Begell House Inc.
Journal of Porous Media
JPM
1091-028X
17
1
2014
TRANSIENT BEHAVIOR OF MICROPOLAR FLUIDS THROUGH A POROUS WAVY CHANNEL
1-15
10.1615/JPorMedia.v17.i1.10
K. Y.
Hung
Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, No. 415, Jiangong Road, Sanmin District, Kaohsiung 80778, Taiwan, R.O.C.
Tsna-Hui
Hsu
Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, No. 415, Jiangong Road, Sanmin District, Kaohsiung 80778, Taiwan, R.O.C.
J. W.
Lin
Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, No. 415, Jiangong Road, Sanmin District, Kaohsiung 80778, Taiwan, R.O.C.
transient convection
porous wavy channel
micropolar fluid
The transient heat convection phenomena of micropolar fluids flowing through wavy channels with porous media are numerically analyzed by using the coordinate transformation and the spline alternating-direction implicit method. Numerical results considering the material characteristics of micropolar fluids and comparing with Newtonian fluid are discussed in detail Calculations are performed on a personal computer by using the Spline Alternating-Direction Implicit method, which applies the theory of coordinate transformation and transforms complex curves into flat surfaces. The governing equations after nondimensional transformation are expressed with stream function, vortex function, angular momentum and temperature function, and the transient heat transfer effect is determined to discuss transient heat convection of micropolar fluid in vertical wavy channels saturated with porous media. The results indicate that the micropolar fluids have higher flow resistance but lower heat transfer rates. As the wavy surface is lumpy, the displacement of boundary causes the flow field to change and further affects the heat transfer rate. A higher Ri value indicates a more apparent buoyancy effect, reduced recirculation flow in the trough region and increased velocity gradient at the surface, thereby leading to a higher Nusselt number and heat transfer rate. In the case of lower Darcy number flow, the porous media provide a higher heat transfer rate than a single phase flow.
MASS TRANSPORT FOR MIXED CO-CULTURE APPLICATIONS IN A PERFUSION BIOREACTOR PARTIALLY FILLED WITH A POROUS LAYER
17-30
10.1615/JPorMedia.v17.i1.20
H. X.
Bai
Department of Mechanical Engineering, National University of Singapore, Singapore 117576
Peng
Yu
Southern University of Science and Technology
Y.
Zeng
Department of Mechanical & Aerospace Engineering, Nanyang Technological University, Singapore 639798
Sonny H.
Winoto
Department of Mechanical Engineering, National University of Singapore, Singapore 117576
Hong-Tong
Low
Division of Bioengineering, Department of Mechanical Engineering, National University of Singapore, Singapore 117576
mass transfer
perfusion bioreactor
porous scaffold
Michaelis-Meten model
cell
co-culture
A simplified analysis is carried out to derive the analytical solution of the mass transfer equation in a microchannel bioreactor, which has a porous wall for the co-culture of two types of cells distributed randomly and uniformly. Based on the analysis, a group of dimensionless parameters is proposed, which can be applied to correlate the numerical data and characterize the mass transfer in the bioreactor. The normalized numerical data, for the concentration at the porous-fluid interface and concentration difference between the interface and the base, show satisfactory correlation when presented as a function of the effective distance parameter. Two cell culture examples are presented to demonstrate the general applications of the correlated results in the design of a co-culture microchannel bioreactor with a porous wall.
NONLINEAR THERMOHALINE MAGNETOCONVECTION IN A SPARSELY PACKED POROUS MEDIUM
31-57
10.1615/JPorMedia.v17.i1.30
A. Benerji
Babu
Department of Mathematics, National Institute of Technology Warangal, Warangal 506004, A.P., India
Ragoju
Ravi
Department of Humanities and Sciences, National Institute of Technology Goa, Ponda, Goa-403401
S. G.
Tagare
Disha Institute of Management and Technology, Satya vihar, Vidhan Sabha-Chandrakhuri Marg 492101, Raipur, India
convection
bifurcation points
Landau-Ginzburg type equations
secondary instabilities
Nusselt number
stability regions of standing and travelling waves
The Darcy-Lapwood-Brinkman model with the Boussinesq approximation is used to study the linear and nonlinear stability analysis and obtain the conditions for the occurrence of various types of bifurcations, viz., Pitchfork bifurcation, Hopf bifurcation, and Takens-Bogdanov bifurcation points. We have used stress-free boundary conditions and derived a nonlinear two-dimensional Landau-Ginzburg equation with real coefficients at the supercritical pitchfork bifurcation and discussed the effect of Nusselt number on the heat transport by convection. We have shown the occurrence of secondary instabilities such as Eckhaus and Zigzag instabilities. We also derive two coupled one-dimensional Landau-Ginzburg type equations with complex coefficients near the onset of oscillatory convection at supercritical Hopf bifurcation and discussed traveling and standing wave convection.
EFFECTS OF PERMEABILITY ON SWIMMING OF A MICRO-ORGANISM IN AN OLDROYD-B FLUID
59-66
10.1615/JPorMedia.v17.i1.40
Muhammad
Sajid
Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
Nasir
Ali
Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
Abdul Majeed
Siddiqui
Department of Mathematics, Pennsylvania State University, York Campus, 1031 Edgecomb Avenue, York, PA 17403, USA
Zaheer
Abbas
Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
Tariq
Javed
Department of Mathematics and Statistics, Faculty of Basic and Applied Science, International
Islamic University, Islamabad 44000, Pakistan
swimming sheet
Oldroyd-B fluid
porous medium
Darcy's law
Self-propulsion or swimming of a micro-organism in an Oldroyd-B fluid flowing through a porous medium is modeled in this paper using a waving sheet having small amplitude. The solution of the problem is obtained using a method of successive approximation up to second order. The results thus obtained for the swimming velocity show that the self-propulsion decreases with an increase in the permeability and converges to the results for a clear medium in the limit when K → ∞. The analytical expression for the rate of work of the propelling sheet is also provided.
HYDROMAGNETIC NATURAL CONVECTION FLOW WITH RADIATIVE HEAT TRANSFER PAST AN ACCELERATED MOVING VERTICAL PLATE WITH RAMPED TEMPERATURE THROUGH A POROUS MEDIUM
67-79
10.1615/JPorMedia.v17.i1.50
Gauri S.
Seth
Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand-826004, India
Syed Modassir
Hussain
Department of Mathematics, O. P. Jindal Institute of Technology, Raigarh-496001, India
Subharthi
Sarkar
KIIT Bhubaneswar
hydromagnetic natural convection
ramped temperature
radiation
thermal diffusion Nusselt number
Unsteady hydromagnetic natural convection flow of an electrically conducting, viscous, and incompressible fluid past an accelerated moving vertical flat plate with ramped temperature through a porous medium in the presence of radiation and thermal diffusion is studied. The exact solutions of momentum and energy equations, under Boussinesq and Rosseland approximations, are obtained in closed form by Laplace transform technique. The expressions for skin friction and Nusselt number are also derived. The numerical values of fluid velocity and fluid temperature are shown graphically whereas that of skin friction and Nusselt number are presented in tabular form for various values of pertinent flow parameters. Natural convection flow near a ramped temperature plate is also compared with the flow near an isothermal plate.
INFLUENCE OF HALL CURRENT ON OSCILLATORY COUETTE FLOW IN THE PRESENCE OF AN INCLINED MAGNETIC FIELD THROUGH POROUS MEDIUM
81-92
10.1615/JPorMedia.v17.i1.60
Masood
Khan
Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan
Saira
Saeed
Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan
Constantin
Fetecau
Academy of Romanian Scientists, Bucuresti 050094, Romania
M.
Azram
Department of Science in Engineering, Faculty of Engineering, IIUM Kuala Lumpur 50727, Malaysia
oscillatory Couette flow
inclined magnetic field
Hall current
porous medium
The aim of this paper is to construct an exact solution corresponding to the oscillatory Couette flow in a rotating system. An incompressible viscous fluid occupies the porous medium in a rotating horizontal parallel-plate channel subject to a uniform strength, static, oblique magnetic field acting at an angle Θ to the positive direction of the axis of rotation. The flow is generated by the nontorsional oscillations of both plates. Hall effects are taken into account and an exact solution is obtained by using the Laplace transform technique. Moreover, asymptotic behavior of the obtained solution is also analyzed for several cases. The effects of the pertinent parameters such as the Hall current parameter (m), rotation parameter (K2), Hartmann number (M2), Darcy number (Da), and magnetic field inclination (Θ) on the velocity profiles are graphically depicted and studied in detail.