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Heat Transfer Materials Storage, Transport, and Transformation Part II: Phase Change

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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

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

- 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

- Condensation
- Endothermic (cooling processes)
- Evaporation/Boiling
- Sweat
- Alcohol is “cool”

- Melting
- Melting ice in drinks

- Sublimation
- Cooling with dry ice

- Evaporation/Boiling

- Solid-Liquid
- Temperature control
- Ablation
- Coating

- Liquid-Vapor
- Evaporative cooling

- 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

- 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

- 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%)

- Availability of small number of materials in the temperature range of interest
- Useful life
- Maintenance
- Stability
- Water loss

- Organic Compounds
- Paraffins
- Fatty Acids

- Salt-Based Compounds
- Salt Hydrates

- Eutectics
- Others
- Ice and water
- Zeolite

- 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.

- 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)

- Cooling (5-15oC)
- Temper diurnal swings
- Heat pumps
- Solar hot-water heating systems
- Absorption air conditioner

Wall

Roof

Window

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

- Conventional CD (read only)
- CD-R (recordable)
- CD-RW (read and write)

- Sodium acetate (trihydrate)
- Tsl = 54oC
- ∆hsl = 1.86x105 J/kg

- Melting of Solids
- Surface Evaporation
- Boiling
- Film Boiling
- Pool Boiling

- Condensation
- Film Condensation
- Dropwise Condensation

- Aerosol Jet Spray
- Nucleation
- Impingement

One-region

Multiple-region

Two-region

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

- Solid
- Liquid
- B.C

Scale analysis

Governing Equations (Neumann problem ):

Boundary Conditions

Solution:

- 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)

- Strong (Classical ) numerical solution

- Two-Region Melting of a Slab
- Assume densities of the liquid and solid phase are equal.

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.

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.]

- 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.

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.

- CARLOS HERNÁN SALINAS LIRA1, SOLIDIFICATION IN SQUARE SECTION, Theoria, Vol. 10: 47-56, 2001.

- 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

- 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

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

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.

- Nucleation
- Homogeneous
- Heterogeneous
- Filmwise
- Dropwise

- 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

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

- 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)

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

- Natural Convection Boiling

Pool Boiling

Effect of substrate (Layered structure of an electric heater)

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

Single round jet:

Multiple jets:

- Single Droplet
- WeD < 30 Bouncing without breakup
- 30< WeD < 80 Deformation with recoil
- WeD >80 Spreading followed by breakup

- Droplet Spray

BCorrelation number

D jet/nozzle diameter

d droplet diameter

K droplet splashing criterion

n number of droplets

number flux of droplets

NuNusselt number, hD/k

Nu0 Nusselt number in absence of particles

ω mass loading

σ surface tension

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

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

Before impact

After impact

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.

Where,

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

Splashing Criteria (Bussmann, 2000)

K<Kcrit,

where:

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

For additional questions, Please email [email protected]

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.