Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
37
1
2010
Solidification from a Cooled Boundary with a Mushy Layer Under Conditions of Nonturbulent and Turbulent Heat and Mass Transfer in the Ocean
1-14
Dmitri V.
Alexandrov
Urals State University, Ekaterinburg, Russian Federation
L G.
Nizovtseva
Department of Mathematical Physics, Urals State University, Ekaterinburg 620083, Russian Federation
D.
Lee
Department of Mathematics, Tunghai University Taichung, 407, Taiwan
H.-N.
Huang
Department of Mathematics, Tunghai University Taichung, 407, Taiwan
We present new analytic results relating to the nonstationary Stefan-type problems for the unidirectional solidification of binary solutions with a mushy layer under conditions of nonturbulent and turbulent heat and mass transfer in the liquid phase. Explicit analytical solutions (thickness of mushy layer and growth rates of its boundaries, temperature and salinity distributions, solid phase fraction) of the nonlinear model under consideration are found. Model predictions are in good agreement with existing experimental data.
Variable Permeability Effect on Vortex Instability of Non-Darcian Mixed Convection Flow Over a Horizontal Permeable Surface Embedded in a Saturated Porous Medium
15-30
Ahmed M.
Elaiw
Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71511, Egypt
Fouad S.
Ibrahim
Department of Mathematics, University College, Umm Al-Qura University, Makkah, Saudi
Arabia; Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
Ahmed A.
Bakr
Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt
Rama Subba Reddy
Gorla
Department of Mechanical Engineering, Cleveland State University, Cleveland, OH, 44115 USA; Department of Mechanical Engineering, University of Akron, Akron, Ohio 44325, USA; Department of Mechanical & Civil Engineering, Purdue University Northwest, Westville, IN 46391, USA
A linear stability theory is used to analyze the vortex instability of a horizontal mixed convection boundary layer flow in a saturated porous medium. The non-Darcian effects, which include the inertia force and surface mass flux are examined. The variation of permeability in the vicinity of the solid boundary is approximated by an exponential function. The variation rate itself depends slowly on the streamwise coordinate, such as to allow the problem to possess a set of solutions, invariant under a group of transformations. Velocity and temperature profiles as well as local Nusselt number for the base flow are presented for the uniform permeability (UP) and variable permeability (VP) cases. An implicit finite difference method is used to solve the base flow and the resulting eigenvalue problems are solved numerically. The critical Peclet number and the associated wave number are obtained for both UP and VP cases. The results indicate that, the inertial coefficient reduces the heat transfer rate and destabilizes the flow to the vortex mode of disturbance. The effect of variable permeability tends to increase the heat transfer rate and destabilize the flow to the vortex mode of disturbance. Further, for blowing, the Nusselt numbers are lower than those for an impermeable surface and the flow is more susceptible to the vortex instability, while the opposite trend is true for suction.
The Onset of Heat Transfer in Multiple Layers
31-41
Salah Abd El-Aziem
El-Kholy
Department of Mathematics, Faculty of Science, Menoufia University Shebin El-Kom, Egypt
Rama Subba Reddy
Gorla
Department of Mechanical Engineering, Cleveland State University, Cleveland, OH, 44115 USA; Department of Mechanical Engineering, University of Akron, Akron, Ohio 44325, USA; Department of Mechanical & Civil Engineering, Purdue University Northwest, Westville, IN 46391, USA
The onset of convection in a system consisting of a horizontal fluid layer and a layer of porous media saturated with the same fluid, with heating from below, are considered. The two surfaces are rigid. A solution is obtained under parallel flow assumption for constant-flux thermal boundary conditions for which the onset of cellular convection occurs. The critical Rayleigh number and Nusselt number depend on the depth ratio η, the thermal conductivity ratio k, and the Darcy number Da. Results are given for a range of values of each of the governing parameters. The results are compared to limiting cases of the problem for standard terrestrial conditions or microgravity and are found to be in good agreement.
Hydrodynamic Channel Flow Modeling Using Combined Large Eddy Simulation and Wall Functions
42-69
Mehdi
Adjami
TMU (Tarbiat Modares University), Iran
Mehdi
Shafieefar
Tarbiat Modares University, Tehran, Iran
Ali Akbar Salehi
Neyshabouri
Tarbiat Modares University, Tehran, Iran
Turbulent wall-bounded flows are commonly encountered in engineering practice and are of considerable interests in a variety of industrial applications. This presence of wall significantly affects turbulence characteristics. If we want to solve the near-wall region a very fine mesh is necessary. The number of points needed increases at least like Re1.8. This requirement makes the application of Large Eddy Simulation (LES) for high Reynolds (order of 106−108) practically impossible. One solution is to apply near-wall modification, or wall models with a coarse mesh near the wall. When the grid is not fine enough to resolve near-wall structure, the near-wall must be modeled by specifying a correlation between the velocity in first node and shear stress at the wall. The objective of this study is to implement wall-function for LES simulation of channel flow. The sub-grid scales are modeled using Smagorinsky and Wale model. The first node is placed at y+ ∼ 49 for Reτ = 4000 and 54 ≤ y+ ≤ 200 for Reτ = 16000. So the first node was located in log-law region and standard wall function was applied. Other modification was introduced in the calculation of the length-scale in the Smagorinsky model using the model proposed by Mason-Callen [7]. Another model introduced was the Werner-Wengler model [6].
Soret and Dufour Effects on Free Convection Heat and Mass Transfer along a Horizontal Plate in Non-Darcy Porous Medium
70-84
P. V. S. N.
Murthy
Department of Mathematics, Indian Institute of Technology, Kharagpur, West Bengal, 721302, India
P. A. Lakshmi
Narayana
Department of Mathematics, Indian Institute of Technology Hyderabad, Hyderabad - 502205, Telangana, India
The effect of Soret and Dufour parameters on the non-Darcy natural convection over a horizontal flat plate in saturated porous medium is studied using similarity technique. Forchheimer extension is considered in the flow equations. Wall temperature and concentration distributions are assumed to be of the form Ax1/2 and Bx1/2 respectively, where x is the distance from the leading edge. The effect of Soret parameter Sr, Dufour parameter Df, diffusivity ratio Le, buoyancy ratio parameter N and the inertia parameter Gr on non-dimensional temperature and concentration, heat and mass transfer coefficients are analyzed. The variation of heat and mass transfer coefficients with these second order effects is presented for various values of the flow governing parameters.
Numerical Prediction of Non-Isothermal Flow Through a Curved Square Duct
85-99
Md. Sharif
Uddin
Mathematics Discipline; Science, Engineering and Technology School, Khulna University, Khulna-9208, Bangladesh
Rabindra Nath
Mondal
Department of Mathematics, Jagannath University, Dhaka, Bangladesh
Shinichiro
Yanase
Department of Mechanical Engineering, Faculty of Engineering, Okayama University Okayama 700-8530, Japan
A numerical study is presented for the solution structure, stability and transitions of non-isothermal flow through a curved square duct by using a spectral method and covering a wide range of the Dean number, Dn, 0 ≤ Dn ≤ 6000 and the curvature, δ, 0 < δ ≤ 0.5. A temperature difference is applied across the vertical sidewalls for the Grashof number Gr = 500, where the outer wall is heated and the inner one cooled. First, steady solutions are obtained by the Newton-Raphson iteration method. As a result, two branches of asymmetric steady solutions are obtained. Linear stability of the steady solutions is then investigated. It is found that only the first branch is linearly stable in a couple of interval of Dn for small δ; for large δ, however, the same branch is linearly stable in a single but wide interval of Dn though the branching pattern of the bifurcation diagram is unchanged. When there is no stable steady solution, time evolution calculations as well as their spectral analysis show that typical transition occurs from steady flow to chaos through various flow instabilities, if Dn is increased. It is also found that the transition to periodic or the chaotic state is delayed if the curvature is increased.