(Solved): i. Calculate the average convection heat transfer coefficient which characterise heat transfer to ...

i. Calculate the average convection heat transfer coefficient which characterise heat transfer to the internal fluid from the cylinder wall. Neglect the effect of the thin water coat. [4 Marks] ii. Calculate the rate of heat transfer by convection to the internal flow. [6 Marks] iii. Determine the rate of heat transfer by water evaporation to the internal flow. [7 Marks] Air Properties: $\begin{array}{l}\text{ At }T=30^{?}\mathrm{C}:?=1.1514\mathrm{kg}/{\mathrm{m}}^3,k=26.5\times 10^{?3}\mathrm{W}/\mathrm{m}.K,?=186\times 10^{?7}\mathrm{N}.\mathrm{s}/{\mathrm{m}}^2\\ \mathrm{Pr}=0.707,c_p=1007\mathrm{J}/\mathrm{kg}?K,?=22.9\times 10^{?6}{\mathrm{m}}^2/\mathrm{s}\\ {\text{ At T }}_{\mathrm{s}}=40^{?}\mathrm{C},?=190.7\times 10^{?6}\mathrm{N}.\mathrm{s}/{\mathrm{m}}^2\end{array}$ Saturated Water Vapour Properties: $\text{ At }T=40^{?}\mathrm{C}:v_g=19.35{\mathrm{m}}^3/\mathrm{kg}{h}_{fg}=2406\mathrm{kJ}/\mathrm{kg}?\mathrm{K}$ Binary Air/Water Vapour $D_{AR}=0.26\times 10^{?4}{\mathrm{m}}^2/\mathrm{s}\text{. }$ Consider a horizontal circular pipe of length $L=0.7\mathrm{m}$ and diameter $D=10\mathrm{mm}$ with walls at a uniform temperature $T_s=40^{?}\mathrm{C}$ (see sketch on Fig. 4). Dry air enters the pipe from the left boundary with a uniform velocity profile and therefore is not fully developed at that point. A thin water film also coats the inner surface of the pipe and has the same uniform surface temperature as the pipe wall. The problem is at a steady state and you can neglect the thickness of the pipe walls. The air enters the pipe at an inlet temperature $T_{m,i}=20^{?}\mathrm{C}$ and velocity $u_m=1.1\mathrm{m}/\mathrm{s}$ with $0\%$ relative humidity. Figure 4 Circular Pipe