4h de? Solid, stubby, cylindrical metal rods (length-to-diameter ratio = 3) are used as fins on a hot surface with surface temperature of 700 C. The ambient air flowing around the rod fins has a temperature of 30 C. The metal thermal conductivity (k) takes a value of 0.247 cal/(s-cm-K). The heat transfer coefficient (h) around the surface of the fins is constant at 3.6 Kcal/(m2h-C). a) Analyze a single rod of 4 mm diameter and show that the steady-state differential balance yields the following differential equation for the case when metal temperature changes mainly in the x- direction (x is directed outward from the hot surface, and rod diameter is D). dT |T1)= (T-1)=0 KD b) Find the characteristic roots for the ODE in part (a). What are the physical units of these roots? c) Find the solution of part (a) using the following boundary conditions. dT negligible heat loss from BC1: T =T: @x=0 (hot surface) BC2: = 0 @ x=L dx the exposed flat tip 2h cosh (L-x) and show that the temperature profile is represented by: KR TH-TA 2h cosh KR T-TA -L