A 1.0 cm diameter steel rod with k = 20W/(m-K) is 20 cm long. It has one end maintained at 35°C and the other at 100°C. It is exposed to convection heat transfer with h=65W/(m^2-K) and an ambient air stream at 20°C. a) Sketch the distribution of temp within the rod. b) Determine the rate of convective heat transfer from the rod. c) What are the conductive heat transfer rates at each end of the rod?
Rate of Convection = (h)(Area)(T-T∞)
Rate of Conduction = -k(Area)(dT/dx)
The Attempt at a Solution
I'm not really sure how to attempt this problem. I know that using an energy balance E(in)=E(out) I could solve for a diff. eq. for the temperature anywhere in the rod. But I'm not sure how that would be useful. For conduction, if its at the end of the rod how is there a change in x direction? And for convection, I'm not sure what temperature I would use for T to find the rate since the entire rod is going to be at different temperatures.