Papers by Keyword: Numerical Solution

Abstract: This article examines laminar mixed convection of a nanofluid within a square cavity that contains a vertical rectangular obstacle serving as a vortex promoter. Employing Buongiorno's theory, the dimensionless governing equations are numerically solved using the finite element method to analyze the distributions of velocity, temperature, nanoparticle concentration, and entropy generation. Attention is paid to the entropy generation. Results are presented and discussed, showing that increasing the Reynolds number generates a large vortex near the obstacle, which diminishes reverse flow, enhances heat conduction, and increases entropy generation. Moreover, thermophoresis drives tiny nanoparticles from hot to cold regions, affecting heat transfer. Indeed, nanoparticle concentration decreases with higher thermophoresis (N_T) and Brownian motion (N_B) constraints, as these parameters are inversely related to the concentration profile.

Abstract: We report on an analytical model for damage description in adhesive butt joints. In themodel, the thin adhesive layer is replaced by a damaging bonding interface. The mechanical behaviorof the interface is described by a nonlinear and rate­dependent imperfect contact law. The law takesinto account both stress and displacement jumps, and it can describe both soft and hard adhesive layers.Unlike classic cohesive zone models, phenomenological in nature, the proposed contact law explicitlyaccounts for material and damage properties of the adhesive layer. A first comparison with literaturedata of adhesive butt joints loaded in torsion indicates that the model can successfully reproduce theirexperimental stress­strain response.

Abstract: A metal extrusion was process that extrusion puncture perforate surface of material to throw and flow across outlet of die. This operation was a complex process in extrusion while penetration occurred at same time. This process can be seen in many production operations, like in forming of making portion of metal strip, and forming of extruded portion in a complex fineblanking with extrusion operation. Also exhibit the operation properties and give the method of numerical solution. So increasing load to 610KN with increased friction factor to 0.7 and increased with increasing the reduction ratio and stroke of operation. For the results and mesh distortion, with allocations of strains may be predicted. Analyzing results was submitted of metal extruded may be classified into two zones for the different lineaments deformation. moreover, energy in the zones of deformation may be classified into two parts for their different lineaments of internal zone and contact zone with the die . Fracture location has been found from simulations. Keyword Load, Extrusion, upper bound, numerical solution

Abstract: An analysis of aCasson fluid flowing over a porous exponentially stretching surface with radiation has been studied. A non-Newtonian fluid model was developed for the flow and similarity analysis used in the transformation process. The model of partial differential equations was transformed into ordinary differential equations and reduced into a system of first order differential equations which was then solved using the Fourth-order Runge-Kutta algorithm alongside the Newton Raphson shooting method. The results have been presented graphically and in tabular form for various controlling parameters of the problem. It is observed that general control can be achieved by the permeability of the surface and the value of the Casson parameter.

Abstract: In the present analysis, we extended Blasius and Sakiadis problems in Carreau fluids by considering a uniform free stream parallel to a fixed or moving flat plate, which has more practical significance. The effects of radiation and convective boundary condition are also taken into account. The resulting nonlinear momentum and energy equations are simplified using similarity transformations. Numerical solutions have been obtained for the velocity and temperature profiles by employing shooting method coupled with Runge-Kutta-Fehlberg integration scheme. Graphical results for the velocity and temperature fields are sketched and discussed. It is found that temperature of the Blasius problem is always higher than the Sakiadis problem.

Abstract: The simplified algorithm of the numerical solution of the differential diffusion equation is presented. The solution is based on the one-dimensional diffusion model with the third kind boundary conditions and the finite difference method. The proposed approach allows for the quick and precise assessment of the carburizing process parameters – temperature and time.

Abstract: In this paper we analyse the heat transfer in a cylindrical spine fin. Here, both the heat transfer coefficient and thermal conductivity are temperature dependent. The resulting 2+1 dimension partial differential equation (PDE) is rendered nonlinear and difficult to solve exactly, particularly with prescribed initial and boundary conditions. We employ the three dimensional differential transform methods (3D DTM) to contract the approximate analytical solutions. Furthermore we utilize numerical techniques to determine approximate numerical solutions. The effects of parameters, appearing in the boundary value problem (BVP), on temperature profile of the fin are studied.

Abstract: This examination manages the impact of magnetic field on the flow and heat transport of an incompressible Carreau liquid over an extending sheet with particle fluid suspension. The significant conditions are first improved under regular boundary layer suppositions, and afterward changed into conventional differential conditions by reasonable transformations. The changed conventional nonlinear differential conditions which are explained numerically by Matlab bvp4c package. The impacts of specific parameters on the dimensionless velocity and temperature are exhibited in graphical structures.

Abstract: The FitzHugh-Nagumo equation is an important nonlinear reaction-diffusion equation used in physics and chemicals. To obtain the numerical solution of partial differential equations, the compact finite difference method is widely applied. In this paper, I propose a new numerical solution to FitzHugh-Nagumo equation by using a fourth-order compact finite difference scheme in space, and a semi-implicit Crank-Nicholson method in time. I further calculate the results in terms of accuracy by leveraging the proposed method and exact solution. In particular, I compare the new method whose convergence order is close to four with the second order central difference method. The simulated results show the new solution is more accurate and effective. The proposed method is expected to be a good solution to some problems in the real world.

Abstract: A combined effect of thermal radiation and viscous dissipation over a melting moving surface is investigated. Casson liquid model is accounted as working liquid. The Brownian motion and thermophoresis in Buogiorno’s type nanofluid are retained. Numerical solutions are obtained for the reduced ordinary differential equations via RKF 45 method. The pertinent parameters on velocity, temperature and concentration are analyzed through plots and tables. Output demonstrated that higher values of melting, thermal radiation and viscous dissipation are enhanced the temperature. Validation of the present work is made with the existing literature.