Derivation of Basic Transport Equation (A. ErtÃ¼rk)

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The Transport Equation The mass balance for this case can be written in the following form ⎡ Change of ⎤ ⎢ ⎥ ⎢ mass in the ⎥ ⎢control volume⎥ = ⎢ ⎥ ⎢ in a time ⎥ ⎢ ⎥ ⎣ interval Δt ⎦ ⎡Mass entering⎤ ⎢ ⎥ ⎢ the control ⎥ ⎢⎣ volume in Δt ⎥⎦ − ⎡Mass leaving⎤ ⎢ ⎥ ⎢ the control ⎥ ⎢⎣ volume in Δt⎥⎦ V ∂C ∂t = A ⋅ J − A 1 J 2 ⋅ Equation 1 4
The Transport Equation A closer look to Equation 1 V ⋅ ∂C ∂t = A ⋅ J − A 1 J 2 ⋅ Flux Flux Volume [L 3 ] Concentration over time [M·L -3 ·T -1 ] Area [L 2 ] [M·L -2 ·T -1 ] Area [L 2 ] [M·L -2 ·T -1 ] [L 3 ]·[M·L -3·T -1 ] = [M·T -1 ] [L 2 ]·[M·L -2·T -1 ] = [M·T -1 ] Mass over time Mass over time 5
Page 1 and 2: DERIVATION OF BASIC TRANSPORT EQUAT
Page 3: The Transport Equation Mass balance
Page 7 and 8: The Transport Equation A.J 1 A.J 2
Page 9 and 10: The Transport Equation Rearrangemen
Page 11 and 12: The Transport Equation We are livin
Page 13 and 14: The Advective Flux 13
Page 15 and 16: Δx is defined as the distance, whi
Page 17 and 18: Δx I II Q = C ⋅ Δx ⋅ A Number
Page 19 and 20: The Dispersive Flux 19
Page 21 and 22: Δx is defined as the distance, whi
Page 23 and 24: I q 1 II q 2 A x q 1 1 = 0.5 ⋅ C
Page 25 and 26: Q A ⋅ Δt = J DISP = − 0.5 ⋅
Page 27 and 28: Ranges of the Dispersion Coefficien
Page 29 and 30: THE ADVECTION-DISPERSION EQUATION F
Page 31 and 32: The Advection-Dispersion Equation
Page 33 and 34: Dimensional Analysis of the Advecti
Page 35 and 36: THE ADVECTION-DISPERSION EQUATION F
Page 37 and 38: 37 The Transport Equation for non c
Page 39 and 40: ⎛ ⎜ ⎝ ∂C ⎞ ⎟ ∂t ⎠ r

Derivation of Basic Transport Equation (A. ErtÃ¼rk)

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