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

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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.

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Abbreviations

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

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

C p :

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

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Acknowledgements

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

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Authors and Affiliations

  1. Faculty of Sciences, HITEC University, Taxila Cantt, Pakistan

    Syed Tauseef Mohyud-Din & Muhammad Hamid

  2. School of Mathematical Science, Peking University, Beijing, 100871, China

    Muhammad Usman & Wei Wang

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  1. Syed Tauseef Mohyud-Din
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Correspondence to Syed Tauseef Mohyud-Din.

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Mohyud-Din, S.T., Usman, M., Wang, W. et al. A study of heat transfer analysis for squeezing flow of a Casson fluid via differential transform method. Neural Comput & Applic 30, 3253–3264 (2018). https://doi.org/10.1007/s00521-017-2915-x

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