Find the temperature w(x, t) in a semi-infinite laterally insulated bar extending from x = 0 along the x-axis to infinity, assuming that the initial temperature is 0, w(x, t) †’ 0 as x †’ ˆž for every fixed t ‰¥ 0, and w(0, t) = f(t). Proceed as follows.

Applying the convolution theorem, show that in Prob. 9,

Data from Prob. 9

Find the temperature w(x, t) in a semi-infinite laterally insulated bar extending from x = 0 along the x-axis to infinity, assuming that the initial temperature is 0, w(x, t) †’ 0 as x †’ ˆž for every fixed t ‰¥ 0, and w(0, t) = f(t). Proceed as follows.

Set up the model and show that the Laplace transform leads to

and

Transcribed Image Text:

х f(t – T)r-3/2e-=²K4c°r}dr. 20VT w (x, t) Pw sW = c2 (W = L{w}) %3D