The heat loss from an insulated rod can be represented by differential equation: (d^2T/dx^2) + h(Ta-T) = 0
The temperatures at its end are maintained at 40oC and 200oC (the rod is 10 m long). Determine the temperature profile along the rod, h=0.01 m-2, Ta =20oC.
Hint: This is a “shooting” problem. You can express the problem in a system of two 1st ODEs:
dT/dx = Z, dZ/dx = -h(Ta-T)
The two initial conditions are Tx=0 = To = 40 , Zx=0 = Zo
For any given value of z0, the system can be numerically solved for temperature at the other end, Tx=10 = Te = 200
Once the table is setup using ODEs code, use Solver to CHANGE Zo so that Te equals 200oC.
Thanks in advance!
The temperatures at its end are maintained at 40oC and 200oC (the rod is 10 m long). Determine the temperature profile along the rod, h=0.01 m-2, Ta =20oC.
Hint: This is a “shooting” problem. You can express the problem in a system of two 1st ODEs:
dT/dx = Z, dZ/dx = -h(Ta-T)
The two initial conditions are Tx=0 = To = 40 , Zx=0 = Zo
For any given value of z0, the system can be numerically solved for temperature at the other end, Tx=10 = Te = 200
Once the table is setup using ODEs code, use Solver to CHANGE Zo so that Te equals 200oC.
Thanks in advance!