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Finite Difference Approach for Critical Value Analysis to Describe Jeffery–Hamel Flow Toward an Inclined Channel with Microrotations

  • Research Article-Mechanical Engineering
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Abstract

The present article is framed to describe the Jeffery–Hamel flow toward an inclined channel through critical value analysis by using finite difference approach in the occurrence of microrotations and viscous dissipation. Study is carried out by utilizing the fundamental equations of fluid flow, and nonlinear problem is solved by using finite difference method of Keller box. The flow regime is investigated by graphical interpretations of the numerical results corresponding to the variation in physical parameters. Likewise, the stability of the flow in divergent channel is studied by tabulating the critical Reynolds number. The critical Reynolds is computed for variation in opening angle of channel, material parameter and Weissenberg number. It is observed that where increase in Weissenberg number and greater channel opening angles seem to be halting the flow in the diverging, increasing the number of micro-rotating structures is bringing about stability in the flow.

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Abbreviations

r, \(\theta \), z :

Cylindrical coordinate

u, v, w :

Velocity components in r-, \(\theta \)- and z-directions, respectively,

\(\rho \) :

Density

P :

Pressure

N :

Angular momentum

\(\tau \) :

Stress tensor

\(\mu _{0}\) :

Dynamic viscosity

\(\gamma \) :

Spin gradient viscosity

\(\alpha _{1},\alpha _{2},\alpha _{3}\) :

Material parameters

D :

Velocity stress tensor

\(\nabla V\) :

Velocity gradient

\(\kappa ^{*}\) :

Rotational viscosity parameter

\(\psi _{1,0}\), \(\psi _{2,0}\) :

Elasticity parameter

\(\eta \) :

Dimensionless space variable

F :

Linear velocity

G :

Angular velocity

\(\mathrm {Re}\) :

Reynold number

Wi:

Weissenberg number

K :

Material parameter

\(C_{\mathrm{f}}\) :

Skinfriction

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Authors and Affiliations

  1. Department of Mathematics, Capital University of Science and Technology, Islamabad, Pakistan

    Abid Kamran & Naveed Akmal

  2. Department of Mathematics and Statistics, PMAS Arid Agriculture University, Rawalpindi, Pakistan

    Ehtsham Azhar & Zaffar Mehmood

  3. Department of Mathematics, Faculty of Sciences, HITEC University, Taxila, Pakistan

    Z. Iqbal

Authors
  1. Abid Kamran
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  2. Ehtsham Azhar
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  3. Naveed Akmal
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  4. Zaffar Mehmood
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  5. Z. Iqbal
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Correspondence to Ehtsham Azhar.

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Kamran, A., Azhar, E., Akmal, N. et al. Finite Difference Approach for Critical Value Analysis to Describe Jeffery–Hamel Flow Toward an Inclined Channel with Microrotations. Arab J Sci Eng 47, 15261–15268 (2022). https://doi.org/10.1007/s13369-021-06532-4

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  • DOI: https://doi.org/10.1007/s13369-021-06532-4

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