Numerical Modelling of Radiant Systems and Phase Change Materials in Building Applications

Vocabulary practice flashcards covering numerical modeling methodologies, governing equations, classification frameworks, and phase change material (PCM) integration techniques for radiant heating and cooling systems.

Hydronic Radiant Systems

Building climatization systems composed of a piping or tubing network, fluid pumps, and fluid heaters or chillers, which condition spaces by circulating a fluid (typically water) that exchanges thermal energy with indoor surfaces via radiation and convection.

Electric Radiant Systems

Radiant heating systems that increase indoor temperature solely for heating purposes through the Joule effect when electric current flows through internal resistors.

Thermoelectric Radiant Systems

Radiant heating and cooling systems where an electric current passing between two dissimilar materials establishes a temperature differential, creating an active hot side and cool side whose orientation dictates whether the system heats or cools the interior.

Phase Change Materials (PCM)

Substances characterized by high latent heat storage capacities that absorb or release large amounts of thermal energy at specific phase transition temperatures, dampening indoor temperature fluctuations and shaving peak thermal loads.

Sharp Interface Model (Stefan Model)

A foundational mathematical model for phase change problems that assumes the solid and liquid phases are separated by an infinitely thin, moving geometric boundary or sharp interface.

Classification of Radiant Cooling System Models

A categorization scheme introduced by Hassan and Abdelaziz classifying radiant cooling models according to system scope (conditioned space, mechanical system, or both), indoor domain (indoor air, radiant panel/slab, or both), operational type (steady or unsteady), and methodology (analytical, empirical, computational, or data-driven).

Thermally Activated Building Systems (TABS)

Radiant cooling and heating systems embedded directly within heavy structural components of a building (such as concrete slabs and walls) that utilize structural thermal mass for thermal storage and space conditioning.

Schumann's Model

The simplest numerical modeling method for packed bed thermal storage systems, which eliminates internal thermal gradients across particles by assuming infinite thermal conductivity.

Capillary Ceiling Radiant Cooling Panel

A hydronic terminal unit consisting of closely spaced capillary tube mats embedded within gypsum plaster beneath insulation, exchanging sensible heat with the space through both convection ($q_c$) and thermal radiation ($q_r$).

Semi-Analytical Models

Hybrid modeling techniques that correlate distinct analytical formulations to accommodate non-constant parameters and complex tube geometries without the severe computational expense of full CFD simulations.

Resistor-Capacitor (R-C) Models

Zero-dimensional ($0\text{D}$) or one-dimensional ($1\text{D}$) simplified thermal network models that represent material thermal resistances and capacitances using electrical circuit analogies to evaluate transient dynamics with low computing effort.

Star-Type R-C Network

A specific resistor-capacitor network configuration used for concrete slabs where a central nodal point corresponds to the slab core layer, linking heat transfer from the chilled fluid to the core and subsequently to the slab surfaces.

Identification Models

Data-driven empirical models derived via statistical techniques from experimental measurements of a specific building, commonly implemented in Model Predictive Control (MPC).

Sensible Energy ($Q_s$)

The thermal energy stored or released by a material through temperature differentials without a change in physical phase, defined mathematically as $Q_s = m \times C_p \times \text{\textbackslash Delta}T$.

Latent Energy ($Q_l$)

The isothermal heat absorbed or released by a substance when transitioning from one physical state to another at its phase change temperature ($T_{pc}$), defined by $Q_l = m \times \text{\textbackslash Delta}H_l$.

Enthalpy Method

A fixed-domain phase change modeling technique where total enthalpy ($H$) is defined as the primary dependent variable in the governing energy equation, avoiding the necessity of explicitly tracking the solid-liquid interface position.

Heat Capacity Method

A numerical phase change formulation that incorporates latent heat by expressing the specific heat capacity as an effective or apparent temperature-dependent function ($C_{\text{eff},p}$) across the phase transition temperature interval.

Liquid Fraction ($\alpha$)

A dimensionless scalar variable bounded between $0$ (completely solid) and $1$ (completely liquid) indicating the melting state of a phase change material and linearly weighting effective properties like density and thermal conductivity.

Rayleigh Number Criterion (in PCM Modeling)

A dimensionless hydrodynamic threshold specifying that when $Ra < 1708$, buoyant forces are weaker than viscous forces, meaning natural convection can be ignored and heat transfer within the PCM occurs exclusively via conduction.

Porous Medium Method

A PCM modeling approach assuming a continuous medium of particles and heat transfer fluid governed by paired fluid-solid energy equations, which neglects internal temperature variations within the individual PCM particles.

Enthalpy-Porosity Method

A single-domain CFD formulation where the phase change boundary is treated as a pseudo-porous medium (mushy zone) governed by porosity-dependent momentum sink terms rather than an explicit moving interface.

Mushy Zone

The intermediate semi-solid, porous region existing between the pure solidus and pure liquidus fronts of a phase change material where solid particles are surrounded by liquid.

Porosity Function ($\beta(\alpha)$)

A function defined by Brent et al. as $\beta(\alpha) = \frac{M_z(1 - \alpha)^2}{\alpha^2 + \omega}$ (where $M_z = 10\,000$ and $\omega = 0.001$), used in the momentum source term of the enthalpy-porosity approach to force fluid velocity to zero in solid regions.

Microencapsulated PCM Radiant Floor Configurations

Two distinct structural configurations evaluated by Plytaria et al. where a $1.4\,\text{cm}$ microencapsulated PCM layer is embedded either (a) directly above the active hydronic pipe layer or (b) directly beneath the active hydronic pipe layer.

Surface Cooling Load ($q''_{\text{surf}}$)

The total heat flux to be extracted by a radiant cooling panel, expressed as the sum of convective flux ($q''_{\text{conv}}$), longwave radiant exchange from room surfaces ($q''_{\text{lwsurf}}$), internal longwave gains ($q''_{\text{lwint}}$), shortwave solar radiation ($q''_{\text{swsol}}$), and shortwave lighting radiation ($q''_{\text{swint}}$).

Fixed Grid Method

A numerical scheme for phase-change simulation where governing equations are solved over a fixed, non-moving spatial grid, circumventing the need to continuously deform mesh elements to track the moving solid-liquid boundary.

Interface Tracking Method

A numerical phase-change approach that tracks the precise instantaneous position of the phase boundary and transforms the irregular physical interface into a regular computational grid at each time step.

EnergyPlus–MATLAB Optimization Workflow

A multivariable co-simulation setup developed by Mohammadzadeh and Kavgic where EnergyPlus simulates thermal loads and outputs CSV files, while MATLAB reads the results, calculates the objective function, generates new variables via mutation and crossover, and writes updated IDF simulation files.