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Thermal analysis for radiative flow of magnetized Maxwell fluid over a vertically moving rotating disk

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Abstract

In the current framework, we study the chemically reactive Maxwell fluid flow over a vertically moving upward/downward rotating disk during the unsteady motion in the presence of magnetic flux. The problem formulation is made in a manner that governing equations of the physical phenomenon ultimately reduce to classical von Karman viscous pumping problem in the absence of vertical motion. Additionally, the aspects of chemical reaction and nonlinear radiations on heat and mass transfer analysis are studied. For the analysis, we use the similarity transformations that convert the governing system of partial differential equations into ordinary ones. The solution of the transformed system is obtained numerically using bvp4c in MATLAB. The numerical outcomes are demonstrated through graphical and tabular depictions. The results of velocity, temperature and concentration fields are discussed in the presence of upward/downward motion of the disk, magnetic parameter, Deborah number, Schmidt number and chemical reaction parameter. Significant outcomes reveal that the impact of disk upward motion parameter boosts the radial and angular flows. It is further noted that the heat transfer rate grows considerably with the disk rotation and radiation parameters. Moreover, Schmidt and chemical reaction parameters play a vital role in enhancing the Sherwood number.

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Abbreviations

\(r,\varphi ,z\) :

Cylindrical coordinate

\(u,\,v,\,w\) :

Velocity components \(( \mathrm{m\,s}^{-1})\)

a(t):

Vertical distance (m)

\(\dot{a}(t)\) :

Vertical velocity \(( \mathrm{m\,s}^{-1})\)

h :

Location of vertically moving disk (m)

T :

Temperature of fluid (k)

\(\Omega (t)\) :

Angular velocity \((\mathrm{rad\,s}^{-1})\)

S :

Up/down motion of disk \(( \mathrm{m\,s}^{-1})\)

\(\lambda _{1}\) :

Relaxation time parameter

\(\nu\) :

Kinematic viscosity \((\mathrm{m}^{2}\,\mathrm{s})\)

M :

Magnetic field

F :

Dimensionless radial velocity

H :

Dimensionless axial velocity

\(\theta _{\mathrm{w}}\) :

Temperature ratio parameter

\(B_{0}\) :

Magnetic field strength \(( \mathrm{N}\,\mathrm{s}\,\mathrm{C}^{-1}\,\mathrm{m}^{-1})\)

D :

Diffusion coefficient

\(\mathrm{Kr}\) :

Reaction rate

c :

Arbitrary constant

\(\gamma\) :

Biot number

\(\alpha _{1}\) :

Wall temperature parameter

\(\alpha _{2}\) :

Wall concentration parameter

\(\alpha\) :

Thermal diffusivity \((\mathrm{m}^{2}\, \mathrm{s}^{-1})\)

Re:

Reynolds number

\(T_{\infty }\) :

Ambient fluid temperature (K)

\(T_{\mathrm{w}}(t)\) :

Wall temperature (K)

\(\rho c_{\mathrm{p}}\) :

Heat capacity of fluid \(( \mathrm{J}\,\mathrm{m}^{-2}\, \mathrm{K}^{-1})\)

\(\eta\) :

Dimensionless variable

\(\theta\) :

Dimensionless temperature

\(\omega\) :

Rotation parameter

\(C_{\infty }\) :

Ambient concentration

\(C_{\mathrm{w}}(t)\) :

Wall concentration

\(\beta _{1}\) :

Deborah number

G :

Dimensionless azimuthal velocity

\(q_{\mathrm{rad}}\) :

Radiative heat flux \(( \mathrm{W}\,\mathrm{m}^{-2})\)

\(\phi\) :

Dimensionless concentration

\(\mathrm{Nu}_{\mathrm{r}}\) :

Local Nusselt number

\(\mathrm{Sh}_{\mathrm{r}}\) :

Local Sherwood number

\(\rho\) :

Fluid density \((\mathrm{kg}\,\mathrm{m}^{-3})\)

\(\mathrm{Pr}\) :

Prandtl number

\(\delta\) :

Boundary layer thickness

\(\mathrm{Rd}\) :

Radiation parameter

\(\mu\) :

Dynamic viscosity \((\mathrm{kg}\,\mathrm{m}^{-1}\,\mathrm{s}^{-1})\)

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Acknowledgements

This work has the financial supports from Higher Education Commission (HEC) of Pakistan under the Project Number: 6210.

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000, Pakistan

    Masood Khan, Jawad Ahmed & Wajid Ali

  2. Department of Basic Sciences, University of Engineering and Technology, Taxila, 47050, Pakistan

    Jawad Ahmed

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  1. Masood Khan
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Correspondence to Jawad Ahmed.

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Khan, M., Ahmed, J. & Ali, W. Thermal analysis for radiative flow of magnetized Maxwell fluid over a vertically moving rotating disk. J Therm Anal Calorim 143, 4081–4094 (2021). https://doi.org/10.1007/s10973-020-09322-6

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