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

• Syed Tauseef Mohyud-Din
• Wei Wang
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.

### Conflict of interest

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

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© The Natural Computing Applications Forum 2017

## Authors and Affiliations

• Syed Tauseef Mohyud-Din
• 1