Universal Journal of Mechanical Engineering 7(5): 264-271, 2019 http://www.hrpub.org
DOI: 10.13189/ujme.2019.070503
Oscillating Free Convection Flow between Two Parallel
Plates with Mass Diffusion
Fasihah Zulkiflee
1
, Ahmad Qushairi Mohamad
1
, Mohd Rijal Ilias
2
, Sharidan Shafie
1,*
1
Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Malaysia
2
Department of Mathematical Sciences, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Malaysia
Received July 1, 2019; Revised August 22, 2019; Accepted September 22, 2019
Copyright©2019 by authors, all rights reserved. Authors agree that this article remains permanently open access under
the terms of the Creative Commons Attribution License 4.0 International License
Abstract This paper studied unsteady free convection
flow between two parallel plates with mass diffusion. One
of the plates is considered oscillating. Appropriate
non-dimensional variables are used to reduce the
dimensional governing equations along with imposed
initial and boundary conditions. The exact solution to
velocity, temperature and concentration profiles are
obtained using the Laplace Transform technique. The
graphical results of the solutions are presented to illustrate
the behavior of the fluid flow with the influence of Schmidt
number, Prandtl number, oscillating parameter, Grashof
and mass Grashof number. The corresponding expressions
for skin friction, Nusselt number and Sherwood number are
also calculated. It is observed that increasing Prandtl and
Schmidt numbers will increased the Nusselt number but
decreased the skin friction.
Keywords Free Convection, Mass Diffusion,
Oscillating, Parallel Plates
1. Introduction
The fluid flows between parallel plates have received
much attention due to the various applications involving
heat transfer. It has various applications such as in
petroleum industry, purification of crude oil, pumps
accelerators and power generators [1]. Researchers have
taken a great interest investigated problem regarding free
convection flow between two parallel plates [2-4]. Singh
investigated transient natural convection between two
vertical walls heated/cooled asymmetrically [5]. Narahari
[6] investigated natural convection flow in vertical channel
with ramped wall temperature at one boundary while Paul
[2] investigated transient free convective flow in vertical
channel with constant temperature and constant heat flux.
In other research, Jha [7] investigate free convection heat
and mass transfer flow in a vertical channel with Dufour
effect and then extended their research with
diffusion-thermo effects on free convective heat and mass
transfer flow in a vertical channel with symmetry boundary
condition [8].
Oscillatory flow between parallel plates has received
some attention of the researchers as because researchers
found that oscillatory plates can higher the rates of heat
transfer [9]. There are many researchers considering
oscillation in their research such as [10-12] but not many
considering oscillations in between two parallel plates. The
literature survey shows that researches on oscillating flow
between two parallel plates are very few. Reddy [13]
investigated unsteady MHD free convection oscillatory
Coette flow through a porous medium with periodic wall
temperature in presence of chemical reaction and thermal
radiation. While MHD oscillatory flow through a porous
channel saturated with porous medium was investigated by
Falade [14]. Bunyonyo [9] investigated unsteady
oscillatory Coette flow between vertical plates with
constant radiative heat flux. Their research shows that the
oscillatory parameter played a greater role in causing the
fluid to oscillate inside the Coette channel.
Motivated by above investigations, the present analysis
is to investigate oscillatory free convection flow between
two parallel plates with mass diffusion. This problem will
be solved using Laplace Transform method to obtain exact
solution.
2. Materials and Methods
Consider an unsteady free convection flow between two
parallel plates with mass diffusion. Oscillating plate at
y’=0 is considered. The configuration flow of the problem
is presented in Figure 1. The flow is governed by the
following equations under the usual Boussinesq’s
approximations: