Consider heat conduction in a uniaxial rod surrounded by a fluid. The left end of the rod is at \(T_{0}\). The free stream temperature is \(T^{\infty}\). There is convective heat transfer across the surface of the rod as well over the right end. The governing equation and boundary conditions are as follows:

where \(k\) is the thermal conductivity, \(h\) is the convective heat transfer coefficient, and \(A\) and \(P\) are the area and circumference of the rod's cross section, respectively. The numerical values (SI units) are: \(L=0.5, k=200, h=10, T_{0}=700, T^{\infty}=400, A=10^{-4}, P=4 \times 10^{-2}\). Use three finite elements to solve the problem. Use elements of lengths \(0.1,0.15\), and 0.25 , respectively.

Transcribed Image Text:

d7 kA +hP(T-T)=0, 0xL, dx T(0)=To, dr x=0, dT =h(T-T), x=L, dr