(Solved): SOLVE PART A, please A "fin" is being used to transfer heat steadily to the surrounding air. The ...

SOLVE PART A, please

A "fin" is being used to transfer heat steadily to the surrounding air. The base of the fin is at temperature \( \mathrm{T}_{\mathrm{b}} \). The ambient air temperature is \( \mathrm{T}_{\mathrm{a}} \) and is has a constant heat transfer coefficient of \( \mathrm{h}_{\mathrm{a}} \). The fin has a cylindrical shape and the length is much longer than the diameter. Assume that any differences in the \( \theta \) direction can be ignored. a. Determine the differential governing equation and boundary conditions for \( \mathrm{T}(\mathrm{r}, \mathrm{z}) \). b. Under what conditions is a one-dimensional analysis in the length (z-direction) valid for the temperature profile of the wire? , Hint: look at the Biot number. c. Use the expression for the average temperature of the wire in the z-direction given below to transform the governing equation. \[ \tilde{T}(z)=\frac{1}{\pi R^{2}} \int_{0}^{R} T(r, z) 2 \pi r d r \] Hint: look at the fin approximation problem in the book (ex. 3.4-2)