# Enthalpy Equations and Their Role in Fluid Systems Analysis

### Key Takeaways

• Enthalpy is the sum of the amount of internal energy plus the product of pressure and volume of the fluid within a system.

• The total enthalpy of a system can be impossible to measure, so the change is measured instead.

• CFD tools can help in identifying enthalpy and heat transfer for compressible or incompressible fluid systems.

# A foundational understanding of computational fluid dynamics (CFD) is necessary to solve the governing equation related to fluid flow. This process involves the numerical analysis of momentum, continuity, and energy equations. The solution to the governing equation is the key to understanding the science behind fluid systems, and calculating enthalpy is an important aspect of this analysis.

Enthalpy relates to the heat content and internal energy in a fluid system. CFD simulations facilitate the calculation of enthalpy and the corresponding heat transfer and energy balance equations in a range of flow and temperature conditions. In this article, we will discuss enthalpy equations and how CFD tools can approach the thermodynamical factor of a flow system.

## Enthalpy Equations and Their Relation to Heat

In a thermodynamic system, enthalpy refers to the sum of all energy, absorbed or released, during a reaction within a system. It can be expressed as the sum of the amount of internal energy plus the product of pressure and volume of a system.

H = U + pV

Note that:

H is the term for enthalpy, U represents the internal energy, p is pressure, and V indicates the volume of the fluid system. The term pV can be explained as the work required in the system when the pressure is assumed to be constant.

The direct and accurate measurement of the total enthalpy of a system can be impossible given that the internal energy components may be unknown or of no use in thermodynamical analysis of the fluid system. Thus, the measurement is made for the change in enthalpy, which is expressed as:

ΔH=ΔU+pΔV (when the pressure is constant)

Here, Δ represents the change in the respective terms.

Integrating the law of thermodynamics, which states that the internal energy is equal to the difference between heat transfer (q) and the work done (w), the above equation can be written as:

ΔH = Δ(q-w) + pΔV; (pΔV=Δw)

Thus, under constant pressure, the change in enthalpy is equal to the heat added or absorbed in the system:

ΔH =Δ q

When an idealized, closed system with pure heat transfer is considered, the enthalpy equation can be interpreted using the second law of thermodynamics as:

ΔH = TΔS + pΔV ; (Δq = TΔH = ΔU + pΔV)

ΔS is the change in entropy of the system, where T is the absolute temperature.

### Summarizing the Enthalpy Equations

The above enthalpy equations can be summarized to describe the relationship between change in internal energy and enthalpy as:

1. The change in heat transfer when the system runs at constant pressure is equal to the change in enthalpy of the fluid system.
2. The change in heat transfer when the system has a constant volume equals the change in internal energy of the system.
3. When considering the fluid system with a liquid medium, the change in heat transfer and enthalpy can be small, as the change in volume can be minimal to none. The change can be large in the case of gaseous media.

## CFD Simulation for Enthalpy Calculations

The measurement of change in enthalpy is an important part of thermal engineering. Not only does it enable the calculation of heat transfer in the reaction, but it also helps determine the type of reaction taking place within the system. In systems where compressive forces act, enthalpy equations provide information on pressure and power requirements.

The calculation of the enthalpy equations for the design of complex fluid systems can be a challenging task when performed manually. CFD simulation packages can provide ease of analysis and interpretation with accurate calculations. Tools from Cadence, such as Omnis 3D Solver, can run high-fidelity simulations for all systems with compressive or non-compressive forces. With a precise numerical approach, heat transfer and enthalpy in a system can be ideally calculated for different pressure and volume conditions.