Series or Physics?

A bar of length a a is at zero temperature. At t = 0 t=0 , the end x = a x=a is raised to a temperature u 0 u_0 and the end x = 0 x=0 is insulated. If the temperature at any point x x of the bar at any time t > 0 t>0 , assuming that the surface of the bar is insulated, can be expressed as:

u ( x , t ) = u 0 + A u 0 π B n = 1 ( 1 ) n ( 2 n 1 ) e ( 2 n 1 ) C π D c 2 t F a G cos ( ( 2 n 1 ) π x H I a J ) \displaystyle u(x,t)=u_0+\frac{Au_0}{\pi^B}\sum_{n=1}^{\infty}\frac{(-1)^n}{(2n-1)}e^{-\frac{(2n-1)^C\pi^Dc^2t}{Fa^G}}\cos\left( \frac{(2n-1)\pi x^H}{Ia^J} \right)

Evaluate A + B + C + D + F + G + H + I + J A+B+C+D+F+G+H+I+J

Details and Assumptions:

Here, c c is arbitrary constant.


The answer is 19.

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1 solution

Thong Liang Kho
Oct 13, 2016

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