Chapter 8, Problem 8.18P

Atmospheric air enters the heated section of a circular tube at a flow rate of 0.005 kg/s and a temperature of $\text{2}0°\text{C}$ . The tube is of’ diameter $D=\text{ 5}0\text{ mm}$ , and fully developed conditions with $h=25{\text{W/m}}^2\cdot \text{K}$ exist over the entire length of $L=\text{ 3 m}$ .

(a) For the case of uniform surface heat flux at $q_s^n=1000{\text{W/m}}^2$ , determine the total heat transfer rate q and the mean temperature of the air leaving the tube $T_{m,0}$ . What is the value of the surface temperature at the tube inlet $T_{s,i}$ and outlet $T_{s,0}$ ? Sketch the axial variation of T, and $T_m$ . On the same figure, also sketch (qualitatively) the axial variation of $T_s$ and $T_m$ for the more realistic case in which the local convection coefficieni varies Withx.

(b) If the surface heat flux varies linearly with x. such that $q_s^n=\left({\text{W/m}}^2\right)=500x\left(\text{m}\right)$ , what are the values of $q,T_{m,o},T_{s,i}$ and $T_{s,o}$ ?, Sketch the axial variation of $T_s$ and $T_m$ . On the same figure. also sketch (qualitatively) the axial variation of $T_s$ and $T_m$ for the more realistic case in which the local convection coefficient varies with x.

(c) For the two heating conditions of parts (a) and (b), plot the mean fluid and surface temperatures. $T_m\left(x\right)$ and $T_s\left(x\right)$ , respectively, as functions of distance along the tube. What effect will a fourfold increase in the convection coefficient have on the temperature distributions?

(d) For each type of heating process, what heat fluxes are required to achieve an air outlet temperature of $125°\text{C}$ ? Plot he temperature distributions.