Boiling and Condensation PDF

Heat and Mass Transfer Boiling and Condensation Boiling Heat Transfer Boiling is a liquid-to-vapor phase change that  Evaporation - occurs at the liquid-vapor occurs at the solid–liquid interface when a interface when the vapor pressure (Pvap) i...

Heat and Mass Transfer Boiling and Condensation Boiling Heat Transfer Boiling is a liquid-to-vapor phase change that  Evaporation - occurs at the liquid-vapor occurs at the solid–liquid interface when a interface when the vapor pressure (Pvap) is liquid at its saturation temperature (Tsat) is brought in contact with a solid surface less than the saturation pressure of the liquid maintained at a temperature (Ts )which is (Psat) at a given temperature (Pvap < Psat). sufficiently above the Tsat that is (Ts ˃Tsat)  Involves no bubble formation or bubble motion Boiling and Condensation Heat transfer coefficients h associated with boiling and condensation are typically much higher than those encountered in other forms of convection processes that involve a single phase Boiling and condensation differ from other forms of convection in that they depend on the latent heat of vaporization hfg of the fluid and the surface tension σ at the liquid–vapor interface, in addition to the properties of the fluid in each phase. Boiling Heat Transfer The boiling heat flux from a solid surface to the fluid is expressed by Newton’s law of cooling as:  Tsat is the saturation temperature of liquid @ given pressure  Ts the surface temperature of heating material , for boiling to take place , Ts ˃ Tsat  ∆Te (excess temperature) = Ts – Tsat , represents the excess of the surface above the Tsat of the liquid  ∆Te is driving force causes heat to flow from the surface into the liquid, which results in the formation of vapor bubbles that move up through the liquid. Boiling Heat Transfer (cont.) Depending on the presence of bulk fluid flow, boiling is clasified as:  Pool Boiling  When boiling occurs in absence of bulk fluid flow (stationary liquids)  The liquid motion is induced by: Natural convection Buble growth and detachement  Flow Boiling  when boiling occurs in presence of bulk fluid motion  the liquid motion is induced by external means (e.g., pumping of liquids through a heated tube and boiling taking place while the liquid is flowing) Boiling Heat Transfer (cont.) Pool and flow boiling are further classified as subcooled boiling or saturated boiling, depending on the bulk liquid temperature  Subcooled (or local) when the temperature of the main body of the liquid is below the saturation temperature Tsat (i.e., the bulk of the liquid is subcooled)  Saturated (or bulk) when the temperature of the liquid is equal to Tsat (i.e., the bulk of the liquid is saturated) Boiling Regimes and the Boiling Curve Boiling Regimes and the Boiling Curve Natural convection boiling (ΔTe < 5 °C)  No bubble formation  HT from heated solid surface to bulk fluid via natural convection  Liquid motion and HT → buoyancy effects  Liquid near the surface slightly heated and rises up Nucleate Boiling (5 oC < ΔTe < 30 oC) When ΔTe increases beyond 5 °C, the system enters the nucleate boiling regime indicated by point A to C on the Boiling Curve  Contain two region 1. Formation and rise up of bubbles but collapsed before reaching free surface (A-B) 2. Formation of jets and columns of vapor on the surface (B-C)  Transition Boiling (30 oC < ΔTe < 120 oC). Indicated by point C to D on boiling curve and characterized by : Transition from nucleate boiling to film boiling - both nucleate and film boiling partially occurs Unstable vapor film layers (vapor blanket) are produced on the heating surface , covers heater surface and act as insulation due to thermal conductivity of vapor less than that of liquid (vapor –film region) HT through the vapor blanket by both conduction and radiation As (ΔTe ) ↑, q”s ↓ until the Leidenfrost point ( the minimum heat flux for film boiling). This is due to fraction of the vapor film formation increased and cover large fraction of heater surface. Leidenfrost point ( Point D) - where the heat flux reaches a minimum  Film Boiling ( ΔTe > 120 oC ). Indicated by point D to E on boiling curve and characterized by : Formation of contionus stable vapor film layers on heater surface Hence, the heater surface is completely covered by a continuous stable vapor film, that has low thermal conductivity (high thermal resistance) HT from the surface to the liquid by Conduction through the film and Radiation through the film ( dominant as ΔTe increases ) As ΔTe ↑, q”s ↑ ( b/c radiation HT is more dominant at high temperatures).  Heat Transfer Correlations in Pool Boiling  Boiling regimes differ considerably in their character ► different heat transfer relations need to be used for different boiling regimes  In the natural convection boiling regime heat transfer rates can be accurately determined using natural convection relations In the nucleate boiling regime the rate of heat transfer strongly depends on the nature of nucleation (the number of active nucleation sites on the surface, the rate of bubble formation at each site, etc.), which is difficult to predict Due to complexity of fluid mechanics and phase-change thermodynamics, boiling heat transfer correlations are empirical  Heat Transfer Correlations in Pool Boiling- Nucleate Boiling regime The rate of heat transfer per unit area in nucleate pool boiling is determined by using Rohsenow correlation : subscripts: l  saturated liquid state v  saturated vapor state Heat Transfer Correlations in Pool Boiling- Nucleate Boiling Regime (cont.) Enthalpy of vaporization hfg of a pure substance decreases with increasing pressure (or temperature) and reaches zero at the critical point. Noting that hfg appears in the denominator of the Rohsenow equation, we should see a significant rise in the rate of heat transfer at high pressures during nucleate boiling.  The maximum/ peak (or critical) heat flux in Nucleate Boiling regime The maximum (or critical) heat flux in nucleate pool boiling was determined by S. S. Kutateladze in where Ccr is a constant whose value depends on the heater geometry. Exhaustive experimental studies by Lienhard and his coworkers indicated that the value of Ccr is about 0.15  Heat Transfer Correlations in Film Boiling The heat flux and Nusselt number for film boiling on a horizontal cylinder or sphere of diameter D was determined Bromley theory for the prediction of heat flux for stable film boiling on the outside of a horizontal cylinder. The heat flux for film boiling on a horizontal cylinder or sphere of diameter D is given by kv : Thermal conductivity of vapor At high heater surface temperatures, radiation heat transfer becomes significant during film boiling Flow Boiling In flow boiling, the fluid is forced to move by an external source such as a pump as it undergoes a phase‐change process  Internal  External The boiling in this case exhibits the combined effects of convection and pool boiling External flow boiling over a plate or cylinder is similar to pool boiling, but the added motion increases both the nucleate boiling heat flux and the critical heat flux considerably The different stages encountered in flow boiling in a heated tube 1. Initially, the liquid is subcooled and heat transfer to the liquid is by forced convection. 2. Then bubbles start forming on the inner surfaces of the tube, and the detached bubbles are drafted into the mainstream. This gives the fluid flow a bubbly appearance, and thus the name bubbly flow regime 22  3. As the fluid is heated further, the bubbles grow in size and eventually coalesce into slugs of vapor. Up to half of the volume in the tube in this slug flow regime is occupied by vapor 4. After a while the core of the flow consists of vapor only, and the liquid is confined only in the annular space between the vapor core and the tube walls.  Condensation Condensation occurs when the temperature of a vapor is reduced below its saturation temperature Tsat This is usually done by bringing the vapor into contact with a solid surface whose temperature Ts is below the saturation temperature Tsat of the vapor Condensation can also occur on the free surface of a liquid or even in a gas when the temperature of the liquid or the gas to which the vapor is exposed is below Tsat  Forms of condensation  Surface condensation may occur in two modes depending upon the conditions of the surface. 1. Drop wise condensation and 2. Film wise condensation Film condensation: the condensate wets the surface and forms a liquid film on the surface that slides down under the influence of gravity Dropwise condensation: the condensed vapor forms droplets Film wise condensation on a surface Drop wise condensation on the surface instead of a continuous film, and the surface is on a surface covered by countless droplets of varying diameters Film Condensation On Vertical Plate liquid film starts forming at the top of the plate and flows downward under the influence of gravity.  δ increases in the flow direction x Heat in the amount ( mhfg ) is released during condensation and is transferred through the film to the plate surface. The temperature of the condensate is Tsat at the interface and decreases gradually to Ts at the wall. HT in condensation also depends on whether the condensate flow is laminar or turbulent Film Condensation on some geometries Film Condensation (cont.) Therefore, the Reynolds number for all the cases can be expressed as 𝐷ℎ 𝜌𝑙 𝑉𝑙 4𝛿𝜌𝑙 𝑉𝑙 4𝐴𝑐 𝜌𝑙 𝑉𝑙 4𝑚ሶ Re = = = = 𝜇𝑙 𝜇𝑙 𝑝𝜇𝑙 𝑝𝜇𝑙  Film Condensation on Vertical Plate (cont.) The condensate in an actual condensation process is cooled further to some average temperature between Tsat and Ts, releasing more heat in the process Modified Latent Heat of Vaporization: Superheated vapor With these considerations, the rate of heat transfer can be expressed as sat Heat Transfer Correlations for Film Condensation 1) Vertical Plate Heat Transfer Correlations for Film Condensation (cond) 1) Vertical Plate From the force balance: Heat Transfer Correlations for Film Condensation The rate of heat transfer from the vapor to the plate through the liquid film is 1) Vertical Plate equal to the heat released as the vapor is condensed and is expressed as which represents the rate of condensation of vapor over a vertical distance dx  Drop wise Condensation Drop wise condensation is characterized by formation of countless droplets of varying diameters on the condensing surface that roll down over the surface instead of a continuous liquid film o small droplets form → growth of small droplets→ coalesce into large droplets→ slide down over surface.  characterized by  Unclean/contaminated/coated surface (inhibits wetting),  There is no resistance film  Therefore, HT coefficients (HT) for drop wise condensation is 10 times more than film condensation..  Example: 1 Water is to be boiled at atmospheric pressure in a mechanically polished stainless steel pan placed on top of a heating unit, as shown in the following Fig. The inner surface of the bottom of the pan is maintained at 108°C. If the diameter of the bottom of the pan is 30 cm, determine: (a) the rate of heat transfer to the water and (b) the rate of evaporation of water. ΔTe = 108 – 100 = 8 °C Fluid properties at 100 °C Example 1 (cont.)