Abstract
The current study explores the magnetized flow of an Oldroyd-B fluid by a rotating disk. In this analysis, we use the modified Fourier’s law instead of classical Fourier’s law to study the fluid thermal features. The impact of homogeneous–heterogeneous reactions for mass transport is also considered. The von Karman variables are used to convert the partial differential equations into non-dimensional ordinary differential equations. The BVP Midrich scheme is utilized to acquire the numerical solution. Diverse effects of various involved parameters on the velocities, temperature and concentration of the liquid are analyzed. Additionally, the comparison table is made for limiting case to see the validity of our numerical results with the past outcomes. It is observed that the fluid velocity reduces with the impact of relaxation time parameter. Further, higher values of thermal relaxation time decline the fluid temperature. Moreover, with an increase in homogenous reaction, the concentration boundary layer thickness becomes thinner. The reduction in wall concentration gradient is noticed against homogeneous reaction rate.
Abbreviations
- \(r,\varphi ,z\) :
-
Cylindrical coordinate
- u, v, w :
-
Components of velocity
- T :
-
Fluid temperature
- \(T_\mathrm{w}\) :
-
Wall temperature
- \(\nu\) :
-
Kinematic viscosity
- C :
-
Fluid concentration
- \(A^{*}\), \(B^{*}\) :
-
Chemical species
- a, b :
-
Concentrations of chemical species
- \(\lambda _{1}\) :
-
Relaxation time
- M :
-
Magnetic field
- \(\beta _{1}\) :
-
Relaxation time parameter
- Pr:
-
Prandtl number
- \(\varepsilon\) :
-
Thermal relaxation time parameter
- \(K_{2}\) :
-
Heterogeneous reaction rate
- \(\Omega\) :
-
Angular velocity
- \(D_\mathrm{A}\), \(D_\mathrm{B}\) :
-
Diffusion coefficients of species
- \(\delta\) :
-
Ratio of diffusion coefficients
- F :
-
Radial velocity
- H :
-
Axial velocity
- \(\theta\) :
-
Dimensionless temperature
- \(\alpha\) :
-
Thermal diffusivity
- \(c_\mathrm{p}\) :
-
Specific heat capacity
- \(T_{\infty }\) :
-
Ambient temperature
- \(C_\mathrm{w}\) :
-
Wall concentration
- \(\rho\) :
-
Fluid density
- \(C_{\infty }\) :
-
Ambient concentration
- \(k_\mathrm{c}\), \(k_\mathrm{s}\) :
-
Rate constants
- \(K_\mathrm{r}\) :
-
Reaction rate
- \(\lambda _{2}\) :
-
Retardation time
- R :
-
Stretching parameter
- \(\beta _{2}\) :
-
Retardation time parameter
- Sc:
-
Schmidt number
- \(K_{1}\) :
-
Homogenous reaction rate
- \(\eta\) :
-
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. Thermal aspects of chemically reactive Oldroyd-B fluid flow over a rotating disk with Cattaneo–Christov heat flux theory. J Therm Anal Calorim 144, 793–803 (2021). https://doi.org/10.1007/s10973-020-09421-4
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DOI: https://doi.org/10.1007/s10973-020-09421-4