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Momentum Heat Mass Transfer

Momentum Heat Mass Transfer. MHMT 12. Heat transfer at phase changes. Heat transfer at melting, condensation and boiling (pool, convective). Whalley P.B.: Boiling, Condensation and Gas-Liquid flow. Oxford Sci.Pub. 1987. Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010.

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Momentum Heat Mass Transfer

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  1. Momentum Heat Mass Transfer MHMT12 Heat transfer at phase changes Heat transfer atmelting, condensation andboiling (pool, convective) Whalley P.B.: Boiling, Condensation and Gas-Liquid flow. Oxford Sci.Pub. 1987 Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010

  2. isobar p=const there is only gas above the critical temperature Tcrcritical temperature T [K] superheated steam Liquid T boiling point temperature at pressure p L+S Gas evaporation S L+G LG evaporation GL condensation heating liquid TTPtriple point temperature melting SG sublimation heating solids Solid s s [kJ/kg.K] entropy Phase changes T-s chart MHMT12 The temperature-entropy chart enables to calculate for example the heat Q [J/kg] necessary for evaporation (Q=Ts), condensation, or melting of 1kg of substance (heat Q is the area under isobar in the case of heating at constant pressure, see the red curve)

  3. HEAT transfer melting MHMT12 Melting, freezing, baking are thermal processes characterised by moving interface between two phases – liquid and solid. Description of the interface motion is so called Stefan problem. Duchamp

  4. TS Tm melting point temperature z (t) (t+dt) HEAT transfer melting MHMT12 Stefan problem in 1D: Let us assume that a semi-infinite space is a solid at a melting point temperature Tm. Since the time zero the temperature of surface is increased to Ts. Enthalpy balance (assuming linear temperature profile in liquefied layer) during time interval dt Solution: where and aL is temperature diffusivity of liquid.

  5. HEAT transfer condensation MHMT12 Dropwise condensation Film condensation Steam at temperature of saturation Tsat T Twall < Tsat Duchamp z

  6. dx Mass flow rate of condensed steam  x Tw Ts=Tw+T HEAT transfer film condensation MHMT12 Film condensation (Nusselt) The following analysis holds only for laminar films (Re<1800). It is usually sufficient, because majority of practical cases are laminar. Transversal parabolic velocity profile and balance of forces gravity Viscous force at wall Transversal linear temperature profile, heat and mass fluxes Thickness of film determines the heat transfer coefficient Gravity acting in the flow direction increases 

  7. Heat transfer – Boiling z T Tw Tsat Tsat overheating MHMT12 Steam bubbles are generated at bottom only it Tsat exceeds a critical limits (pressure of steam inside the bubbles must overcome surface tension and hydrostatic pressure) temperature of liquid Tsat increases with hydrostatic pressure Duchamp

  8. Heat transfer – Boiling MHMT12 Nukyama curve (q-TSAT) see A.Bejan, A.Kraus: Heat transfer handbook. Willey 2003 Boiling crisis of the first kind

  9. Heat transfer – Pool Boiling MHMT12 All parameters are related to liquid L Nucleate (pool) boiling Rohsenow (1952) uL - velocity of liquid surface Rohsenow W.M., Trans.ASME, Vol.74,pp.969-975 (1952) Exponent mis 0,7 for all liquids with the exception of water (m=0). The coefficientCLSdepends upon the combination surface-liquid (tables see Özisik (1985)) and for the most common combination steel-water CLS=0,013. Db is the Laplace constant characterizing diameter of bubble Interpretation of Db follows from the equilibrium of surface stress  and buoyancy forces

  10. Heat transfer – Flow Boiling MHMT12 Flow boiling in vertical pipes is characterized by gradual changes of flow regime and thevapor qualityx increase along the pipe Enthalpy of liquid at saturation temperature Annular flow (rising film) Vapor quality x<0 means subcooled liquid, vapor quality x=0 liquid at the beginning of evaporation, x=1 state when all liquid is evaporated and x>1 superheated steam. Slug flow Vapor quality is related to the Martinelli’s parameter (ratio of pressure drops corresponding to liquid and vapor) Nucleate boiling (bubbles), e.g. Rohsenow correlation Vapor quality and Martinelli’s parameter are used in most correlations for convective boiling heat transfer. Heat transfer by forced convection (e.g.Dittus Boelter)

  11. EXAM MHMT12 Heat transfer at phase changes

  12. What is important (at least for exam) MHMT12 Film Condensation Pool boiling Reynolds and Nusselt numbers use Laplace constant (diameter of a bubble) as a characteristic dimension

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