6.81 An industrial process involves evaporation of a thin water film from a contoured surface by heating it from below and forcing air across it. Laboratory measure- ments for this surface have provided the following heat transfer correlation: 0.58 Nut = 0.43 Re8 P,04 The air flowing over the surface has a temperature of 290 K, a velocity of 10 m/s, and is completely dry ( = 0). The surface has a length of 1 m and a surface area of 1 m². Just enough energy is supplied to maintain its steady-state temperature at 310 K. (a) Determine the heat transfer coefficient and the rate at which the surface loses heat by convection. (b) Determine the mass transfer coefficient and the evaporation rate (kg/h) of the water on the surface. (c) Determine the rate at which heat must be supplied to the surface for these conditions.

Elements Of Electromagnetics
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### Problem 6.81

An industrial process involves the evaporation of a thin water film from a contoured surface by heating it from below and forcing air across it. Laboratory measurements for this surface have provided the following heat transfer correlation:

\[
\overline{Nu}_L = 0.43 \, \text{Re}_L^{0.58} \, \text{Pr}^{0.4}
\]

The air flowing over the surface has the following properties:
- Temperature: 290 K
- Velocity: 10 m/s
- Humidity: Completely dry (\(\phi = 0\))

The specifications of the surface are:
- Length: 1 m
- Surface area: 1 m²

Enough energy is supplied to maintain a steady-state temperature of 310 K on the surface.

#### Questions:

(a) Determine the heat transfer coefficient and the rate at which the surface loses heat by convection.

(b) Determine the mass transfer coefficient and the evaporation rate (kg/h) of the water on the surface.

(c) Determine the rate at which heat must be supplied to the surface for these conditions.

---

### Explanation:

To solve this problem, consider the following:

- **Heat Transfer Coefficient**: Use the Nusselt number correlation to find the heat transfer coefficient.
- **Convection Rate**: Evaluate the rate of heat loss using the heat transfer coefficient and the temperature difference.
- **Mass Transfer Coefficient**: Use appropriate relations to find the mass transfer coefficient.
- **Evaporation Rate**: Calculate based on the mass transfer coefficient and the given conditions.
- **Required Heat Supply**: Determine the energy input needed to maintain the steady-state temperature.
Transcribed Image Text:### Problem 6.81 An industrial process involves the evaporation of a thin water film from a contoured surface by heating it from below and forcing air across it. Laboratory measurements for this surface have provided the following heat transfer correlation: \[ \overline{Nu}_L = 0.43 \, \text{Re}_L^{0.58} \, \text{Pr}^{0.4} \] The air flowing over the surface has the following properties: - Temperature: 290 K - Velocity: 10 m/s - Humidity: Completely dry (\(\phi = 0\)) The specifications of the surface are: - Length: 1 m - Surface area: 1 m² Enough energy is supplied to maintain a steady-state temperature of 310 K on the surface. #### Questions: (a) Determine the heat transfer coefficient and the rate at which the surface loses heat by convection. (b) Determine the mass transfer coefficient and the evaporation rate (kg/h) of the water on the surface. (c) Determine the rate at which heat must be supplied to the surface for these conditions. --- ### Explanation: To solve this problem, consider the following: - **Heat Transfer Coefficient**: Use the Nusselt number correlation to find the heat transfer coefficient. - **Convection Rate**: Evaluate the rate of heat loss using the heat transfer coefficient and the temperature difference. - **Mass Transfer Coefficient**: Use appropriate relations to find the mass transfer coefficient. - **Evaporation Rate**: Calculate based on the mass transfer coefficient and the given conditions. - **Required Heat Supply**: Determine the energy input needed to maintain the steady-state temperature.
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