Chapter 13, Problem 13.98P

Boiler tubes exposed to the products of coal combustion in a power plant are subject to fouling by the ash (mineral) content of the combustion gas. The ash forms a solid deposit on the tube outer surface, which reduces heat transfer to a pressurized water/steam mixture flowing through the tubes. Consider a thin-walled boiler tube $\left(D_t=0.05\text{m}\right)$ whose surface is maintained at $T_t=600\text{K}$ by the boiling process. Combustion gases flowing over the tube at $T_{\infty }=1800\text{K}$ provide a convection coefficient of $\bar{h}=100{\text{W/m}}^{\text{2}}\cdot \text{K}$ , while radiation from the gas and boiler walls to the tube may be approximated as that originating from large surroundings at $T_{\text{sur}}=1500\text{K}$ .

(a) It the lube surface is diffuse and gray, with ${\epsilon }_t=0.8$ , and there is no ash deposit layer, what is the rate of heat transfer per unit length, q’, to the boiler tube?
(b) If a deposit layer of diameter $D_d=0.06\text{m}$ and thermal conductivity $k=1\text{W/m}\cdot \text{K}$ forms on the tube, what is the deposit surface temperature, $T_d$ ? The deposit is diffuse and gray, with ${\epsilon }_d=0.9$ , and T_t, $T_{\infty }$ , $\bar{h}$ , and $T_{\text{sur}}$ remain unchanged. What is the net rate of heat transfer per unit length, q’, to the boiler tube?
(c) Explore the effect of Variations in D_dand $\bar{h}$ on q’, as well as on relative contributions of convection and radiation to the net heat transfer rate. Represent your results graphically.