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51 articles for “Partial Differential Equation”
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Research ArticleOpen accessIn the abstractHeat-Modeling of Microwave Assisted Epoxidation of Palm Acid OilN. Saifuddin, L. Wei Zhan, K. Xin NingProblem statement: While microwave chemistry could well be the most convenient, rapid and energy-saving way to initiate a chemical reaction, the issues of thermal versus microwave specific effect remain unaddressed. Approach: A three-dimensional Finite Element Model (FEM) was developed to predict temperature profile during the enzymatic epoxidation of palm acid oil using microwave heating. Three-dimensional partial differential equations are formulated … …American Journal of Applied Sciences, Vol. 8, Issue 3 · 25 Mar 2011 · 7,676 accessesView PDFCite
Research ArticleOpen accessIn the abstractNew Family of Exact Soliton Solutions for the Nonlinear Three-Wave Interaction EquationsSahar M. Alqaraleh, Adeeb G. TalafhaProblem statement: To obtain new exact traveling wave soliton solutions for the threewave interaction equation in a dispersive medium and a non zero phase mismatch. Approach: The tanh method is usually used to find a traveling wave analytic soliton solutions for one nonlinear wave and evolution partial differential equation. Here, we generalize this method to solve a system of nonlinear … …Journal of Mathematics and Statistics, Vol. 7, Issue 1 · 31 Jan 2011 · 7,426 accessesView PDFCite
Research ArticleOpen accessIn the abstractRoughness Effect on an Unsteady Flow in Pipelines by Profilometry and Imaging TechniquesMabrouk Benkhedimallah, Rabah Zegadi, Mohamed BouafiaProblem statement: Currently the aero dynamical calculation in gas pipes is carried out under the assumption of steady state conditions. However real steady in a network is scarcely quasisteady. Approach: The unsteady state is governed by non-linear partial differential equations leading to mathematical difficulties. And there are fore gas pipe dimensions are computed at steady state under extreme conditions. Results: … …American Journal of Engineering and Applied Sciences, Vol. 4, Issue 1 · 29 Jan 2011 · 8,152 accessesView PDFCite
Research ArticleOpen accessIn the abstractBioengineering Assessment on Sloppy GroundMu'azu Mohammed Abdullahi, Nazri Bn Ali, Kamarudin Bn Haj AhmedProblem statement: Soft engineering solution of sloppy surface utilizes mechanical and hydrological effects of vegetation. The hydrological effects driven by transpiration, induces an increase in matric suction and consequently tension also increase along with the decrease of moisture. Therefore once the horizontal stress of the soil exceeds the limit of tensile strain of the soil cracks occurs. Approach: The negative … …American Journal of Environmental Sciences, Vol. 6, Issue 4 · 31 Aug 2010 · 7,242 accessesView PDFCite
Research ArticleOpen accessIn the abstractSimilarity Solutions for Free Convection Between Two Parallel Porous Walls at Different TemperaturesA. J. Omowaye, O. K. KorikoProblem statement: A two dimensional steady laminar free convective flow of viscous incompressible fluid between two parallel porous walls is considered. Approach: Using the similarity variable, the partial differential equations were reduced to ordinary differential equations. The coupled ordinary differential equations were solved numerically using shooting method. The effect of various physical parameters, such as the Prandtl number, Grashof number, … …Journal of Mathematics and Statistics, Vol. 6, Issue 2 · 30 Jun 2010 · 7,783 accessesView PDFCite
Research ArticleOpen accessIn the abstractApproximate Solutions of a Higher Order MHD Flow of a Uniformly Stretched Vertical Permeable Surface in the Presence of Heat Generation/Absorption which Resulted from a Quadratic ReactionO. K. KorikoHigher order MHD flow of a uniformity stretched vertical permeable surface in the presence of heat generation/absorption which resulted from a quadratic reaction was studied. The resulting coupled nonlinear partial differential equations is solved by asymptotic expansion. It was discovered that the maximum value of velocity occurs in the body of the fluid close to the surface not at the … …Journal of Mathematics and Statistics, Vol. 6, Issue 2 · 30 Jun 2010 · 7,445 accessesView PDFCite
Research ArticleOpen accessIn the abstractEffect of Size of Heated Obstruction within Room on Three Dimensional Air Flow CharacteristicsAbduljabbar Muttair Ahmed, Mukhtar Ahmad, Abdur RahimProblem statement: This study reported a numerical investigation of three-dimensional turbulent buoyant recirculating flow within a room with heated obstruction. Approach: The study involved the solution of partial differential equations for the conservation of mass, momentum, energy, concentration, turbulent energy and its dissipation rate. These equations were solved together with algebraic expressions for the turbulent viscosity and the heat diffusivity, … …American Journal of Engineering and Applied Sciences, Vol. 3, Issue 2 · 30 Jun 2010 · 6,934 accessesView PDFCite
Research ArticleOpen accessIn the abstractNumerical Solution of Second-Order Linear Fredholm Integro-Differential Equation Using Generalized Minimal Residual MethodElayaraja Aruchunan, Jumat SulaimanProblem statement: This research purposely brought up to solve complicated equations such as partial differential equations, integral equations, Integro-Differential Equations (IDE), stochastic equations and others. Many physical phenomena contain mathematical formulations such integro-differential equations which are arise in fluid dynamics, biological models and chemical kinetics. In fact, several formulations and numerical solutions of the linear Fredholm integro-differential equation of second … …American Journal of Applied Sciences, Vol. 7, Issue 6 · 30 Jun 2010 · 8,198 accessesView PDFCite
Research ArticleOpen accessIn the abstractModeling of an Industrial Riser in the Fluid Catalytic Cracking UnitMehran Heydari, Habib Ale Ebrahim, Bahram DabirProblem statement: The aim of this study is to obtain a model that can simulate the performance of an industrial fluid catalytic cracking unit in steady state. Approach: The reactions in the riser occur in a transported bed with the fluid and the solids in ideal plug flow. One of the main advantages of the model is that it does … …American Journal of Applied Sciences, Vol. 7, Issue 2 · 28 Feb 2010 · 8,117 accessesView PDFCite
Research ArticleOpen accessIn the abstractCost Analysis of Two-Dissimilar-Unit Cold Standby System with three States and Preventive Maintenance Using Linear First Order Differential EquationsM. Y. HaggagProblem statement: Several researchers have studied the reliability behavior of a three state systems, but no attention was paid to the reliability evaluation due to preventive maintenance. The better maintenance of the system originates better reliability. Also, standby support increases the reliability of the system. Approach: Determine the efficacy of preventive maintenance on the reliability and performance of the system. … …Journal of Mathematics and Statistics, Vol. 5, Issue 4 · 31 Dec 2009 · 6,873 accessesView PDFCite