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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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

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 • 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 • Solid-Liquid • Temperature control • Ablation • Coating • Liquid-Vapor • Evaporative cooling

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 • 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 Qualities • Chemical Criteria • Chemical stability • Non-corrosive, non-flammable, non-toxic • Others • Long shelf-life • Applicability • Reliability • Commercial availability • Low cost

Encapsulation • Without encapsulation (container shape and material) • Encapsulation • Building materials (PCM 50-80%, unsaturated polyester matrix 45-10%, and water 5-10%)

Difficulties with PCM • Availability of small number of materials in the temperature range of interest • Useful life • Maintenance • Stability • Water loss

PCM Types • Organic Compounds • Paraffins • Fatty Acids • Salt-Based Compounds • Salt Hydrates • Eutectics • Others • Ice and water • Zeolite

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

Application: Solar Heating 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.

Comparison • Based on 9 m2 of solar collector area

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

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) 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 • 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 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 • 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

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 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.