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The number of transfer units (NTU) method is used to calculate the rate of heat transfer in heat exchangers (especially parallel flow, counter current, and cross-flow exchangers) when there is insufficient information to calculate the log mean temperature difference (LMTD). Alternatively, this method is useful for determining the expected heat ...
Computational Fluid Dynamics (CFD) modeling and simulation for phase change materials (PCMs) is a technique used to analyze the performance and behavior of PCMs. The CFD models have been successful in studying and analyzing the air quality, natural ventilation and stratified ventilation, air flow initiated by buoyancy forces and temperature space for the systems integrated with PCMs.
This is accomplished by solving heat equations in both regions, subject to given boundary and initial conditions. At the interface between the phases (in the classical problem) the temperature is set to the phase change temperature. To close the mathematical system a further equation, the Stefan condition, is required. This is an energy balance ...
However, if the specific heat changes, the LMTD approach will no longer be accurate. A particular case for the LMTD are condensers and reboilers, where the latent heat associated to phase change is a special case of the hypothesis. For a condenser, the hot fluid inlet temperature is then equivalent to the hot fluid exit temperature.
A computer simulation of high velocity air flow around the Space Shuttle during re-entry A simulation of the Hyper-X scramjet vehicle in operation at Mach-7. The fundamental basis of almost all CFD problems is the Navier–Stokes equations, which define many single-phase (gas or liquid, but not both) fluid flows.
If different phases of the same pure substance are present in a multiphase system, interphase heat transfer will result in a change of phase, which is always accompanied by interphase mass transfer. The combination of heat transfer with mass transfer during phase change makes multiphase systems distinctly more challenging than simpler systems.
Note that the thermodynamic relations for the internal energy and enthalpy are given by: = + = + We may also obtain an equation for the kinetic energy by taking the dot product of the Navier-Stokes equation with the flow velocity to yield: = + The second term on the righthand side may be expanded to read: = () With the aid of the thermodynamic relation for enthalpy and the last result, we may ...
Temperature vs. heat load diagram of hot stream (H 2 O entering at 20 bar, 473.15 K, and 4 kg/s) and cold stream (R-11 entering at 18 bar, 303.15 K, and 5 kg/s) in a counter-flow heat exchanger. "Pinch" is the point of closest approach between the hot and cold streams in the T vs. H diagram.