What are the basic assumptions to set up the control volume and why do we need them?
Assumption 1: Continuum
Subdivide infinitely; each part has enough molecules.
Needed for average property calculations.
May not be valid in systems with very small scales (e.g., nanoscale).
Assumption 2: Inertial Frame of Reference
Simplifies equations by assuming no acceleration.
Provides a stable reference to analyze motion and balance.
How is the flux defined? What is the difference between diffusive and convective flux?
Flux (ϕψ):
Measure of how much of a quantity passes through a surface per unit time.
Formula: ϕψ=ΦΨ/A
Diffusive Flux:
Caused by concentration gradients.
Movement from high to low concentration areas.
Example: Fick's law of diffusion.
Convective Flux:
Caused by bulk movement of the medium.
Transport with fluid motion.
Example: Transport in a flowing river.
Give examples for general properties Ψ\PsiΨ which are scalar and vectorial, respectively.
Scalar Properties:
Mass (m)
Energy (E)
Density (ρ)
Vectorial Properties:
Momentum (m⋅v)
Velocity (v)
Force (F)
What are the terms of the general differential balance?
Accumulation:
∂ψ/∂t
Rate of change of property density over time.
Convective Transport:
∇⋅(ψw)
Transport due to bulk motion.
Diffusive Transport:
∇⋅ϕψ
Transport due to concentration gradients.
Production/Consumption:
σPψ
Internal generation or consumption within the control volume.
External Source:
σFψ
Influence of external forces or fields.
Why is the diffusive flux included in the species mass but not in the total mass balance?
Species Mass Balance:
Includes Diffusion: Accounts for individual species' movement relative to the mixture.
Equation:
Total Mass Balance:
Excludes Diffusion: Total mass considers bulk movement only, as diffusion doesn't change total mass.
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