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A Short Course by Reza Toossi, Ph.D., P.E. California State University, Long Beach. Heat Transfer Materials Storage, Transport, and Transformation Part II: Phase Change. Outline. Phase Change Materials Applications Properties Modeling Melting and Solidification Boiling and Condensation

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A short course by reza toossi ph d p e california state university long beach

A Short Course by

Reza Toossi, Ph.D., P.E.

California State University, Long Beach

Heat Transfer MaterialsStorage, Transport, and TransformationPart II: Phase Change


  • Phase Change Materials

    • Applications

    • Properties

  • Modeling

    • Melting and Solidification

    • Boiling and Condensation

    • Evaporation

    • Aerosol Jet Impingement

Energy storage materials
Energy Storage Materials

Abhat, A., “Low temperature latent heat thermal energy storage: heat energy storage materials,” Solar Energy, 30 (1983) 313-332.

Heat of fusion
Heat of Fusion

  • Exothermic (warming processes)

    • Condensation

      • Steam radiators

    • Freezing

      • Orange growers spray oranges with iced water

    • Deposition

      • Snowy days are warmer than clear days in the winter

  • Endothermic (cooling processes)

    • Evaporation/Boiling

      • Sweat

      • Alcohol is “cool”

    • Melting

      • Melting ice in drinks

    • Sublimation

      • Cooling with dry ice

Phase change applications
Phase Change Applications

  • Solid-Liquid

    • Temperature control

    • Ablation

    • Coating

  • Liquid-Vapor

    • Evaporative cooling

Pcm applications
PCM Applications

  • Energy Storage in Buildings

    • Thermal Inertia and Thermal protection

    • Passive heating and cooling

    • Thermoelectric Refrigeration

  • Transport of temperature sensitive materials

  • Thermal Control

    • Industrial Forming (casting, laser drilling)

    • Food and Pharmaceutical Processing

    • Telecom Shelters

    • Human-comfort footwear and clothes

    • Thermos and coolers

  • Electrical Generation

    • Cogeneration

    • Thermoelectric Power Generation

  • Security of Energy Supply

  • Flow-through heat exchangers

    • Microencapsulated PCMs

Desirable qualities
Desirable Qualities

  • Thermodynamic Criteria

    • A melting point at the desired operating temperature

    • A high latent heat of fusion per unit mass

    • A high density

    • A high specific heat

    • A high thermal conductivity

    • Congruent melting

    • Small density differences between phases

    • Little supercooling during freezing

Desirable qualities1
Desirable Qualities

  • Chemical Criteria

    • Chemical stability

    • Non-corrosive, non-flammable, non-toxic

  • Others

    • Long shelf-life

    • Applicability

    • Reliability

    • Commercial availability

    • Low cost


  • Without encapsulation (container shape and material)

  • Encapsulation

    • Building materials (PCM 50-80%, unsaturated polyester matrix 45-10%, and water 5-10%)

Difficulties with pcm
Difficulties with PCM

  • Availability of small number of materials in the temperature range of interest

  • Useful life

  • Maintenance

  • Stability

  • Water loss

Pcm types
PCM Types

  • Organic Compounds

    • Paraffins

    • Fatty Acids

  • Salt-Based Compounds

    • Salt Hydrates

  • Eutectics

  • Others

    • Ice and water

    • Zeolite

Organic pcms
Organic PCMs

  • Advantages

    • A wide range of melting points

    • Non-toxic, non-corrosive

    • Chemically stable

    • Compatible with most building materials

    • High latent heat per unit mass

    • Melting congruity

    • Negligible supercooling

    • Are available for wide range of temperatures

  • Disadvantages

    • Expensive

    • Low density

    • Low thermal conductivity (compared to inorganic compounds)

    • Large coefficient of thermal expansion

    • Flammable

    • Do not have a well-defined melting temperatures.

Salt hydrates molten salts
Salt Hydrates (Molten Salts)

  • Advantages

    • Lower cost

    • High latent heat per unit mass and volume

    • High thermal conductivity

    • Wide range of melting points (7-117oC)

  • Disadvantages

    • High rate of water loss

    • Corrosive

    • Phase separation

    • Substantial Subcooling

    • Phase segregation (lack of thermal stability)

Operating temperatures
Operating Temperatures

  • Cooling (5-15oC)

  • Temper diurnal swings

  • Heat pumps

  • Solar hot-water heating systems

  • Absorption air conditioner

Application solar heating
Application: Solar Heating




Velraj, R. , and Pasupathy, A., “PHASE CHANGE MATERIAL BASED THERMAL STORAGE FOR ENERGY CONSERVATION IN BUILDING ARCHITECTURE “Institute for Energy Studies, CEG, Anna University, Chennai - 600 025. INDIA.


  • Based on 9 m2 of solar collector area

Application data storage
Application: Data Storage

  • Conventional CD (read only)

  • CD-R (recordable)

  • CD-RW (read and write)

Application heat pad
Application: Heat Pad

  • Sodium acetate (trihydrate)

    • Tsl = 54oC

    • ∆hsl = 1.86x105 J/kg

Heat transfer modeling phase change
Heat Transfer Modeling: Phase Change

  • Melting of Solids

  • Surface Evaporation

  • Boiling

    • Film Boiling

    • Pool Boiling

  • Condensation

    • Film Condensation

    • Dropwise Condensation

  • Aerosol Jet Spray

    • Nucleation

    • Impingement

Solid liquid transition
Solid-Liquid Transition




Analytical solutions in phase change problems
Analytical Solutions in Phase Change Problems

Contact Melting (melting of a solid under its own weight)

Solidification one region problem
Solidification (One-Region Problem)

Solidification two region problem
Solidification (Two-Region Problem)

  • Solid

  • Liquid

  • B.C

Scale analysis

Two region problem
Two-Region Problem

Governing Equations (Neumann problem ):

Boundary Conditions


Numerical simulation in phase change problems
Numerical Simulation in Phase Change Problems

  • Analytical  1D and some 2D conduction-controlled

  • Numerical

    • Strong (Classical ) numerical solution

      • Velocity u and pressure p satisfy Navier-Stokes equations pointwise in space-time.

    • Weak (Fixed-Grid) solution

      • Enthalpy Method (Shamsunder and Sparrow, 1975)

      • The Equivalent Heat Capacity Method ( Bonacina et al ., 1973)

      • The Temperature-Transforming Model ( Cao and Faghri, 1990)

Enthalpy method
Enthalpy Method

  • Two-Region Melting of a Slab

    • Assume densities of the liquid and solid phase are equal.

Algorithm explicit scheme
Algorithm (explicit scheme)

Choose ∆t and ∆x to meet Neumann’s stability criterion

Determine the initial enthalpy at every node hjo (j = 1)

Calculate the enthalpy after the first time step at nodes (j = 2 ,..., N -1) by using equation (1).

Determine the temperature after the first time step at node (j = 1 ,..., N) by using equations (2) and (3).

Find a control volume in which the enthalpy falls between 0 and hsl , and determine the location of the solid-liquid interface by using equation (4).

Solve the phase-change problem at the next time step with the same procedure.

Algorithm implicit scheme
Algorithm (implicit scheme)

Unconditionally stable but is more complex because two unknown variables enthalpy and temperature are involved.

[See Alexiades , A ., and Solomon , A . D ., 1993 , Mathematical Modeling of Melting and Freezing Processes , Hemisphere , Washington , DC .]

Transform the energy equation into a nonlinear equation with a single variable h.

[See Cao , Y ., and Faghri , A ., 1989 , " A Numerical Analysis of Stefan Problem of Generalized Multi-Dimensional Phase-Change Structures Using the Enthalpy Transforming Model ," International Journal of Heat and Mass Transfer , Vol . 32 , pp . 1289-1298.]

Equivalent heat capacity method
Equivalent Heat Capacity Method

  • 3-D Conduction controlled melting/solidification

  • Heat capacity during the phase change is infinite.

  • Assume Cp and k change linearly from liquid to solid

  • Advantage: Simplicity

  • Disadvantage: Unstable if right choices for ∆x, ∆t, and ∆T are not made.

Temperature transforming model
Temperature-Transforming Model

Combination of the two methods [Cao , Y ., and Faghri , A ., 1990a , " A Numerical Analysis of Phase Change Problem including Natural Convection ," ASME Journal of Heat Transfer, Vol . 112 , pp . 812-815.]

Use finite volume approach by Patankar to solve the diffusion equation.

Melting solidification with natural convection
Melting/Solidification with Natural Convection


  • Assumptions

    • “Enthalpy Method” approach is considered

    • Newtonian incompressible fluid with constant properties, except the density that is evaluated s linear function of temperature (Bousinessq approximation)

    • Effective conductivity in the mushy zone

    • Isotropic

    • Heat transfer by conduction, convection and phase change

Porous media averaging techniques for multiphase transport
Porous Media: Averaging Techniques for Multiphase Transport

  • Eulerian Averaging

    • Averaged over space, time, or both within the domain of integration

      • Based on time-space description of physical phenomena

      • Consistent with the c.v. analysis used to develop governing equations.

      • Eulerian time-averaging

      • Eulerian volume-averaging

    • Phase-averages:

      • Intrinsic phase average

      • Extrinsic phase average

  • Lagrangian Averaging

    • Follow a particle and average its properties during the flight

  • Molecular Statistical Averaging

    • Boltzmann statistical distribution rather than individual particle is the independent variable.

Porous media one region melting
Porous Media : One-Region Melting

Governing Equations:

Jany , P ., and Bejan , 1988 , " Scaling Theory of Melting with Natural Convection in an Enclosure ," International Journal of Heat and Mass Transfer , Vol . 31 , pp . 1221-1235.

Solution porous media one region melting
Solution: Porous Media : One-Region Melting

Correlations liquid solid vapor
Correlations: Liquid  Solid  Vapor

Liquid vapor transition
Liquid–Vapor Transition

  • Nucleation

    • Homogeneous

    • Heterogeneous

      • Filmwise

      • Dropwise

Phase change parameters
Phase Change Parameters

  • Liquid and gas properties

  • Latent heat of vaporization, Dhlg

  • Surface tension at the interface, s

  • Phase density difference, (rl- rg)

  • Surface roughness and orientation

  • Contact angle, θc

Water moving materials
Water-moving Materials

Rubner and Cohen, Nano Letters 6(6), 1213-1217 (2006)

  • Inspired by Namib desert beetle

    • Mimics wing with a microscopic pattern of water-attracting and water-repelling areas

    • Also seen on lotus leaves

  • Applications include

    • Self-decontaminating surfaces

    • Antifogging surfaces

    • Microfluidic chips

    • Harvesting dews as drinkable water

    • Pocket-sized chemical testing devices

Microfluidic chips
Microfluidic Chips

  • Nano-structured film made of alternating layers of positively and negatively charged polymers and silica nanoparticles

  • Dual quality material can be patterned to repel water in some areas (spherical droplets) and attract it in others (flattened ones).


  • The type of boiling depends on

    • Pool Boiling (water in a pan on top of a stove)

      • Subcooled (local)  Tliq < Tsat

      • Saturated (bulk)  Tliq= Tsat

    • Film Boiling (flow in a heated pipe)

  • Surface Superheat ∆T = Ts-Tsat

  • Surface roughness


  • Tap water on a stove

    • Natural Convection Boiling

      • A-B Air bubbles burst (Subcooled boiling)

    • Nucleate Boiling

      • B-C Saturated boiling (Tbulk= 100oC) –no bubbles yet!

      • C -D Quenching - unstable, insulating bubble blanket

    • Film Boiling

      • D-E Bulk motion (convection and radiation)

Conjugate conduction surface convection
Conjugate Conduction-Surface Convection

Effect of substrate (Layered structure of an electric heater)

Jet spray
Jet Spray

Garbero, et al., “Gas/surface heat transfer in spray deposition processes,” Intl. J. Heat and Fluid Flow, Vol. 27, Issue 1, Feb 2006, pp. 105-122

Two-layer model with enhanced wall function

  • Macroscale (jet flow)

  • Microscale (droplet dynamics)

    • Impact of single droplet

    • Impact of multiple droplets

Impingement no boiling
Impingement (no boiling)

Single round jet:

Multiple jets:

Impingement with boiling
Impingement (with boiling)

  • Single Droplet

    • WeD < 30 Bouncing without breakup

    • 30< WeD < 80 Deformation with recoil

    • WeD >80 Spreading followed by breakup

  • Droplet Spray

Correlation number
Correlation Number

B Correlation number

D jet/nozzle diameter

d droplet diameter

K droplet splashing criterion

n number of droplets

number flux of droplets

Nu Nusselt number, hD/k

Nu0 Nusselt number in absence of particles

ω mass loading

σ surface tension

Results impacting jet
Results (impacting jet)

Comparison with parallel flow

Example: Substrate cooling of a plastic sheet

L = 20 cm, Ts = 95OC, Tf,∞= 20OC,

Uf,∞= 5 m/s for parallel flow; <uf> = 25 m/s in nozzle

Fluid: water

Effect on heat transfer
Effect on Heat Transfer

Droplet deformation (spreading) during impact (dp = 200 μm, Up = 10 m/s).

Before impact

After impact

Single and multiple droplets
Single and Multiple droplets

Contours of total surface heat flux (seen from below)

Velocity vectors during the impact of three droplets: three-droplet

Garbero, Vanni, and Fritscling, “Gas/surface heat transfer in spray deposition processes,” Int’l J. Heat and Fluid Flow, Vol. 27, Issue 1. Feb 2006, pp. 105-122.

Wall spray impaction
Wall Spray Impaction


Cwb = 1/3

Park, K., and Watkins, A. P., “Comparison of wall spray impaction models with experimental data on drop velocities and sizes,” Int. J. Heat and Fluid Flow, Vol. 17, No. 4, August 1996.

Bai and Gosman (1995): Drop collision model

(Stick, Spread, Rebound, Rebound with breakup, Boiling-induced breakup, Random breakup, Splash)

Wang and Watkins (1990)

We < 80 We > 80

Micro scale analysis
Micro-Scale Analysis

Splashing Criteria (Bussmann, 2000)



K = WeD Ohd-0.4

Kcrit = 649 + 3.76 ReD-0.63

Rebound, Rebound with breakup, Break-up, and Splash (Park and Watkins, 1996)

Spreading velocity

Film thickness

Part v q a
Part V- Q/A

For additional questions, Please email [email protected]

Heat transfer enhancement using pcm
Heat Transfer Enhancement Using PCM

Finned tubes

  • [1] A. Abhat, S. Aboul-Enein, N. Malatidis, Heat of fusion storage systems for solar heating applications, in: C. Den Quden (Ed.), Thermal Storage of Solar Energy, MartinusNijhoff, 1981.

  • [2] V.H. Morcos, Investigation of a latent heat thermal energy storage system, Solar Wind Technol. 7 (2/3) (1990) 197–202.

  • [3] M. Costa, D. Buddhi, A. Oliva, Numerical Simulation of a latent heat thermal energy storage system with enhanced heat conduction, Energy Convers. Mgmt. 39 (3/4) (1998) 319–330.

  • [4] P.V. Padmanabhan, M.V. Krishna Murthy, Outward phase change in a cylindrical annulus with axial fins on the inner tube, Int. J. Heat Mass Transfer 29 (1986) 1855–1868.

  • [5] R. Velraj, R.V. Seeniraj, B. Hafner, C. Faber, K. Schwarzer, Experimental analysis and numerical modelling of inward solidification on a finned vertical tube for a latent heat storage unit, Solar Energy 60 (1997) 281– 290.

  • [6] R. Velraj, R.V. Seeniraj, B. Hafner, C. Faber, K. Schwarzer, Heat transfer enhancement in a latent heat storage system, Solar Energy 65 (1999) 171–180.

    Embedding in Graphite Matrices

  • [7] P. Satzger, B. Exka, F. Ziegler, Matrix-heat-exchanger for a latent-heat cold-storage, Proceedings of Megastock 98, Sapporo (Japan), 1998.

  • [8] H. Mehling, S. Hiebler, F. Ziegler, Latent heat storage using a PCM-graphite composite material: advantages and potential applications, Proceedings of the 4th Workshop of IEA ECES IA Annex 10, Bendiktbeuern (Germany), 1999.

  • [9] X. Py, R. Olives, S. Mauran, Paraffin/porous-graphite-matrix composite as a high and constant power thermal storage material, Int. J. Heat Mass Transfer 44 (2001) 2727–2737.