What does the energy balance consist of?
Internal Energy (u): Energy stored within the system.
Kinetic Energy (k): Energy due to the motion of the particles.
Potential Energy (ϕ): Energy due to the position in a force field.
Total Energy (e=u+k+ϕ): The sum of internal, kinetic, and potential energy.
Convective Transport: Movement of energy with fluid flow.
Diffusive Transport: Energy transfer due to gradients (e.g., heat conduction).
Irreversible and Reversible Processes: Includes irreversible production, reversible production, and external volumetric forces.
What are the terms of the mechanical energy balance, and what do they stand for?
Storage Term (∂ρk/∂t): Change in kinetic energy over time.
Convective Transport (∇⋅ρkv): Transport of kinetic energy with fluid motion.
Non-convective Transport (∇⋅[Π⋅v]): Transport due to stress and pressure.
Irreversible Production (τ:∇v): Energy dissipation due to viscous forces.
Reversible Production (v⋅∇p): Energy change due to pressure forces.
Volumetric Forces (v⋅ρf): External forces acting on the fluid.
How can the existence of source terms on the right side of the total energy balance be explained?
The source terms in the total energy balance can be explained by:
Energy Supply (ρ%): External energy inputs like radiation.
Change of Field: Energy change due to time-varying fields.
Reaction Term: Energy due to chemical reactions or phase changes.
External Forces and Inputs: Contributions from sources like heaters or motors.
Do differential balances account for points at every point of the domain and at any point in time? If not, what else is needed?
Differential balances describe behavior at each point in the domain, but require additional information:
Initial Conditions: Needed for transient problems to describe the state at the start.
Boundary Conditions: Necessary to describe interactions at the system's boundaries.
Coupling Conditions: Used when dealing with multiple domains or interacting systems.
Constitutive Equations: Required to close the system of equations with material-specific properties.
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