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Saturated steam condenses on a vertical plate maintained at a constant wall temperature. If $x$ is the vertical distance from the top edge of the plate, then the local heat transfer coefficient $h\left ( x \right ) \alpha \:\Gamma \left ( x \right )^{\frac{-1}{3}}$, where $\Gamma (x)$ is the local mass flow rate of the condensate per unit plate width. The ratio of the average heat transfer coefficient over the entire plate to the heat transfer coefficient at the bottom of the plate is

  1. $4$
  2. $\frac{4}{3}$
  3. $\frac{3}{4}$
  4. $3$
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