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(-1)(*+1) + 1 -sin L NAX sinh (nxy/L) 0(x, y) = Σ n sinh (naW/L) n=1 Using this expression, calculate the temperature at the point (x,y) = (0.75, 0.5) by considering the first five nonzero terms of the infinite series that must be evaluated. Assume that L = 1.5 m. iM:

(-1)(*+1) + 1 -sin L NAX sinh (nxy/L) 0(x, y) = Σ n sinh (naW/L) n=1 Using this expression, calculate the temperature at the point (x,y) = (0.75, 0.5) by considering the first five nonzero terms of the infinite series that must be evaluated. Assume that L = 1.5 m. iM:

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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A two-dimensional rectangular plate is subjected to prescribed boundary conditions, T1 = 50°C, T2 = 140°C. The temperature distribution equation, derived by applying separation of variable methods to a two-dimensional conduction problem for a thin rectangular plate or long rectangular rod, is as follows. (-1)*+1) + 1 -sin L sinh (nty/L) sinh (naW/L) nAX 0(x, y) = = Σ n n=1 Using this expression, calculate the temperature at the point (x,y) = (0.75, 0.5) by considering the first five nonzero terms of the infinite series that must be evaluated. Assume that L = 1.5 m. у (m) T2 1 T = 50°C- T = 50°C →x (m) L L -T = 50°C
Transcribed Image Text:A two-dimensional rectangular plate is subjected to prescribed boundary conditions, T1 = 50°C, T2 = 140°C. The temperature distribution equation, derived by applying separation of variable methods to a two-dimensional conduction problem for a thin rectangular plate or long rectangular rod, is as follows. (-1)*+1) + 1 -sin L sinh (nty/L) sinh (naW/L) nAX 0(x, y) = = Σ n n=1 Using this expression, calculate the temperature at the point (x,y) = (0.75, 0.5) by considering the first five nonzero terms of the infinite series that must be evaluated. Assume that L = 1.5 m. у (m) T2 1 T = 50°C- T = 50°C →x (m) L L -T = 50°C
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