Numerical Investigation was done for steady state laminar mixed convection and thermally and hydrodynamic fully developed flow through horizontal rectangular duct including circular core with two cases of time periodic boundary condition, first case on the rectangular wall while keeping core wall constant and other on both the rectangular duct and core walls. The used governing equations are continuity momentum and energy equations. These equations are normalized and solved using the Vorticity-Stream function and the Body Fitted Coordinates (B.F.C.) methods. The Finite Difference approach with the Line Successive Over Relaxation (LSOR) method is used to obtain all the computational results the (B.F.C.) method is used to generate the grid of the problem. A computer program (Fortan 90) is built to calculate Nusselt Number (Nu) in steady state. The fluid Prandtl number is 0.7 Rayleigh Number 1<Ra<106, Reynolds number 1<Re<2000. For the range of parameters considered, results show that the time periodic boundary condition enhance heat transfer. It is also indicated in the results that heat transfer from the surface of the circle exceeds that of the rectangle duct. Comparisons with other research show good agreement.
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In this article, the boundary value problem of convection propagation through the permeable fin in a natural convection environment is solved by the Haar wavelet collocation method (HWCM). We also compare the solutions with the application of a semi-analytical method , namely the Temimi and Ansari (TAM), that is characterized by accuracy and efficiency.The proposed method is also characterized by simplicity and efficiency. The possibility of applying the proposed method to many types of linear or nonlinear ordinary and partial differential equations.
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A numerical study of the two-dimensional steady free convection flow in an inclined annulus between two concentric square cavities filled with a porous medium is presented in this paper for the case when the side outer walls are kept with differentially heated temperature while the horizontal outer walls and the inner walls are insulated. The heated wall is assumed to have spatial sinusoidal temperature variation about a constant mean value. The Darcy model is used and the fluid is assumed to be a standard Boussinesq fluid. For the Cartesian coordinate system, the governing equations which were used in stream function form are discretized by using the finite difference method with successive under – relaxation method (SUR) and are solv
... Show MoreThis paper is dealing with an experimental study to show the influence of the geometric characteristics of the vortex generators VG son the thickness of the boundary layer (∂) and drag coefficients (CD) of the flat plate. Vortex generators work effectively on medium and high angles of attack, since they are "hidden" under the boundary layer and practically ineffective at low angles.
The height of VGs relative to the thickness of the boundary layer enables us to study the efficacy of VGs in delaying boundary layer separation. The distance between two VGs also has an effect on the boundary layer if we take into
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In this paper, the problem of developing turbulent flow in rectangular duct is investigated by obtaining numerical results of the velocity profiles in duct by using large eddy simulation model in two dimensions with different Reynolds numbers, filter equations and mesh sizes. Reynolds numbers range from (11,000) to (110,000) for velocities (1 m/sec) to (50 m/sec) with (56×56), (76×76) and (96×96) mesh sizes with different filter equations. The numerical results of the large eddy simulation model are compared with k-ε model and analytic velocity distribution and validated with experimental data of other researcher. The large eddy simulation model has a good agreement with experimental data for high Reynolds number with the first, seco
... Show MoreThis paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-
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Model birefringence was measured for elliptical-core fibers with low ellipticities, note the birefringence depends strongly on the frequency, especially when fiber is being operated near the higher mode cutoff where ν for circular fiber of the single-mode type that correspond to the birefringence maximum. When ν this also correspond to the birefringence maximum that can be introduced in an elliptical core fiber while still operating in the single-mode regime near the higher mode cutoff. Also the birefringence is proportional to the fiber core ellipticity when core ellipticity is much less than unity, but this birefringence deviates from the linear for the large core ellipticities.
In the present work, steady, laminar natural convection in nonrectangular enclosures is analyzed numerically with and without fin. Vertical walls insulated while horizontal walls maintained isothermal at different temperature and the fin was placed on horizontal surface. The length of fin was equal (B/L=0.22, 0.44 and 0.66) and thickness of fin was constant. Various parameters are studied: Rayleigh number (from 104 to 107 ), Prandtl number (0.7), number of fin change from (1-3) and aspect ratio (H/L= 0.15 to 0.5). The problem is formulated in terms of the vorticity-stream function procedure. A numerical solution based on program in Fortran 90 with Tec plot program. The finite difference method is used. Streamlines and isotherms are prese
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