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For all following problems, consider the differential equation for steady-state heat transfer in a square plate, V²T = m²(T – T„), T(1,y) where 0

For all following problems, consider the differential equation for steady-state heat transfer in a square plate, V²T = m²(T – T„), T(1,y) where 0

Advanced Engineering Mathematics
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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For all following problems, consider the differential equation for steady-state heat transfer in a square plate, V'T = m²(T – T), T(x, y) where 0<r< L, 0<y <L T(r,0) = 0, T(1, y) = 0, T(x, 1) = Tu, (0, y) = y? 1. Interior Points (a) Using Central difference approximations for the derivatives derive the equation for approximating the interior points of this system. Write your final answer in the following form: a,T,-1, + a,T+1j + azT,+1 + a,Tj-1 + a,T, = b where a are constant coefficients and b includes any forcing terms. (b) What order of accuracy is this approximation?
Transcribed Image Text:For all following problems, consider the differential equation for steady-state heat transfer in a square plate, V'T = m²(T – T), T(x, y) where 0<r< L, 0<y <L T(r,0) = 0, T(1, y) = 0, T(x, 1) = Tu, (0, y) = y? 1. Interior Points (a) Using Central difference approximations for the derivatives derive the equation for approximating the interior points of this system. Write your final answer in the following form: a,T,-1, + a,T+1j + azT,+1 + a,Tj-1 + a,T, = b where a are constant coefficients and b includes any forcing terms. (b) What order of accuracy is this approximation?
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