Understanding the Nucleate Boiling Regime

Boiling is a phase transition process where a liquid turns into a vapor. When heat is added to a liquid, its temperature rises until it reaches the saturation temperature. Further heat addition at constant pressure results in boiling. Boiling can occur in different regimes depending on the temperature difference between the heating surface and the saturation temperature of the liquid. This temperature difference is often called the excess temperature, denoted by $\Delta T_{\text{excess}}$.

$\Delta T_{\text{excess}} = T_{surface} - T_{saturation}$

Where:

• $T_{surface}$ is the temperature of the heating surface.
• $T_{saturation}$ is the saturation temperature of the liquid at the given pressure.

Boiling Regimes and Excess Temperature

As the excess temperature increases, the boiling process changes significantly, leading to different boiling regimes:

1. Natural Convection Boiling: At very low excess temperatures (typically less than 5°C), heat transfer occurs mainly through natural convection. There is some evaporation from the free surface, but no bubbles form on the heating surface.
2. Nucleate Boiling: As the excess temperature increases further, vapor bubbles start forming at specific points (nucleation sites) on the heating surface. These bubbles grow and detach, causing vigorous liquid agitation and significantly enhancing heat transfer. This regime is characterized by high heat transfer coefficients. The nucleate boiling regime is typically observed over a specific range of excess temperatures.
3. Transition Boiling (or Unstable Film Boiling): Beyond the nucleate boiling regime, increasing the excess temperature causes the bubbles to form so rapidly that they begin to coalesce and form a partial vapor film on the surface. This film insulates the surface, and the heat transfer rate starts to decrease with increasing $\Delta T_{\text{excess}}$. This regime is unstable.
4. Film Boiling: At high excess temperatures, a stable, continuous vapor film covers the entire heating surface. Heat transfer occurs through conduction and radiation across this vapor film. The heat transfer rate is relatively low compared to nucleate boiling but increases with increasing $\Delta T_{\text{excess}}$ in this regime due to increased radiation.

Nucleate Boiling Regime Temperature Range

The nucleate boiling regime is particularly important because it provides very effective heat transfer. This regime starts when discrete bubbles begin to form and ends when the surface becomes mostly covered by a vapor film (the critical heat flux point). The range of excess temperature for nucleate boiling depends on the fluid and the surface properties, but for water boiling at atmospheric pressure on a clean surface, typical values are:

• It begins at an excess temperature of about 5°C.
• It extends up to an excess temperature of about 30°C to 50°C.

Thus, the nucleate boiling regime is formed approximately between 5°C and 50°C excess temperature.

Analyzing the Options

Let's look at the given options for the range of $\Delta T_{\text{excess}}$ for the nucleate boiling regime:

• Option 1: 5°C $\le \Delta T_{\text{excess}} \le$ 10°C - This range is too narrow and only covers the lower part of the nucleate boiling regime.
• Option 2: 5°C $\le \Delta T_{\text{excess}} \le$ 50°C - This range aligns well with the typical temperature range for nucleate boiling, covering the onset of boiling up to the critical heat flux for many common fluids like water.
• Option 3: 50°C $\le \Delta T_{\text{excess}} \le$ 80°C - This range falls into the transition boiling regime or even early film boiling.
• Option 4: 80°C $\le \Delta T_{\text{excess}} \le$ 100°C - This range is clearly in the film boiling regime.

Based on the typical characteristics of boiling curves and the ranges for different boiling regimes, the range 5°C $\le \Delta T_{\text{excess}} \le$ 50°C corresponds to the nucleate boiling regime.