Begell House
Journal of Porous Media
Journal of Porous Media
1091-028X
18
7
2015
ANALYTICAL INVESTIGATION FOR FREE CONVECTIVE FLOW OF NON-NEWTONIAN NANOFLUIDS FLOW IN POROUS MEDIA WITH GYROTACTIC MICROORGANISMS
An approximate analytical investigation for free convection of non-Newtonian nanofluids over an isothermal impermeable horizontal flat plate, which is placed in a porous quiescent medium filled with non-Newtonian power law nanofluids, is carried out in this paper. A further assumption is also made that the medium contains both nanoparticles and gyrotactic microorganisms. The horizontal plate is deemed to have uniform surface temperature, solute, nanoparticles concentration, and density of motile microorganisms. The governing equations are transformed into a system of non-linear ordinary differential equation using suitable similarity transformations. Approximate analytical solutions for the dimensionless velocity, temperature, nanoparticle concentration, and density of the motile microorganisms are obtained using the optimal homotopy asymptotic method (OHAM). The effects of important control parameters on the dimensionless velocity, temperature, nanoparticles concentration, and density of motile microorganisms, as well as on the local Nusselt, Sherwood, and motile microorganism numbers, are obtained and analyzed. It is found that nanofluid and bioconvection parameters have strong effects on local Nusselt, Sherwood, and density numbers.
FAZLE
MABOOD
Edwardes College Peshawar, Pakistan
Waqar A.
Khan
Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada
Ahmad I. Md.
Ismail
School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia
653-663
MULTIPLE SLIP EFFECTS ON UNSTEADY MHD REAR STAGNATION POINT FLOW OF NANOFLUIDS IN A DARCIAN POROUS MEDIUM
The unsteady magnetohydrodynamic flow of a viscous incompressible fluid past a permeable vertical plate in a Darcian porous medium is investigated theoretically and numerically. A time-dependent magnetic field is applied normal to the plate. Cu-water nanofluid with different solid volume fraction of copper nanoparticles is considered. Using suitable similarity transformations, the governing partial differential equations are reduced to a system of nonlinear ordinary differential equations; linearized using a successive linearization method and then solved using a finite difference method. The effects of the controlling parameters on the dimensionless velocity, temperature, concentration, wall shear stress, heat and mass transfer rates are investigated. The numerical results are compared to published results and good agreement is observed.
Waqar A.
Khan
Department of Engineering Sciences, PN Engineering College, National University of Sciences and Technology, Karachi; CHASHMA Nuclear Power Plant, Pakistan Atomic Energy Commission, Mianwai, Pakistan
Mohammed Jashim
Uddin
School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia; Department of Mathematics, American International University-Bangladesh, Banani, Dhaka 1213, Bangladesh
Ahmad I. Md.
Ismail
School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia
665-678
FLUID FLOW AND HEAT TRANSFER THROUGH AN ANNULAR SECTOR DUCT FILLED WITH POROUS MEDIA
In this paper we have numerically studied the forced convection heat transfer to fully developed flow of constant properties incompressible Newtonian fluid through an annular sector duct filled with Darcy-Brinkman porous media. The problem is modeled subject to constant heat flux boundary conditions applied at the heat transferring surfaces. The mean velocity and the product of friction factor with Reynolds number are used to study the flow characteristics, whereas the bulk temperature and the Nusselt number are used to characterize the convective heat transfer. The results of the limiting cases obtained in this study are in agreement with the literature, thus validating the mathematical model and solution procedure used in this study.
Mazhar
Iqbal
SNS, National University of Sciences and Technology, Islamabad, Pakistan
Hamna
Afaq
SNS, National University of Sciences and Technology (NUST), Islamabad, Pakistan
679-687
RADIAL VOIDAGE VARIATION IN PACKED BEDS OF UNIFORMLY SIZED SPHERES: THEORY AND EXPERIMENT
The porosity of 0.377 far away from the wall of cylindrical containers is deduced based on three possible stable and quasi-stable packed configurations, and the probability of each configuration is assumed the same. A model considering the bulk porosity 0.377 and the influence of column-to-sphere diameter ratio D/d is proposed to predict the radial porosity distribution in cylindrical containers packed with uniformly sized spheres. The model is validated by available experimental data in the literature and the present experimental work.
Yin-Bin
Lu
MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, P.R. China
Gui-Hua
Tang
MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, P.R. China
689-698
CONJUGATE NATURAL CONVECTION IN A DIFFERENTIALLY HEATED COMPOSITE ENCLOSURE FILLED WITH A NANOFLUID
Laminar natural convection inside a square composite vertically layered cavity is studied numerically using under a successive relaxation (USR) upwind-scheme finite difference method. The cavity is set up as follows from the left: a solid wall, a porous layer, and a nanofluid layer. The porous layer is saturated with the same nanofluid. The cavity is heated isothermally from the solid wall and cooled from the right wall. The top and bottom walls are kept adiabatic. All the walls are assumed impermeable, except the interface between the porous and nanofluid layers. The Darcy−Brinkman model is invoked for the porous layer. Double-domain formulation is followed for the porous and nanofluid layers. The studied parameters are Darcy number Da (10−7−10−1), Rayleigh number Ra (103−106), wall thermal conductivity kw (0.269, 14.589 W/m.°C), thicknesses of layers Ww (0.1−0.7), Wp (0.1−0.5), and the Cu nanoparticle volume fraction φ (0.0−0.05). Alternative models for the nanofluid thermal conductivity and dynamic viscosity are used, and a comparison among different models combinations is conducted. The results show that the enhancement of natural convection is attained when the permeability (Da) of the porous medium is very low and the porous layer thickness is greater than 0.5, provided that the Rayleigh number is less than or equal to 104. The solid wall type is found to play a considerable role in the flow and heat transfer fields. It is also found that the conduction heat transfer within the solid wall is affected by the permeability of the porous layer.
Muneer A.
Ismael
Mechanical Engineering Department, Engineering College, University of Basrah, Basrah, Iraq
Ali J.
Chamkha
Department of Mechanical Engineering, Prince Mohammad Bin Fahd University, P.O. Box
1664, Al-Khobar 31952, Kingdom of Saudi Arabia;
Prince Sultan Endowment for Energy and Environment, Prince Mohammad Bin Fahd
University, Al-Khobar 31952, Saudi Arabia
699-716
ESTIMATING THE UNSATURATED SOIL HYDRAULIC PROPERTIES FROM A REDISTRIBUTION EXPERIMENT: APPLICATION TO SYNTHETIC DATA
In this study, we used HYDRUS-1D to simulate redistribution of water flow from a wet soil sample on the top into the dry soil sample at the bottom and to estimate soil hydraulic properties by inverse solution. Real-time surface contact tensiometers were assumed to monitor soil pressure head at two depths (one at a depth of 0 cm, located on the wet sample, the other at a depth of 12 cm, located at the bottom of the dry sample) during a 5-hour-long laboratory water redistribution experiment. Soil water retention curve, soil hydraulic parameters (saturated water content θa, soil bulk density, saturated hydraulic conductivity Ka), and soil organic matter were assumed as known. The soil hydraulic parameters (empirical shape parameters α and n) were estimated from time-varying pressure head measurements and soil water retention data by solving a one-dimensional, inverse water redistribution problem using HYDRUS-1D. The simulated pressure head and soil water retention curve during the redistribution experiment compared favorably with their corresponding observed values. To find answers to the questions of uniqueness, identifiability, and stability of different experimental setups, a numerical example of redistribution was carried out. The uniqueness of the inverse solution was analyzed using numerical experiments to estimate two soil hydraulic parameters (α, n) of the Mualem−van Genuchten model. To study the shape of the objective function near its minimum, response surfaces for the estimated parameters were generated. The response surfaces for both cases (with and without error in observations) indicated that the performance of the redistribution experiment is reasonable for inverse parameter estimation.
Mohammad
Nakhaei
Faculty of Earth Sciences, Kharazmi University, Tehran, Iran
Vahab
Amiri
Faculty of Earth Sciences, Kharazmi University, Tehran, Iran
717-729
A MATHEMATICAL MODEL FOR THERMAL FLOODING WITH EQUAL ROCK AND FLUID TEMPERATURES
Accurate prediction of the temperature profile within a reservoir undergoing a thermal recovery process is a key factor in process design, production forecasting, and reservoir management. Such a profile is governed by the rock and fluid properties and heat transfer between them. As a result, the temperature distribution is highly dependent on the thermal and rheological properties of the rock and fluids. The present research investigates the role of temperature-dependent rock and fluid properties in the development of the temperature profile during thermal flooding of an oil reservoir. The concept of "memory" is included to analyze the evolution of rock/fluid properties as continuous time functions. A mathematical model is developed in terms of a group of heat transfer dimensionless numbers that correlate the varying rock and fluid properties. The model equation was solved numerically through MATLAB programming language to produce temperature profiles for a typical thermal flood where the rock attains the fluid temperature instantaneously. The temperature distribution was found to concave down smoothly within the heated region. The proposed heat transfer dimensionless numbers, which characterize the process and encompass many of its variables, provide relationships between the rock and fluid properties within the porous medium. They have significant roles in the temperature profile as related to continuous alteration phenomena in addition to system fluid velocity, time, and other rheological parameters of rock and fluid. The mathematical model and its numerical solution are useful for better prediction of reservoir performance.
M. Enamul
Hossain
King Fahd University of Petroleum & Minerals (KFUPM), Dhahran, Saudi Arabia; Memorial University of Newfoundland, St. John's, Newfoundland and Labrador, Canada
Sidqi A.
Abu-Khamsin
Department of Petroleum Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Kingdom of Saudi Arabia
Abdul-Aziz
Al-Helali
Department of Computer Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Kingdom of Saudi Arabia
731-744