III (25 pts) A plate of thickness L is initially at zero temperature. For times t>...

 

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III (25 pts) A plate of thickness L is initially at zero temperature. For times t> 0, the boundary surface at x = L is kept insulated while the surface at x =0 is subjected to a heat flux f(t) varying with time as ƏT əx -k- Using the Duhamel's theorem, develop an expression for the temperature distribution T(x,t) in the slab for times (i) t < ti, and (ii) t > ti a²T (x, t) əx² (t = f(t) = {t for 0<t<t₁ for t>T₁ ƏT əx = 1 ƏT a at ƏT -k=f(t) atx = 0, t> 0 əx = 0 in 0 < x<L and t > 0 T(x, t) = 0 at x = L, t> 0 fort = 0 III (25 pts) A plate of thickness L is initially at zero temperature. For times t> 0, the boundary surface at x = L is kept insulated while the surface at x =0 is subjected to a heat flux f(t) varying with time as ƏT əx -k- Using the Duhamel's theorem, develop an expression for the temperature distribution T(x,t) in the slab for times (i) t < ti, and (ii) t > ti a²T (x, t) əx² (t = f(t) = {t for 0<t<t₁ for t>T₁ ƏT əx = 1 ƏT a at ƏT -k=f(t) atx = 0, t> 0 əx = 0 in 0 < x<L and t > 0 T(x, t) = 0 at x = L, t> 0 fort = 0

Answer rating: 100% (QA)

Solution for 0 t 1 Txt n1 An sinn x L expn2 2 t L2 n1 1 n sinn x L expn2 2 t L2 0t t dt Solution for t 1 Txt n1 An sinn x L expn2 2 t L2 Note n1 represents the summation from n 1 to infinity An are co... View the full answer