Question 24.3: Use the shooting method to solve Eq. (24.6) for the rod in E...

Use the shooting method to solve Eq. (24.6) for the rod in Example 24.1 : L = 10 m, h^′ = 0.05 m^{−2} [ h = 1 J/(m^2 · K · s), r = 0.2 m, k = 200 J/(s · m · K)], T_∞ = 200 K, and T(10) = 400 K. However, for this case, rather than having a fixed temperature of 300 K, the left end is subject to convection as in Fig. 24.5.
For simplicity, we will assume that the convection heat transfer coefficient for the end area is the same as for the rod’s surface .

0=\frac{d^2}{d x^2}+h^{\prime}\left(T_{\infty}-T\right)            (24.6)