Step 1: Understanding the Problem:
The question asks to compare the convective heat transfer coefficient of dropwise condensation to that of film-type condensation on a chilled heat exchanger surface.
Step 2: Key Formula or Approach:
The rate of convective heat transfer ($q$) during condensation is given by:
\[ q = h A (T_{\text{sat}} - T_w) \]
where:
$h$ = condensation heat transfer coefficient ($\text{W/m}^2\cdot\text{K}$),
$T_{\text{sat}}$ = saturation temperature of the steam ($\text{K}$),
$T_w$ = surface wall temperature ($\text{K}$).
Step 3: Detailed Explanation:
• Condensation Mechanisms: When steam contacts a surface below its saturation temperature, it condenses via one of two mechanisms:
• Film Condensation: The condensed liquid wets the surface, forming a continuous liquid film. This film acts as a thermal resistance layer, reducing heat transfer rates because thermal energy must conduct through the liquid film to reach the wall.
• Dropwise Condensation: The liquid does not wet the surface, instead forming discrete droplets that roll off under gravity, leaving the metal surface bare. This allows fresh steam to contact the cold metal directly, maximizing heat transfer.
• Comparison of Heat Transfer Coefficients ($h$): Because there is no insulating liquid film, the heat transfer coefficient for dropwise condensation is significantly higher (typically $5 - 10$ times higher) than that of film condensation.
• Industrial Goal: Designers often apply hydrophobic promoters or coatings to condenser tubes to promote dropwise condensation, maximizing thermal efficiency.
Step 4: Final Answer:
The heat transfer coefficient during dropwise condensation is significantly higher than that of film-type condensation, corresponding to option (B).