Question

The end a And B of arod of length l are maintained temperature 0 degree celcius and 100 degree celcius until steady state condition. Suddenly temperature at the end Ais increased to 20 degree celcius and B decreased to 60 degree celcius find the temperature distance in th rod at time t

Answer 1

as stead state is achieved,

$\frac{dT}{dt} =0$

the heat equation

$\frac{d2T}{d2t} =0$

$\frac{dT}{dx} =A$

T = Ax + B

usin the boundary condition

T=0

0=a(0) +B

B=0

x=100L T=100

100=AL

T(r.t)=$\frac{100u}{L}+0$

after that at t=0 the temp temp at b is reduced to

u=o a + r=0

u=o a + x=0

Ts(r,t) = $\frac{(0-0)}{L}r=0$

=0

T(r,t) = Ts(r) + Tt(r,t)

T(r,0) = 0 +100r/L + Tt(r,0)

on trial value condition

Tt(r,t) =

$\frac{2 x100(-1)n+1}{n}$