Steady natural convection in a square enclosure with wall length (L= 20 cm) partially filled by saturated porous medium with same fluid (lower layer) and air (upper layer) is investigated. The conceptual study of the achievements of the heat transfer is performed under effects of bottom heating by constant heat flux (q=150,300,450,600W/m2 ) for three heaters size (0.2,0.14,0.07)m with symmetrically cooling with constant temperature on two vertical walls and adiabatic top wall. The relevant filled studied parameters are four different porous medium heights (Hp=0.25L,0.5L, 0.75L, L), Darcey number (Da1) 3.025×10-8 and (Da2) 8.852×10-4 ) and Rayleigh number range (60.354 - 241.41), (1.304×106 – 5.2166×106 ) for Da1 and Da2 cases respectively. Numerically, COMSOL Multiphysics 5.5a® based on the Galerkin finite element method is used for solving the governing equations with depending Brinkman- Darcy extended mode for porous media region. The results show that, effects of increasing the Rayleigh number on the temperature profile besides the progressively increasing the average Nusselt number. Moreover, symmetrical distribution of local Nu along the bottom heated wall and it is be minimum at midpoint of bottom. Also, the heat transfer and fluid flow are affected by thickness of porous layer and are maximum at porous layer thickness (0.25L) which clearly observed with large heater size to be approximately (93%) for the average Nu. Generally, the heat transfer is enhanced for large Darcy number (8.852×10-4 ) and influenced by the convection regime improvement while it is mainly conduction mode for (Da1) for all Raleigh number with a little effect of convection when increase (Ra).
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A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.
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Film condensation of steam on a vertical tube is investigated numerically and experimentally, in the present work. A mathematical model was set based on the basic conservation laws of mass and energy, Nusselts analysis of film condensation, and empirical equations available in the literature. Then, a simulation program in FORTRAN language was developed which simulates the film condensation of steam on a vertical tube. A complete steam tables subprogram was also developed and incorporated with the main program. The experimental work was carried out using a steam condensation test bench. The inlet and outlet cooling water temperatures, steam temperature and pressure, tube surface temperature at center, and co
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Friction Stir Welding (FSW) is one of the most effective solid states joining process and has numerous potential applications in many industries. A FSW numerical tool, based on ANSYS F.E software, has been developed. The amount of the heat gone to the tool dictates the life of the tool and the capability of the tool to produce a good processed zone. Hence, understanding the heat transfer aspect of the friction stir welding is extremely important for improving the process. Many research works were carried out to simulate the friction stir welding using various softwares to determine the temperature distribution for a given set of welding conditions. The objective of this research is to develop a finite element sim
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In this research we solved numerically Boltzmann transport equation in order to calculate the transport parameters, such as, drift velocity, W, D/? (ratio of diffusion coefficient to the mobility) and momentum transfer collision frequency ?m, for purpose of determination of magnetic drift velocity WM and magnetic deflection coefficient ? for low energy electrons, that moves in the electric field E, crossed with magnetic field B, i.e; E×B, in the nitrogen, Argon, Helium and it's gases mixtures as a function of: E/N (ratio of electric field strength to the number density of gas), E/P300 (ratio of electric field strength to the gas pressure) and D/? which covered a different ranges for E/P300 at temperatures 300°k (Kelvin). The results show
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Background This study establishes a mathematically consistent and computational framework for the simultaneous identification of two time-dependent coefficients in a one-dimensional second-order parabolic partial differential equation. The considered problem is governed by nonlocal initial, boundary, and integral overdetermination conditions. Methods The direct problem is solved using the Crank-Nicolson finite difference method (FDM), which ensures unconditional stability and second-order accuracy in both spatial and temporal discretizations. The corresponding inverse problem is reformulated as a nonlinear regularized least-squares optimization problem and efficiently solved used the MATLAB subroutine
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A mathematical model was proposed to study the microkinetics of esterification reaction of oleic acid with ethanol over prepared HY zeolite catalyst. The catalyst was prepared from Iraqi kaolin source and its properties were characterized by different techniques. The esterification was done under different temperature (40 to 70˚C) with 6:1 for molar ratio of ethanol to oleic acid and 5 % catalyst loading.
The microkinetics study was done over two period of time each period was examined individually to calculate the reaction rate constant and activation energy. The impact of the mass transfer resistance to the reactant was also investigated; two different studies have been accomplished to do this purpose.
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... Show MoreA mathematical model was proposed to study the microkinetics of esterification reaction of oleic acid with ethanol over prepared HY zeolite catalyst. The catalyst was prepared from Iraqi kaolin source and its properties were characterized by different techniques. The esterification was done under different temperature (40 to 70˚C) with 6:1 for molar ratio of ethanol to oleic acid and 5 % catalyst loading. The microkinetics study was done over two period of time each period was examined individually to calculate the reaction rate constant and activation energy. The impact of the mass transfer resistance to the reactant was also investigated; two different studies have been accomplished to do this purpose. The e
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