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dw with w(0.t) = 0, w(1.t) = 0 w(x.0) - 40 – 80x.

dw with w(0.t) = 0, w(1.t) = 0 w(x.0) - 40 – 80x.

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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Please note that i have already slove part of the equation remaining is to slove the 3 equation with these parameters in red square

Subject is Partial differentiation.

Thank you if you can detail the answer.

Given a metal bar of 1m long and of constant section (s) which is very clos to zero. The temperature at the x = 0 end is maintained at 10°C and th temperature at the end x = 1 is maintained at 90 ° c. The temperatur variation(0) along the bar at time t = 0 is given by 0(x,0) = 50 pour 0<x<1. Determine 0(x,), the thermal diffusivity is 4 m²/s. Use the separation variable (x,t) = 80x + 10 + w(x,t). Exercice 6: Heat equations = 4 at (1) avec 0(0,t) = 10, 0(1.t) = 90 et 0(x.0) = 50. use change variable equations On a: 0(x.t) = 80x + 10 + w(x.t). (2) aw ae = 80 + at at use equation 1 in terms of W a?w = 4 at let x= determine condions for equations (3). let x =0 (2) : e(0.t) = 10 + w(0.t) * 10 = 10 + w(0.t) * w(0,t) = 0. let (2) : 6(1,t) = 80 +10 + w(1,t) * 90 = 90 + w(1.t) * w(1.t) = 0. t=0 x= 1 (2) : let 0(x.0) = 80x +10 + w(x.0) * 50 = 80x + 10 + w(x.0) * w(x.0) = 40 – 80x. use equations 3 to slove the following aw - 4 at with w(0,t) = 0, w(1.t) = 0 w(x.0) = 40 – 80x.
Transcribed Image Text:Given a metal bar of 1m long and of constant section (s) which is very clos to zero. The temperature at the x = 0 end is maintained at 10°C and th temperature at the end x = 1 is maintained at 90 ° c. The temperatur variation(0) along the bar at time t = 0 is given by 0(x,0) = 50 pour 0<x<1. Determine 0(x,), the thermal diffusivity is 4 m²/s. Use the separation variable (x,t) = 80x + 10 + w(x,t). Exercice 6: Heat equations = 4 at (1) avec 0(0,t) = 10, 0(1.t) = 90 et 0(x.0) = 50. use change variable equations On a: 0(x.t) = 80x + 10 + w(x.t). (2) aw ae = 80 + at at use equation 1 in terms of W a?w = 4 at let x= determine condions for equations (3). let x =0 (2) : e(0.t) = 10 + w(0.t) * 10 = 10 + w(0.t) * w(0,t) = 0. let (2) : 6(1,t) = 80 +10 + w(1,t) * 90 = 90 + w(1.t) * w(1.t) = 0. t=0 x= 1 (2) : let 0(x.0) = 80x +10 + w(x.0) * 50 = 80x + 10 + w(x.0) * w(x.0) = 40 – 80x. use equations 3 to slove the following aw - 4 at with w(0,t) = 0, w(1.t) = 0 w(x.0) = 40 – 80x.
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