g 1 pnt Estimate the time when temperature the midpoint diff

(g) 1 pnt. Estimate the time when temperature the mid-point differs the at from its steady-state value by less than 1% a Just replace the series with its first term. You may use a calculator. My calculation yields just above 8 min.

Solution

The steady state distbn is T =-16x/25 +10

Midpt 2deg C

Initial temp 29.5 C

BVP set up as U(x,0)=29.5,

U(0,t) =10

U(L,t)= -6

assume a series soln U(x,t)= Bn sin(npix/L) exp( -(k(npi/L)²t}

Taking the first term as suggested, the coeff B1 comes to 1.98/37.56 at 99% of 2deg wich is the steady state value at Midpt.

calculations give 1.98/37.56 =exp ( -.0073t)

t = 403 seconds