Chapter 8, Problem 8.81P

Air at $\text{25}°\text{C}$ flows at $30\times {10}^{-6}kg/s$ within $\text{1}00-\text{mm}$ -long channels used to cool a high thermal conductivity metal mold. Assume the flow is hydro-dynamically and thermally fully developed

(a) Determine the heat transferred to the air for a circular channel $\left(\text{D = 10 mm}\right)$ when the mold temperature is $\text{5}0°\text{C}$ (case A).
(b) Using new manufacturing methods (see Problem 8.105), channels of complex cross section can readily fabricated within metal objects, such as molds. Consider air flowing under the same conditions as in case A. except now the channel is segmented into six smaller triangular sections. The flow area of case A is equal to the total (low area of case B. Determine the heat transferred to the air for the segmented channel.
(c) Compare the pressure drops for cases A and B