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**Exact solutions for unsteady free convection flow of Casson fluid over an oscillating vertical plate with constant wall temperature.**
*(English)*
Zbl 1356.35179

Summary: The unsteady free flow of a Casson fluid past an oscillating vertical plate with constant wall temperature has been studied. The Casson fluid model is used to distinguish the non-Newtonian fluid behaviour. The governing partial differential equations corresponding to the momentum and energy equations are transformed into linear ordinary differential equations by using nondimensional variables. Laplace transform method is used to find the exact solutions of these equations. Expressions for shear stress in terms of skin friction and the rate of heat transfer in terms of Nusselt number are also obtained. Numerical results of velocity and temperature profiles with various values of embedded flow parameters are shown graphically and their effects are discussed in detail.

### MSC:

35Q35 | PDEs in connection with fluid mechanics |

76A05 | Non-Newtonian fluids |

76T20 | Suspensions |

35C05 | Solutions to PDEs in closed form |

44A10 | Laplace transform |

76R10 | Free convection |

34A30 | Linear ordinary differential equations and systems |

### Keywords:

Casson fluid; non-Newtonian fluid; linear ordinary differential equations; Laplace transform; Nusselt number
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\textit{A. Khalid} et al., Abstr. Appl. Anal. 2015, Article ID 946350, 8 p. (2015; Zbl 1356.35179)

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### References:

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