A bar of length a is at zero temperature. At t = 0 , the end x = a is raised to a temperature u 0 and the end x = 0 is insulated. If the temperature at any point x of the bar at any time t > 0 , assuming that the surface of the bar is insulated, can be expressed as:
u ( x , t ) = u 0 + π B A u 0 n = 1 ∑ ∞ ( 2 n − 1 ) ( − 1 ) n e − F a G ( 2 n − 1 ) C π D c 2 t cos ( I a J ( 2 n − 1 ) π x H )
Evaluate A + B + C + D + F + G + H + I + J
Details and Assumptions:
Here, c is arbitrary constant.
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