Answer to Question #159233 in Mechanical Engineering for Uthara

Question #159233

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


1
Expert's answer
2021-02-15T05:39:40-0500

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}"


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