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Transport Phenomena. Fourier heat conduction law. Q = - k t A dT Δ t dx. Transport Phenomena. Fourier heat conduction law. Q = - k t A dT Δ t dx k t = thermal conductivity. Transport Phenomena. Fourier heat conduction law. Q = - k t A dT - PowerPoint PPT Presentation
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Transport PhenomenaFourier heat conduction law.
Q = - kt A dT
Δt dx
Transport PhenomenaFourier heat conduction law.
Q = - kt A dT
Δt dx
kt = thermal conductivity.
Transport PhenomenaFourier heat conduction law.
Q = - kt A dT
Δt dx
kt = thermal conductivity.
Heat Equation
∂T = K ∂2T
∂t ∂x2
Transport PhenomenaFourier heat conduction law.
Q = - kt A dT
Δt dx
kt = thermal conductivity.
Heat Equation
∂T = K ∂2T
∂t ∂x2
K = kt /ρc
Transport PhenomenaFourier heat conduction law.
Q = - kt A dT Δt dx
kt = thermal conductivity. Heat Equation ∂T = K ∂2T ∂t ∂x2
K = kt /ρc ρ= density, c =specific heat
Conductivity of an ideal gas
• Mean Free Path λ = l ≈ 1/4πr2 V/N
•
Conductivity of an ideal gas
• Mean Free Path λ = l ≈ 1/4πr2 V/N
• in FGT λ = 1/(√2 nσ)
Conductivity of an ideal gas
• Mean Free Path λ = l ≈ 1/4πr2 V/N
• in FGT λ = 1/(√2 nσ) where σ= 4πr2
• and n =N/V
Conductivity of an ideal gas
• Mean Free Path λ = l ≈ 1/4πr2 V/N
• in FGT λ = 1/(√2 nσ) where σ= 4πr2
• and n =N/V
• Thermal conductivity of an ideal gas is
kt = ½ CV l vave V
Conductivity of an ideal gas
• Mean Free Path λ = l ≈ 1/4πr2 V/N
• in FGT λ = 1/(√2 nσ) where σ= 4πr2
• and n =N/V
• Thermal conductivity of an ideal gas is
kt = ½ CV l vave vave ~ √T
V
Conductivity of an ideal gas
• Mean Free Path λ = l ≈ 1/4πr2 V/N• in FGT λ = 1/(√2 nσ) where σ= 4πr2
• and n =N/V• Thermal conductivity of an ideal gas is
kt = ½ CV l vave vave ~ √T V
where CV = f Nk = f P V 2 V 2T
Viscosity
• Viscosity transfers momentum in a fluid.
Viscosity
• Viscosity transfers momentum in a fluid.
• Motion of one layer sliding on another, if slow and the motion is laminar the resistance to shearing is viscosity
Viscosity
• Viscosity transfers momentum in a fluid.
• Motion of one layer sliding on another, if slow and the motion is laminar the resistance to shearing is viscosity
The equation for the coefficient is similar
to a modulus η = stress =
strain
Viscosity
• Viscosity transfers momentum in a fluid.
• Motion of one layer sliding on another, if slow and the motion is laminar the resistance to shearing is viscosity
The equation for the coefficient is similar
to a modulus η = stress = Fx / dux
strain A dz
Viscosity
• Viscosity transfers momentum in a fluid.
• Motion of one layer sliding on another, if slow and the motion is laminar the resistance to shearing is viscosity
The equation for the coefficient is similar
to a modulus η = stress = Fx / dux
strain A dz
η ~ √T and independent of P
Diffusion• Movement of particles is diffusion
•
Diffusion• Movement of particles is diffusion
• Jx = - D dn/dx (Fick’s Law)
•
Diffusion• Movement of particles is diffusion
• Jx = - D dn/dx (Fick’s Law)
• D is the diffusion coefficient n = N/V
Diffusion• Movement of particles is diffusion
• Jx = - D dn/dx (Fick’s Law)
• D is the diffusion coefficient n = N/V
D ranges from 10-5 for CO to 10-11 for large molecules SI unit is m2 /s.
Diffusion• Movement of particles is diffusion
• Jx = - D dn/dx (Fick’s Law)
• D is the diffusion coefficient n = N/V
D ranges from 10-5 for CO to 10-11 for large molecules SI unit is m2 /s.
Summary: Q/ΔT ~ dT/dx heat
l ~ n number
η ~ dux/dz velocity
Jx ~ dn/dx number
