1. Two-Phase: Overview Two-Phase Boiling Condensation
two-phase heat transfer describes phenomena where a change of phase (liquid/gas) occurs during and/or due to the heat transfer process
two-phase heat transfer generally considers processes that occur at a solid/fluid interface and are therefore a sub-field of convection
because of the change of phase, the latent heat (hfg) of the fluid must be considered
the surface tension (σ) is another parameter that plays an important role
Boiling
heat transfer process where a liquid undergoes a phase change into a vapor (gas)
Condensation
heat transfer process where a vapor (gas) liquid undergoes a phase change into a liquid

2. Boiling: Overview Boiling Modified Newton’s Law of Cooling
associated with transformation of liquid to vapor (phase change) at a solid/liquid interface due to convection heat transfer from the solid
agitation of the fluid by buoyant vapor bubbles provides for large convection coefficients  large heat fluxes at low-to-moderate surface-to-fluid temperature differences
Modified Newton’s Law of Cooling
surface temperature
saturation temperature of liquid
excess temperature

3. Boiling: Overview Flow Cases Temperature Cases Pool Boiling
liquid motion is due to natural convection and bubble-induced mixing
Forced Convection Boiling (Flow Boiling/2-Phase Flow)
liquid motion is induced by external means and there is also bubble-induced mixing
Temperature Cases
Saturated Boiling
liquid temperature is slightly higher than saturation temperature
Subcooled Boiling
liquid temperature is less than saturation temperature

4. Boiling: The Boiling Curve
identifies different regimes during saturated pool boiling
nucleate boiling
inflection point
transition
boiling
film
boiling
free convection
Leidenfrost point
Water at Atmospheric Pressure

5. Boiling: Boiling Curve
Free Convection Boiling (ΔTe < 5 °C)
little vapor formation
liquid motion is primarily due to buoyancy effects
Nucleate Boiling (5 °C < ΔTe < 30 °C)
onset of nucleate boiling ΔTe ~ 5 °C (ONB)
isolated vapor bubbles (5 °C < ΔTe < 10 °C)
liquid motion is strongly influenced by nucleation of bubbles on surface
h and q”s increase sharply with increasing ΔTe
heat transfer is primarily due to contact of liquid with the surface (single-phase conduction) and not to vaporization
jets and columns (10 °C < ΔTe < 30 °C)
increasing number of nucleation sites causes bubble interactions and coalescence into jets and slugs
liquid/surface contact is impaired by presence of vapor columns
q”s increases with increasing ΔTe
h decreases with increasing ΔTe

6. Boiling: Boiling Curve
Nucleate Boiling (5 °C < ΔTe < 30 °C)
critical heat flux (CHF) (ΔTe ~ 30 °C)
maximum attainable heat flux in nucleate boiling
water at atmospheric pressure
CHF ~ MW/m2
hmax ~ W/m2-K
Transition (30 °C < ΔTe < 120 °C) & Film Boiling (ΔTe > 120 °C)
heat transfer is by conduction and radiation across the vapor blanket
liquid/surface contact is impaired by presence of vapor columns
q”s decreases with increasing ΔTe until the Leidenfrost point corresponding to the minimum heat flux for film boiling and then proceeds to increase
a reduction in the surface heat flux below the minimum heat flux results in a abrupt reduction in surface temperature to the nucleate boiling regime
Heat flux controlled heating: burnout potential
if the heat flux at the surface is controlled it can potentially increase beyond the CHF
this causes the surface to be blanketed by vapor and the surface temperature can spontaneously achieve a value that potentially exceeds its melting point (ΔTe > 1000 °C)
if the surface survives the temperature shock, conditions are characterized as film boiling

7. Boiling: Pool Boiling Correlations
Due to complexity of fluid mechanics and phase-change thermodynamics, boiling heat transfer correlations are empirical
Rohsenow Correlation: Nucleate Boiling
note: can be as much as 100% inaccurate!
Critical Heat Flux
subscripts:
l  saturated liquid state
v  saturated vapor state
correction factor required for surfaces with small characteristic lengths

8. Boiling: Pool Boiling Correlations
Rohsenow Correlation

9. Boiling: Pool Boiling Correlations
Minimum Heat Flux
Film Boiling
correlation for spheres & cylinders
total average heat transfer coefficient due to cumulative & coupled effects of convection (due to boiling) and radiation across the vapor layer
Leidenfrost point
reduced latent heat

10. Condensation: Overview
occurs when the surface temperature is less than the saturation temperature of an adjoining vapor
heat is transferred from vapor the surface to the surface
Film Condensation
entire surface is covered by the condensate which flows continuously from the surface and presents a thermal resistance to heat transfer from the vapor to the surface
typically due to clean, uncontaminated surfaces
can be reduced by using short vertical surfaces & horizontal cylinders
Dropwise Condensation
surface is covered by drops ranging from a micron to large agglomerations
thermal resistance is lower than that of film condensation
surface coatings may inhibit wetting and stimulate dropwise condensation

11. Condensation: Film Condensation
Vertical Plate
thickness and flow rate of condensate increase with increasing x
generally, the vapor is superheated (Tv,∞>Tsat) and may be part of a mixture that contains noncondensibles
a shear stress at the liquid/vapor interface induces a velocity gradient in the vapor as well as the liquid
Laminar Flow Analysis
assume pure vapor
assume negligible shear stress at liquid/vapor interface
negligible advection in the film

12. Condensation: Film Condensation
Vertical Plate: Laminar Flow Analysis
film thickness
flow rate per unit width
average Nusselt number
heat transfer rate
condensation rate
modified latent heat
Jakob number

13. Condensation: Film Condensation
Vertical Plate: Turbulence
transition may occur in the film and three flow regimes may be delineated
wave-free laminar region (Reδ<30)
wavy laminar region (30<Reδ<1800)
turbulent region (Reδ>1800)

14. Condensation: Film Condensation
Vertical Plate: Calculation Procedure
assume a flow regime and use the corresponding equation for to determine Reδ
if Reδ value is consistent with flow regime assumption, calculate total heat rate and mass flow rate
if Reδ value is inconsistent with flow regime assumption, iterate on flow regime assumption until it is consistent

15. Condensation: Film Condensation
Radial Systems: Single Tubes/Spheres
Tube: C =0.729
Sphere: C=0.826

16. Condensation: Film Condensation
Radial Systems: Vapor Flow in a Horizontal Tube
if vapor flow rate is low, condensation in both circumferential and axial directions
for high flow rates, flow is two-phase annular flow

17. Condensation: Dropwise Condensation
heat transfer rates ~order of magnitude greater than film condensation
heat transfer coefficients highly dependant on surface properties
Steam on copper with surface coating