressure and temperature
- C :
-
Fluid concentration
- \(\mathbf {A}_{1}\) :
-
First Rivlin Ericksen tensor
- \(\mathbf {S}\) :
-
Extra stress tensor
- \(\lambda _{1}\) :
-
Fluid relaxation time
- \(\nu ,\mu \) :
-
Kinematic and dynamic viscosities
- \(\mathbf {\nabla V}\) :
-
Gradient of velocity vector
- \(\alpha \) :
-
Thermal diffusivity
- \(B_{0}\) :
-
Magnetic field strength
- W :
-
Suction/injection velocity
- \(T_{\infty },\ \) :
-
Ambient fluid temperature
- \(C_{\infty }\) :
-
Ambient fluid concentration
- \(c_{p}\) :
-
Specific heat at constant pressure
- \(c,\Omega \) :
-
Stretching and rotation rate constants
- \(q_{rad}\) :
-
Radiative heat flux
- \(\sigma ^{*}\) :
-
Stephan–Boltzmann constant
- \(k^{*}\) :
-
Mean absorption coefficient
- Re :
-
Local Reynolds number
- \(\eta \) :
-
Dimensionless variable
- \(\theta \) :
-
Dimensionless temperature
- \(\omega \) :
-
Rotation parameter
- D :
-
Diffusion coefficient
- \(\rho \) :
-
Fluid density
- \(k_{T}\) :
-
Thermal diffusion ratio
- \(T_{m}\) :
-
Mean fluid temperature
- \(c_{s}\) :
-
Concentration susceptibility
- \(\phi \) :
-
Dimensionless concentration
- M :
-
Magnetic parameter
- \(\beta _{1}\) :
-
Deborah number
- Du :
-
Dufour number
- Ec :
-
Eckert number
- Sr :
-
Soret number
- Sc :
-
Schmidt number
- Ws :
-
Suction/injection parameter
- Rd :
-
Thermal radiation parameter
- \(\theta _{w}\) :
-
Temperature ratio parameter
- \(Nu_{r}\) :
-
Local Nusselt number
- \(Sh_{r}\) :
-
Local Sherwood number
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Ahmed, J., Khan, M. & Ahmad, L. Joule Heating Effects in Thermally Radiative Swirling Flow of Maxwell Fluid Over a Porous Rotating Disk. Int J Thermophys 40, 106 (2019). https://doi.org/10.1007/s10765-019-2561-x
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DOI: https://doi.org/10.1007/s10765-019-2561-x