Question

P Problem 4 Consider a semi-infinite solid that is initially at temperature To. Assume that the surface temperature of the solid is suddenly changed to T. Find the unsteady temperature in the solid. (Hint: use the Laplace Transform method)

Answer 1

Solutioni- consider a solid al constant temperature diffusion eqn.can be given as, Subject to initial condition, W(x,0) =To w(x, t) =0 W (4,t) → o as x) Laplace Transformation, we get to Applying iegn (1) o t can ) =1 (2) - SW – w(2,0) : sw - To - cotie a sew - To as de -sw = -to - WR.ID = A ge! + Bc0e"len (x, 5) = 70

W(2,5) = a(s)e 5/6?+8699215/4 to Isletter so we have a Ich + 10 =WCY,S) = ACs) e F19+86) 3 . B(s) =0 > Luck,) - ACs) e '%c'+ To - W (0,t) =0 we have w (0,5) = 0 => A) +10.50. & WOU,S) - Toe? Applying Inverse laplace, => L'() = 1 -1" (***)= erfeli - [l-ers (in] whire, eric is error factor, final solution is wcxt) = To of (Ice) —C) * Integrate the above eqn fiom To to The . Joog Contact
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