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CHAPTER

Boiling and condensation 11

11.1  Introduction

Conduction heat transfer and single-phase convective heat transfer were presented in the previous chapters. Two-phase heat transfer, which involves conversion of liquid into vapor, referred to as boiling, or conversion of vapor into liquid, referred to as condensation, takes place in equipment such as boilers and condensers in thermal power plants, evaporators and condensers in refrigeration systems, water-cooled nuclear reactors, major equipment in process industry, and modern heat sinks for thermal management of electronics. Of particular importance in the design of the equipment are the rates of heat transfer or heat transfer coefficients and the associated pressure losses. In boiling and condensation, the coupling between the fluid dynamic process and the heat transfer process is stronger than what exists in single-phase flows. In a two-phase flow with phase change, there is a continuous variation in the fraction and distribution of each phase and hence the flow pattern, which influences the local heat transfer processes. Therefore, the flow at any axial location in the tube can never be fully developed thermally or hydrodynamically, unlike a single-phase flow. The flow also involves transient properties and deviations from thermodynamic equilibrium. In this chapter, the commonly observed regimes of pool boiling and flow patterns in flow boiling are discussed. Prior to the presentation of the correlations used to predict the heat transfer coefficients and the critical heat flux, the chapter presents a brief discussion on the wall superheat required for nucleation from a heating surface. This is followed by a discussion on the film condensation that occurs on flat plates and horizontal tubes and a presentation of the respective heat transfer coefficient correlations. The chapter ends with an introduction to the prediction of pressure drop in two-phase flows with phase change.

11.2  Boiling

Boiling can occur with the heating surface immersed in a pool of an initially stagnant liquid, referred to as pool boiling, or with the liquid forced over the heating surface by some external means such as a pump, which is referred to as flow boiling or forced convective boiling. As long as the heating surface temperature is greater than the saturation temperature of the liquid, there is a possibility of boiling, whether the bulk liquid is at saturation temperature (saturated boiling) or below the saturation

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352 CHAPTER 11  Boiling and condensation

temperature (subcooled boiling). Heat transferred from the heating surface to the liquid is given by the expression

where Tsup = (Tw − Tsat ) is the wall superheat.

Single-phase convection is influenced by fluid density, thermal conductivity, viscosity, specific heat, geometric parameter, and velocity in case of forced convection and the difference between the temperatures of the heating surface and the fluid and volumetric coefficient of thermal expansion in case of natural convection. Boiling, on other hand, is influenced by additional properties that include latent heat of vaporization, saturation temperature, vapor density, surface tension, and heating surface characteristics. Because of the large number of influencing variables and different mechanisms of heat transfer involved depending on the flow patterns and the wall superheat, the boiling process is complex, and it is difficult to obtain an equation (or a correlation) for the heat transfer coefficient as a function of pertinent parameters regardless of whether our approach is theoretical or experimental.

11.3  Pool boiling

Pool boiling, especially nucleate pool boiling, due to its high heat transfer coefficients, finds applications in chemical and petrochemical industries, refrigeration and desalination of sea water (for example, flooded evaporators), metallurgical industry (for example, quenching process), and cooling of electronic components (for example, vapor chamber heat sink). The typical temperature profile in the saturated pool boiling is shown in Fig. 11.1. There is a large temperature gradient close to the heating surface, with the temperature varying from the wall temperature, Tw , at the heating surface to nearly the saturation temperature, Tsat , across the thin thermal boundary

FIGURE 11.1

Temperature profile in the liquid during pool boiling.

11.3 Pool boiling 353

layer. The liquid is superheated in this region. There are different regimes of pool boiling, and the heat transfer mechanism in each of the regimes differs greatly.

11.3.1  Pool boiling curve

A typical pool boiling curve for water boiling at atmospheric pressure is shown in Fig. 11.2. When the heat flux or wall superheat is low, no vapor bubbles emanate from the heating surface and the heat transport occurs by natural convection currents in the region AB. This stage is shown in Fig. 11.3A. The evaporation that occurs at the free surface is called “silent evaporation” or “silent boiling.” In laminar natural convection, the heat transfer coefficient (h) varies as Tsup1/4 or q1/5 , and in turbulent natural convection, it varies as Tsup1/3 or q1/4 . As the heat flux or the wall superheat increases, vapor bubbles form on the heating surface when a certain wall superheat is attained (B). This is called the onset of nucleate boiling (ONB). Because of the formation of vapor bubbles, there is an increase in the heat transfer coefficient that leads to a sudden decrease in the wall temperature (B'). With further increase in the heat flux, more bubbles are formed on the heating surface and the heat transport occurs by both vapor bubbles and natural convection in the areas not influenced by the bubbles. This results in an increase in the heat transfer coefficient and hence the slope of the boiling curve (B"). Fig. 11.3B shows typical nucleate boiling. A further increase in the heat flux or the wall temperature results in the increased nucleations on the heating surface, and the nucleation site density will be so high that there will not be any area available for natural convection, and the heat transfer coefficient increases drastically (C). In nucleate boiling, h typically varies as Tsup3 or q3/4 . At still higher heat fluxes, the vapor bubble generation frequency and the nucleation site density will be so high that the increased vapor generation rate results in the formation of

FIGURE 11.2

Pool boiling curve for water at atmospheric pressure.

354 CHAPTER 11  Boiling and condensation

FIGURE 11.3

Different stages in the pool boiling curve.

a vapor film, which tends to prevent the surrounding liquid from coming in contact with the heating surface (D). This causes a sharp reduction in the heat transfer coefficient, which leads to the wall temperature shooting up (DD') in the case of constant heat flux of the heating surface. If the heating surface is maintained at constant wall temperature, there is a reduction in the wall heat flux. This point is commonly known as the critical heat flux, and terms such as “boiling crisis” and “burnout” are also used, although it need not necessarily result in the actual burnout that depends on the metallurgical properties. Sometimes, this is also referred to as the departure from nucleate boiling (DNB), a term that is more appropriate from the point of view of physics and is illustrated in Fig. 11.3C. With further increase in the wall temperature (for the case of wall temperature–controlled heating surface), there will be a reduction in the heat flux, and the region DE is known as the unstable (or metastable) film boiling, characterized by the rapid formation and collapse of the vapor film, and at point E the vapor film becomes stable. If the wall temperature is increased further, there will be an increase in the heat flux (EF), caused by the contributions from both convection (conduction through the vapor film) and radiation, and the film remains stable, which is shown in Fig. 11.3D. The point E, where the heat flux is minimum, is

356CHAPTER 11  Boiling and condensation

compared with that for a planar interface, for the same liquid temperature. The equation of equilibrium vapor nucleus derived considering this effect eventually simplifies

to Eq. (11.6) for (2σ / pf r ) <<1 and Tg ~ Tsat . For details, see Collier and Thome (1994).

Homogeneous nucleation refers to the process of vapor formation in a superheated (metastable) liquid, as, for example, in the microwave heating of a liquid. But the most common one is heterogeneous nucleation, which refers to the process of vapor formation from pre-existing nuclei such as non-condensable gas bubbles suspended in the liquid, and vapor or gas-filled cavities and scratches on the container wall. These sites where the pre-existing nuclei are present are called nucleation sites.

Eq. (11.6) gives the liquid superheat required for a vapor nucleus in a liquid of uniform temperature field. For nucleation from the heating surface, the temperature gradient away from the heating surface needs to be taken into account. Fig. 11.4 shows a hemispherical vapor nucleus of radius rc , sitting at the mouth of a conical cavity (nucleation site). The liquid temperature profile shown in the figure is assumed to be linear through the thermal boundary layer of thickness δ, which is approximately equal to (k f /h). According to Hsu (1962), the criterion for nucleation from this cavity is that the temperature of the liquid close to the top of the bubble should be greater than that necessary for the equilibrium of the vapor nucleus (Eq. 11.6). Nucleation occurs if the liquid temperature line intersects the equilibrium vapor nucleus curve. As the heat flux increases, at a certain heat flux, the liquid temperature profile makes a tangent to the equilibrium vapor nucleus curve, which results in the first nucleation site to be activated, and the corresponding wall temperature is Tw,ONB , as shown in Fig. 11.4.

FIGURE 11.4

Onset of nucleation from the heating surface during pool boiling.

358CHAPTER 11  Boiling and condensation

shown in Fig. 11.4, though the equilibrium vapor nucleus curve (Eq. 11.6) shown in Fig. 11.4 suggests that rougher surfaces (that contain cavities of larger size) readily nucleate, that is, they need lower wall superheat for nucleation. Even so, this need not necessarily be the case, as they may not be able to trap the vapor required for nucleation. Example 11.1 presents some calculations on the wall superheat required

for nucleation for water at atmospheric pressure. The thermal boundary layer thickness δ can be calculated using single phase natural convection correlations such as the one below for turbulent natural convection on a horizontal surface (Fishenden and Saunders, 1950).

where β and Pr are the volumetric coefficient of thermal expansion and the liquid Prandtl number, respectively.

Surface wettability is another important factor that influences nucleation. For solid-liquid systems with low surface wettability, superheat required for nucleation at the surface is low. For a perfectly non-wetting surface (contact angle measured through the liquid is 180°), no superheat is required for vapor bubble nucleation at the surface. For details on the influence of surface wettability, cavity shape and cavity mouth radius on the possibility of nucleation (vapor being trapped in the cavity), the wall superheat required for nucleation, and the stability of nucleation sites, the interested reader can refer to advanced texts such as Collier and Thome (1994) and Tong and Tang (1997).

Example 11.1: Estimate the wall superheat required for nucleation from a horizontal surface immersed in water at atmospheric pressure, with the liquid pool at the saturation temperature, if cavities (nucleation sites) of all sizes are active, and if cavities (nucleation sites) of sizes 3 µm or smaller only are active.

Solution:

Fluid properties corresponding to 100 °C:

ρ f = 958 kg/m3 , µf = 283 ×10−6 Ns/m2 , Prf = 1.75,

k f = 0.681 W/mK, β = 7.51×10−4 K−1, R = 462 J/kgK

Using Eq. (11.14)