Page 52 - programme book

FD-003
Slip Velocity Effect on Unsteady Free Convection Flow of Casson Fluid in a
Vertical Cylinder

Wan Faezah Wan Azmi 1, a) , Ahmad Qushairi Mohamad 1, b) , Lim Yeou Jiann 1, c) and Sharidan
Shafie 1, d)

1 Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia,
81310 UTM Johor Bahru, Johor, Malaysia

a) wanfaezah@graduate.utm.my
b) Corresponding author: ahmadqushairi@utm.my
c) jiann@utm.my
d) sharidan@utm.my

Abstract. Fluid flow velocity is influenced by slip velocity at the boundary, and it does exist in real-
life applications such as blood flow in the arteries. The study aims to obtain analytical solutions and
understand the fluid flow behavior with the slip velocity effect for the unsteady free convection flow
of Casson fluid in a cylinder. Governing equations of momentum and energy are converted into
dimensionless forms by using the appropriate dimensionless variables. Then, the joint methods of
Laplace transform with respect to time variable and finite Hankel transform of zero-order with respect
to the radial coordinate are employed to obtain dimensionless equations of velocity and temperature
together with the initial and boundary conditions. The expression of analytical solutions of velocity
and temperature profiles are obtained. The obtained analytical solutions satisfy all the initial and
boundary conditions. The behavior of velocity and temperature profiles are plotted and discussed
graphically. Based on the obtained result, it can be observed that increase in the Casson parameter,
Grashof number, time and slip velocity will lead to increment in fluid velocity and temperature.
Meanwhile, increment of Prandtl number leads to the decrement of fluid velocity and fluid
temperature. Lastly, the present result is validated when the obtained analytical solution of velocity is
compared with the published result and found in a good mutual agreement. Thus, the study is
significant to explore the uniqueness of Casson fluid behavior since it is related to the nature of blood
flow in small blood vessels.

Keywords: Casson fluid, slip velocity, free convection, Laplace transform, finite Hankel transform

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