A thin-walled stainless steel processing vessel has a condensing steam jacket on the outside with convective film coefficient $h_o = 5000\text{ W/(m}^2\cdot\text{K)}$ and a liquid food product on the inside with film coefficient $h_i = 500\text{ W/(m}^2\cdot\text{K)}$. Neglecting metal wall conduction resistance and fouling, the overall heat transfer coefficient ($U$) in $\text{W/(m}^2\cdot\text{K)}$ is ________ (round off to 1 decimal place).
Answer Key:
454.5
Step-by-Step Solution & Explanation
The overall heat transfer coefficient for negligible wall and fouling resistance is:
$\frac{1}{U} = \frac{1}{h_i} + \frac{1}{h_o} = \frac{1}{500} + \frac{1}{5000} = \frac{10 + 1}{5000} = \frac{11}{5000}$
$U = \frac{5000}{11} = 454.545\text{ W/(m}^2\cdot\text{K)} \approx 454.5\text{ W/(m}^2\cdot\text{K)}$