Sunday, December 29, 2019

Applying An Analytical Model Of A Plane Wall - 1293 Words

Abstract To conduct a proper analysis of the 1-D transient conduction in a plane wall we must take the necessary mathematical procedures to obtain an analytical model that accurately represents the heat transfer that occurs. The equation must accurately model a plane wall that has a thickness L, is well-insulated on one side, but is still vulnerable to convection on the other side. In order to complete the model, one must scale the problem in terms of both a length scale and a time scale to transform the variables to a dimensionless form that allows for a set of solutions that can be narrowed down to the simple parameter, Bi=hL/k. Introduction Mathematical Model This analysis looks into the phenomena of 1-D transient conduction in a plane wall of thickness L that is insulated on one side and subject to convection on the other. The conduction is governed by the differential heat equation: u_t=∠u_xx (1) Here, u signifies the temperature of the entire body and ∠ signifies the thermal diffusivity. Furthermore, the differential heat equation above must respect the following boundary conditions: u_x |_(x=0)=0 -ku_x |_(x=L)=h(u|-T_∞) u|_(t=0)=T_i In the above boundary conditions, k represents a material property commonly referred to as thermal conductivity, whereas T_i represents the initial temperature throughout the wall. In this instance the flow conditions are such that they sustain constantShow MoreRelatedStructural Suitability and Modelling of Glass Fiber Reinforced Polymers3865 Words   |  16 Pagesinterwoven in two perpendicular directions, resulting in an in-plane orthotropic material of increased specific stiffness in the directions of the glass fibres. 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