Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
16
4
2013
VARIATIONAL ITERATION METHOD FOR THERMAL DIFFUSION AND DIFFUSION THERMO EFFECTS OF THIXOTROPIC FLUID THROUGH BIOLOGICAL TISSUES WITH LASER RADIATION EXISTENCE
Thermal diffusion and diffusion thermoeffects on the thixotropic fluid obeying Harris rheological model with laser applications through biological tissues have been modeled by using a group of partial nonlinear differential equations with appropriate boundary conditions. The system of nonlinear partial differential equations describing the momentum, energy, mass, and bioheat transfer has been solved by using a variational iteration method. The distributions of the fluid temperature and concentration are obtained as a function of physical parameters of the fluid. During the course of discussion the tissue temperatures, shear stress, and fluid pressure are also obtained. The effects of the problem parameters on these solutions are discussed numerically and illustrated by a set of figures.
Assma F.
Elsayed
Mathematics Department, Faculty of Applied Science, Tibah University Almadinah Al Monwara, Saudi Arabia, and Mathematics Department, Faculty of Education, Ain Shams, University, Heliopolis, Cairo, Egypt
277-289
CONJUGATE NATURAL CONVECTION IN AN OPEN-ENDED POROUS SQUARE CAVITY
Conjugate natural convection-conduction heat transfer in an open-ended porous square cavity with a finite wall thickness is studied numerically in the present article for a wide variety of thermal boundary conditions. The Forchheimerâ€“Brinkmanâ€“extended Darcy model is used in the mathematical formulation for the porous layer, and the COMSOL is applied to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (103 ≤ Ra ≤ 106), the porosity of the porous medium (0.4 ≤ ε ≤ 0.99), the wall-to-porous medium conductivity ratio (0.1 ≤ Kr ≤ 10.0), and the ratio of wall thickness to its width (0.02 ≤ D ≤ 0.4). The results are presented to show the effect of these parameters on the fluid flow and heat-transfer characteristics. The fluid in the bottom cavity was found stagnant at the relative low- and moderate-conductivity ratio for a case heating from above. It is also found that decreasing the thickness of the solid wall and/or increasing the porosity increases the flow circulation and the heat transfer for the various conductivity ratios and several thermal configurations.
Habibis
Saleh
School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia
I
Hashim
291-302
PULSATING FLOW OF AN INCOMPRESSIBLE MICROPOLAR FLUID BETWEEN PERMEABLE BEDS WITH AN IMPOSED UNIFORM MAGNETIC FIELD
In this paper, we investigate the pulsating flow of an incompressible and slightly conducting micropolar fluid between two homogeneous permeable beds under the influence of imposed uniform magnetic field. The micropolar fluid is injected into the channel from the lower permeable bed with a certain velocity and is sucked into the upper permeable bed with the same velocity. The fluid is driven by an unsteady pulsating pressure gradient. It is assumed that the uniform magnetic field is imposed in a direction normal to the flow. The flow between the permeable beds is assumed to be governed by micropolar fluid flow equations of A. C. Eringen and that in the permeable regions by Darcy's law. The Beavers-Joseph (BJ) slip boundary conditions are employed at the interfaces of the permeable beds. The equations are solved analytically
and the expressions for velocity and microrotation are obtained. The effects of the magnetic parameter and the other material parameters on velocity and microrotation are studied and the results are presented through graphs.
T. K. V.
Iyengar
Department of Mathematics, National Institute of Technology, Warangal-506004, Andhra Pradesh, India
Punnamchandar
Bitla
Dept of Mathematics, Amrita School of Engineering, Coimbatore, Amrita Vishwa Vidyapeetham, Amrita University, India, 641112
303-314
THERMO-DIFFUSION AND DIFFUSION-THERMO EFFECTS ON FREE CONVECTION FLOW PAST A HORIZONTAL CIRCULAR CYLINDER IN A NON-DARCY POROUS MEDIUM
An analysis is presented for the steady free convection heat and mass transfer past a horizontal circular cylinder plate in a non-Darcy porous medium with Soret (thermo-diffusion) and Dufour (diffusion-thermo) effects included. The non-Darcy effects are simulated via a second-order Forchheimer drag force term in the momentum boundary-layer
equation. A parametric study illustrating the influence of Darcy parameter Da, Forchheimer parameter Λ, Grashof
number Gr, Schmidt number Sc, Soret number Sr, Dufour number Du, transpiration parameter fw, on the fluid velocity, temperature, and concentration profiles, as well as local skin friction, Nusselt, and Sherwood numbers, is conducted. Increasing Darcy number accelerates the flow due to a corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance. Applications of the model arise in metallurgical materials processing, chemical engineering, flow control, etc.
V. Ramachandra
Prasad
Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle,
India
B
Vasu
Motilal Nehru National Institute of Technology Allahabad
O. Anwar
Bég
Fluid Mechanics, Nanosystems and Propulsion, Aeronautical and Mechanical Engineering,
School of Computing, Science and Engineering, Newton Building, University of Salford,
Manchester M54WT, United Kingdom
315-334
PULSATILE FLOW IN A CYLINDRICAL TUBE WITH POROUS WALLS: APPLICATIONS TO BLOOD FLOW
The present paper concerns the analytical study of pulsatile flow of Newtonian fluid in a cylindrical tube with a rigid permeable wall. The Brinkman equation is used to formulate flow through the porous region and the Navier-Stokes equation is used for flow of clear fluid. The effect of permeability on wall shear stress and vascular impedance is analyzed. For limiting cases our results agree with that of Womersley.
Ashish
Tiwari
Department of Mathematics, Birla Institute of Technology and Science, Pilani
Satya
Deo
Department of Mathematics, University of Allahabad, Allahabad-211002, India
335-340
SERIES SOLUTION FOR CONVECTIVE-RADIATIVE POROUS FIN USING DIFFERENTIAL TRANSFORMATION METHOD
Enhancement of heat-transfer rate through porous fins is one of the common choices nowadays. As the energy equation is nonlinear, researchers did not concentrate on analyzing porous fins analytically. In this article, the convective-radiative rectangular porous fin was analyzed. The calculations are carried out using the differential transformation method (DTM), which is an analytical solution technique that can be applied to various types of differential equations. The current results are then compared with previously obtained results using the well-known fourth-order Runge-Kutta numerical solution method in order to verify the accuracy of the proposed technique. From the findings, it is revealed that the DTM can achieve accurate results in predicting the solution of such problems. After this verification, the fin
efficiencies and effects of some heat transfer characteristics of the system in this problem, such as porous parameter and radiation parameter, were analyzed.
Mohsen
Torabi
Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Hong Kong
Hessameddin
Yaghoobi
Faculty of Mechanical Engineering, Semnan University, Semnan; Young Researchers and Elite Club, Central Tehran Branch, Islamic Azad University, Tehran, Iran
341-349
INVASION OF PRESSURIZED CLAY SUSPENSIONS INTO GRANULAR SOIL
Soil plastering is important in trenchless tunneling to ensure the stability and the integrity of the wall of a borehole. Two key processes in soil plastering with clay suspensions are viscous invasion (mud spurt) and filter cake formation. This study describes the conditions under which these two different processes occur. The results of experimental and theoretical developments are compared with some data from tunneling projects. Filter cake formation can only commence when the invasion velocity falls below the Peclet criterion for undrained behavior of the suspension. Whether a deep layer of invaded clay suspension or a filter cake develops (and situations in between) depends on the ratio between the time scale of viscous invasion and the time scale of filter cake formation. In clay suspensions with quartz flour filler or
suspended sand, filter cake formation commenced earlier, in agreement with classical filter rules for filter cake formation. The analysis shows how the permeable compressible fabric of colloids influences invasion depth. The presented concept, in which consolidation and rheology are considered, can be utilized to develop drilling fluids designed for specific tasks in tunneling and drilling for hydrocarbon reservoirs. The test results can be used as verification material for porous media models containing a fluid with a permeable compressive fabric of colloids.
A. M.
Talmon
Delft University of Technology, Faculty of Mechanical, Maritime, and Materials Engineering, Mekelweg 2, 2628 CD Delft; Deltares, Marine and Coastal Systems, P.O. Box 177, 2600 MH Delft, The Netherlands
D. R.
Mastbergen
Deltares, Marine and Coastal Systems, P.O. Box 177, 2600 MH Delft, The Netherlands
M.
Huisman
Heerema Marine Contractors, Vondellaan 55, 2332 AA Leiden, The Netherlands
351-365
IMPLICATIONS OF PLACING A POROUS BLOCK IN A MIXED-CONVECTION HEAT-TRANSFER, LID-DRIVEN CAVITY HEATED FROM BELOW
The current numerical study investigates the characteristics of an incompressible laminar, mixed-convection heat transfer in a square lid-driven cavity in the presence of a porous block. The cavity consists of two adiabatic vertical boundaries, a cold top lid that is sliding rightward at a constant speed, and a heated bottom boundary. The governing transport equations within the porous media were treated according to the volume-average theory, while Navier-Stokes equations were employed to represent the transport phenomena in the rest of the cavity. Further, the governing equations were solved
using a finite element formulation based on the Galerkin method of weighted residuals. Comparisons of streamlines,
isotherms, and average Nusselt number were exhibited to show the impact of the Richardson number, porous block size, and location on the transport phenomena within the cavity. The increase of Richardson number brings about an appreciated increase in natural convection effects, which enhances flow mixing and heat-transfer rate. Moreover, the presence of the porous block results in an appreciated increase in Nusselt number when compared against the case with no block, especially for Ri ≈ 1. What is more, the considered blockage ratios of 0.125, 0.25, and 0.5 show close Nusselt number predictions between the two aforementioned cases. It was interesting to notice that the latter third case falls considerably
behind in Nusselt number predictions for Ri < 1 but it surpasses them when Ri exceeds 7. Finally, the optimal heattransfer results were obtained when placing the porous block at the center of the cavity for Ri ≤ 1 while placing it at the bottom section rendered the same objective for Ri > 1.
Abdalla M.
AlAmiri
Mechanical Engineering Department, United Arab Emirates University
367-380