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

A Short Course by

Reza Toossi, Ph.D., P.E.California State University, Long Beach

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Outline

Phase Change Materials Applications Properties

Modeling Melting and Solidification Boiling and Condensation Evaporation Aerosol Jet Impingement

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Energy Storage Materials

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

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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

Melting Point (oC)

Latent Heat (kJ/kg)

Density (kg/m3)

Steel 1400 247 7800Copper 1086 206 8900Ice 0 335 917Sodium Sulfate

32 252 1495

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Phase Change Applications

Solid-Liquid Temperature control Ablation Coating

Liquid-Vapor Evaporative cooling

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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

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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

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Desirable Qualities

Chemical Criteria Chemical stability Non-corrosive, non-flammable, non-toxic

Others Long shelf-life Applicability Reliability Commercial availability Low cost

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Encapsulation

Without encapsulation (container shape and material)

Encapsulation Building materials (PCM 50-80%, unsaturated

polyester matrix 45-10%, and water 5-10%)

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Difficulties with PCM

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

Useful lifeMaintenanceStabilityWater loss

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PCM Types

Organic Compounds Paraffins Fatty Acids

Salt-Based Compounds Salt Hydrates

Eutectics Others

Ice and water Zeolite

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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.

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Organic PCMs (Paraffins)

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Organic PCMs (Fatty Acids)

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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)

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Inorganic PCMs

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Inorganic PCMs

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Inorganic Mixtures

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Eutectic Salts

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Transition in Binary Mixtures

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Commercial PCMs

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Operating Temperatures

Cooling (5-15oC)Temper diurnal swingsHeat pumpsSolar hot-water heating systemsAbsorption air conditioner

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Application: Solar Heating

Roof

Wall

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.

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Comparison

Based on 9 m2 of solar collector area

TES Systems Cost ($) Volume (m3)

Water 54 0.72

Rock 217 @ $8/ton 2.46

Glauber’s Salt 146 0.18

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Application: Solar Refrigeration

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Application: Data Storage

Conventional CD (read only)

CD-R (recordable)

CD-RW (read and write)

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Application: Heat Pad

Sodium acetate (trihydrate) Tsl = 54oC

∆hsl = 1.86x105 J/kg

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

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Moving Boundary Problems

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Solid-Liquid TransitionOne-region

Multiple-region

Two-region

Analytical Solutions in Phase Change Problems

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

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Solidification (One-Region Problem)

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Solidification (Two-Region Problem)

Solid

Liquid

B.C

Scale analysis

Two-Region Problem

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Governing Equations (Neumann problem ):

Boundary Conditions

Solution:

Convective Effects

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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)

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Enthalpy Method

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

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Discretization

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Algorithm (explicit scheme)

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

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

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

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

5. 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).

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

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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.]

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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.

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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.

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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

43CARLOS HERNÁN SALINAS LIRA1, SOLIDIFICATION IN SQUARE SECTION, Theoria, Vol. 10: 47-56, 2001.

Governing Equations

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Results

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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.

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Porous Media : One-Region Melting

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.

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Governing Equations:

Solution: Porous Media : One-Region Melting

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Correlations: Liquid Solid Vapor

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Liquid–Vapor Transition

Nucleation Homogeneous

Heterogeneous▪ Filmwise▪ Dropwise

Dropwise and Film Condensation

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Phase Change Parameters

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Liquid and gas propertiesLatent heat of vaporization, Dhlg

Surface tension at the interface, sPhase density difference, (rl - rg)Surface roughness and orientationContact angle, θc

Water-moving Materials

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Inspired by Namib desert beetleMimics 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

video.mpg

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

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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).

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Boiling

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

Boiling

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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)

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Pool Boiling

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Theoretical maximum heat flux

Correlations

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Correlations: Boiling

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Correlations: Boiling

Conjugate Conduction-Surface Convection

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Effect of substrate (Layered structure of an electric heater)

Correlation for Multiphase Flow Systems

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Correlations: Condensation

Correlations: Liquid Vapor

Surface Evaporation

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Jacob Number

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Jet Spray

Two-layer model with enhanced wall function

Macroscale (jet flow) Microscale (droplet

dynamics) Impact of single droplet Impact of multiple droplets

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

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Impingement (no boiling)

Single round jet:

Multiple jets:

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Impingement (with boiling)

Single Droplet WeD < 30 Bouncing without

breakup 30< WeD < 80 Deformation with

recoil WeD >80 Spreading followed by

breakup

Droplet Spray

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Correlations: Jet Impingement

Macro-scale analysis

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Combined micro and macro effects

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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

Correlations

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Results (impacting jet)

Comparison with parallel flow Example: Substrate cooling of a plastic

sheetL = 20 cm, Ts = 95OC, Tf,∞= 20OC, Uf,∞= 5 m/s for parallel flow; <uf> = 25 m/s in nozzleFluid: water

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Effect on Heat Transfer

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

Before impact

After impact

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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.

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Wall Spray Impaction

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

Where,

Cwb = 1/3

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Micro-Scale Analysis

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

Spreading velocity

Film thickness

Splashing Criteria (Bussmann, 2000)K<Kcrit , where:

K = WeD Ohd-0.4

Kcrit = 649 + 3.76 ReD

-0.63

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Part V- Q/A

For additional questions, Please email rtoossi@csulb.edu.

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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, Martinus Nijhoff, 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.