5) Determine the equilibrium temperature distributionfor a one-dimensional rod with constant thermalproperties with the following sources and boundaryconditions:Ju2 = x², u(0) = T, (L) = 0dxQKo

Given that a one -dimensional rod with constant thermal properties with the following sources and…

Answered: 5) Determine the equilibrium…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the Laplace Equation with 0≤x≤2, 0≤x≤1 and the meshsize equal to 0.5. The boundary conditions are : u(0,y)=0, u(2,y) = 120, u(x, 0) = 0, and u(x, 1) = 0. What is u(1.5, 0.5) Round to closest integer...
The cross section of a rectangular bar with aspect ratio a has temperature distribution T(x, y, t). The bar is sufficiently long, and has uniformity along its z-dimension, so it can be idealized as a two-dimensional problem. Three sides of the bar are kept at a uniform temperature To. The fourth side of the bar is subject to a temperature profile f(x). Y To To aL f(x) This temperature profile is governed by the partial differential equation * = *(+) T*(x,y,t) = Σ. An sin ( n=1 მე-2 To x where k is the coefficient of thermal conductivity. This equation has the analytical solution for T*(x, y, t) = T(x, y,t) - To of (25) sinh ( (--Đ))- En("E). Bn, Sin m aL m-1 exp 2(1-(-1)) and Bn.m nāsinh(nĩa) - m²))]. _kπ² (n²a² + m²) = m(exp(nña)-exp(-nña)) π(n²a²+m²) where the coefficients for f(x) = 1+T are An Set up the finite difference equation using the second order central difference method in the spatial dimensions and the explicit Euler method in the temporal dimension. Solve the equation…
Answer in type format Differential Eqautions
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Q. No. 1: Consider a perfectly insulated sheet with dimension 1*1, sheet is heated with external heat source qo (1). assuming that temperature in the sheet is uniformly distributed and initially the sheet has constant room temperature. a) Model the problem mentioned in the statement b) Solve the modeled problem by suitable method c) Classify the resulting pde and its boundary conditions
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5) Determine the equilibrium temperature distribution for a one-dimensional rod with constant thermal properties with the following sources and boundary conditions: