Section PQ: In section PQ, initially when the wire temperature is slightly above the saturation temperature of the liquid, the liquid in contact with the heating surface get slightly superheated. The free convection of this heated fluid element is responsible for motion of the fluid, and it subsequently evaporated when it rises to the surface. This regime is called the interfacial evaporation regime.
Section QS: The section QS is composed of section QR and section RS. In QR section, bubbles begin to form on the surface of the wire and are dissipated in the liquid after detaching from the heating surface. If the excess temperature ( further increases, bubbles form rapidly on the surface of the heating wire, and released from it, rise to the surface of the liquid, and are discharged into the top of the water surface (fig 6.3). This particular phenomenon is shown in section RS. Near the point S, the vapour bubbles rise as columns and bigger bubbles are formed. The vapour bubbles break and coalesce thus an intense motion of the liquid occurs which in-turn increases the heat transfer coefficient or heat transfer flux to the liquid from the heating wire. The section QS is known as nucleate boiling.
Fig. 6.3: (a) Formation of tiny bubbles, and (b) Grown up bubbles
Section ST: At the beginning of the section ST or at the end of the section , the maximum number of bubbles are generated from the heating surface. The bubbles almost occupy the full surface of the heating wire. Therefore, the agitation becomes highest as they discharge from the surface. Thus, maximum heat transfer coefficient is obtained at point S. However, once the population of the bubbles reaches to maximum, the nearby bubbles coalesce and eventually a film of vapour forms on the heating surface. This layer is highly unstable and it forms momentarily and breaks. This is known as transition boiling (nucleate to film). In this situation the vapour film (unstable) imparts a thermal resistance and thus the heat transfer coefficient reduces rapidly.
Section TU: If the excess temperature is further increased, the coalesced bubbles form so rapidly that they blanket the heating surface (stable vapour film) and prevent the inflow of fresh liquid from taking their place. The heat conducts only by the conduction through this stable vapour film. As a result the flux of heat transfer decreases continuously and reaches a minimum at point U. All the resistance to the heat transfer is imposed by this layer stable layer of vapour film.
Section UV: At very high excess temperature the heat transfer is facilitated by the radiation through the vapour film and thus the heat transfer coefficient start increasing. Infact the excess temperature in this regime is so high that the heating wire may get melted. This situation is known as boiling crises. The combine regime of ST, TU, and UV is known as film boiling regime.
At this stage it would be interesting to know the Leidenfrost phenomenon, which was observed by Leidenfrost in 1756. When water droplets fall on a very hot surface they dance and jump on the hot surface and reduces in size and eventually the droplets disappear. The mechanism is related to the film boiling of the water droplets. When water droplet drops on to the very hot surface, a film of vapour forms immediately between the droplet and the hot surface. The vapour film generated provide and up-thrust to the droplet. Therefore, the droplet moves up and when again the droplet comes in the contact of the hot surface, the vapour generated out of the water droplet and the phenomenon continues till it disappears.
The effectiveness of nucleate boiling depends primarily on the ease with which bubbles form and free themselves from the heating surface. The important factor in controlling the rate of bubble detachment is the interfacial tension between the liquid and the heating surface. If this interfacial tension is large the bubbles tends to spread along the surface and blocked the heat transfer area, rather than leaving the surface, to make room for other bubbles. The heat transfer coefficient obtained during the nucleation boiling is sensitive to the nature of the liquid, the type and condition of the heating surface, the composition and purity of the liquid, agitation, temperature and pressure.
Fact: Film boiling is not normally desired in commercial equipment because the heat transfer rate is low for such a large temperature drop.
6.2.1 Nucleation boiling
Rohsenow correlation may be used for calculating pool boiling heat transfer
|q is the heat flux (W/m2)|
|μl is the liquid viscosity (Pa.s)|
|λ is the enthalpy of liquid vaporisation (J/kg)|
|ρl and ρv are the liquid and vapour density, respectively, (kg/m3)|
|cp1 is the specific heat of liquid (J/kg/°C)|
|σ is the surface tension (N/m)|
|Te is the excess temperature of the boiling surface, Tw - Tsat, (K)|
|Pr1 is the liquid Prandtl number|
Csf and n are the constants and depend on the liquid and heating surface combination for boiling operation, for example,
All the properties are to be evaluated at film temperature.
6.2.2 Maximum heat flux
Maximum heat flux corresponding to the point S in the fig.6.2 can be found by Leinhard correlation,
The notations are same as for eq.6.2.
6.2.3 Film boiling
where, kv is the thermal conductivity of the vapour, µv is the viscosity of the vapour, d is the characteristic length (tube diameter or height of the vertical plate), other notations are same as for eq. 6.2.
If the surface temperature is high enough to consider the contribution of radiative heat transfer, the total heat transfer coefficient may be calculation by,
where, hr is the radiative heat transfer coefficient and is given in eq.6.4.
Upto this section, we have discussed about the boiling phenomenon where the liquid phase changes to vapour phase. In the subsequent sections, we will study the opposite phenomena of boiling that is condensation, where the vapour phase changes to the liquid phase.
6.3 Heat transfer during condensation
Condensation of vapours on the surfaces cooler than the condensing temperature of the vapour is an important phenomenon in chemical process industries like boiling phenomenon. It is quite clear that in condensation the phase changes from vapour to liquid. Consider a vertical flat plate which is exposed to a condensable vapour. If the temperature of the plate is below the saturation temperature of the vapour, condensate will form on the surface and flows down the plate due to gravity. It is to be noted that a liquid at its boiling point is a saturated liquid and the vapour in equilibrium with the saturated liquid is saturated vapour. A liquid or vapour above the saturation temperature is called superheated. If the non-condensable gases will present in the vapour the rate of condensation of the vapour will reduce significantly.
Condensation may be of two types, film condensation and dropwise condensation. If the liquid (condensate) wets the surface, a smooth film is formed and the process is called film type condensation. In this process, the surface is blocked by the film, which grows in thickness as it moves down the plate. A temperature gradient exists in the film and the film represents thermal resistance in the heat transfer. The latent heat is transferred through the wall to the cooling fluid on the other side of the wall. However, if the liquid does not wet the system, drops are formed on the surface in some random fashion. This process is called dropwise condensation. Some of the surface will always be free from the condensate drops (for a reasonable time period).
Now, with the help of the above discussion one can easily understand that the condensate film offers significant heat transfer resistance as compared to dropwise condensation. In dropwise condensation the surface is not fully covered by the liquid and exposed to the vapour for the condensation. Therefore, the heat transfer coefficient will be higher for dropwise condensation. Thus the dropwise condensation is preferred over the film condensation. However, the dropwise condensation is not practically easy to achieve. We have to put some coating on the surface or we have to add some additive to the vapour to have dropwise condensation. Practically, these techniques for dropwise condensation are not easy for the sustained dropwise condensation. Because of these reasons, in many instances we assume film condensation because the film condensation sustained on the surface and it is comparatively easy to quantify and analyse.