A study of heat transfer analysis for squeezing flow of a Casson fluid via differential transform method

  • Syed Tauseef Mohyud-Din
  • Muhammad Usman
  • Wei Wang
  • Muhammad Hamid
Original Article

Abstract

In this article, differential transform method is proposed and applied for semi-analytic solution of heat transfer analysis for the squeezing flow of a Casson fluid between parallel circular plates. Similarity transformation reduces this model into an equivalent system of two strongly nonlinear ordinary differential equations. Fourth-order Runge–Kutta method has also been applied to support our analytical solution, and the comparison shows an excellent agreement.

Keywords

Differential transform method Casson fluid Squeezing flow and numerical solution 

List of symbols

\( z = \pm l\sqrt {1 - \alpha t} \)

Distance between two plates

\( \mu_{B} \)

Dynamic viscosity of the non-Newtonian fluid

\( p_{y} \)

Stress of fluid

\( \pi \)

Product of component of deformation rate

\( e_{ij} \)

Deformation rate

\( \hat{u} \) and \( \hat{v} \)

Velocity components in \( \hat{x} \) and \( \hat{y} \) directions

\( \hat{p} \)

Pressure

T

Temperature parameter

m

Kinematic viscosity

\( \beta = \mu_{{\mathbf{B}}} \sqrt {2\pi_{c} } /p_{y} \)

Casson fluid parameter

q

Density

Cp

Specific heat

k

Thermal conductivity

\( S = \frac{{\alpha l^{2} }}{2v} \)

Non-dimensional squeeze number

\( Pr = \frac{{\mu C_{p} }}{k} \)

Prandtl number

\( C_{f} = v\left( {1 + \frac{1}{\beta }} \right)\frac{{\left( {\frac{{\partial \hat{u}}}{{\partial \hat{y}}}} \right)_{{\hat{y} = h\left( t \right)}} }}{{v_{w}^{2} }} \)

Skin friction

\( Nu = \frac{{ - lk\left( {\frac{\partial T}{{\partial \hat{y}}}} \right)_{{\hat{y} = h\left( t \right)}} }}{{kT_{H} }} \)

Nusselt number

\( Ec = \frac{1}{{C_{p} }}\left( {\frac{{\alpha \hat{x}}}{{2\left( {1 - \alpha t} \right)}}} \right)^{2} \)

Eckert number

S

Squeeze number describes movement of the plates

Notes

Acknowledgements

Authors are highly grateful to the unknown referees’ for their valuable comments.

Compliance with ethical standards

Conflict of interest

All the authors declare that there is no conflict of interest.

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Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  • Syed Tauseef Mohyud-Din
    • 1
  • Muhammad Usman
    • 2
  • Wei Wang
    • 2
  • Muhammad Hamid
    • 1
  1. 1.Faculty of SciencesHITEC UniversityTaxila CanttPakistan
  2. 2.School of Mathematical SciencePeking UniversityBeijingChina

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