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Similarity solution
About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.
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TL;DR: In this article, a class of nonlinear convection-diffusion equation is studied and asymptotic analytical solutions are obtained by using double-parameter transformation perturbation expansion method (DPTPEM), where the influences of convection functional coefficient and power law index on the heat transport characteristics are discussed and shown graphically.
Abstract: A class of nonlinear convection-diffusion equation is studied in this paper. The partial differential equation is converted into nonlinear ordinary differential equation by introducing a similarity transformation. The asymptotic analytical solutions are obtained by using double-parameter transformation perturbation expansion method (DPTPEM). The influences of convection functional coefficient and power law index on the heat transport characteristics are discussed and shown graphically. The comparison with the numerical results is presented and it is found to be in excellent agreement. The method and technique used in this paper have the significance in studying other engineering problems.
13 citations
TL;DR: The problem of steady Marangoni boundary layer flow and heat transfer over a flat plate in a nanofluid is studied using different types of nanoparticles using the Runge-Kutta-Fehlberg (RKF) method.
Abstract: The problem of steady Marangoni boundary layer flow and heat transfer over a flat plate in a nanofluid is studied using different types of nanoparticles. The general governing partial differential equations are transformed into a set of two nonlinear ordinary differential equations using unique similarity transformation. Numerical solutions of the similarity equations are obtained using the Runge-Kutta-Fehlberg (RKF) method. Three different types of nanoparticles are considered, namely, Cu, Al2O3, and TiO2, by using water as a base fluid with Prandtl number . The effects of the nanoparticle volume fraction and the constant exponent m on the flow and heat transfer characteristics are obtained and discussed.
13 citations
TL;DR: In this article, a similarity solution to the problem of film condensation in a porous medium along the surface of a body of arbitrary shape was obtained under an appropriate distribution of lateral mass flux at the boundary.
13 citations
TL;DR: In this paper, a solution to the integro-differential equation of batch grinding has been presented which maps the trajectory of particle size spectra of continuous size and time domains.
13 citations
TL;DR: In this paper, a numerical analysis for slamming impact phenomena was carried out when 2-dimensional wedge shaped structure with finite deadrise angles entered the free surface by using a commertial CFD code, FLUENT.
Abstract: Numerical analysis for slamming impact phenomena has been carried out when 2-dimensional wedge shaped structure with finite deadrise angles enter the free surface by using a commertial CFD code, FLUENT. Fluid is assumed incompressible and entry speed of the structure is kept constant. Geo-reconstruct scheme (or PLIC-VOF scheme) is used for the tracking of the deforming free surface. User defined function of 6 degrees of freedom motion and moving dynamic mesh option are used for the expression of the downward motion of the structure and deforming of unstructured meshes adjacent to the structure. The magnitude and the location of impact pressure and the total drag force which is the summation of pressures distributed at the bottom of the structure are analyzed. Results of the analysis show good agreement with the results of similarity solution, asymptotic solution and the solution of BEM. ※Keywords: Slamming(슬래밍), Impact pressure(충격압력), Wedge structure(쐐기 구조물), CFD (계산유체역학), VOF scheme, Geo-reconstruct scheme(도형-재구성법),
13 citations