University:
Massachusetts Institute of Technology
Course:
3.185 | Transport Phenomena in Materials Engineering
Academic year:

2024
Views:

174

Pages:

1
Author:

Lowpegelswa

Dimensionless Numbers 3.185 November 24, 2003 Note: you are not responsible for knowing the diﬀerent names of the mass transfer dimensionless numbers, just call them, e.g., “mass transfer Prandtl number”, as many people do. Those names are given here because some people use them, and you’ll probably hear them at some point in your career. Heat Transfer Mass Transfer Biot Number M.T. Biot Number Ratio of conductive to convective H.T. resistance Ratio of diﬀusive to reactive or conv MT resistance Determines uniformity of temperature in solid Determines uniformity of concentration in solid Bi = hL/ksolid Bi = kL/Dsolid or hD L/Dsolid Fourier Number Ratio of current time to time to reach steadystate Dimensionless time in temperature curves, used in explicit ﬁnite diﬀerence stability criterion Fo = αt/L2 Fo = Dt/L2 Knudsen Number: Ratio of gas molecule mean free path to process lengthscale Indicates validity of lineofsight (> 1) or continuum (< 0.01) gas models kT λ Kn = L = √2πσ 2P L Reynolds Number: Ratio of convective to viscous momentum transport Determines transition to turbulence, dynamic pressure vs. viscous drag Re = ρU L/µ = U L/ν Prandtl Number M.T. Prandtl (Schmidt) Number Ratio of momentum to thermal diﬀusivity Ratio of momentum to species diﬀusivity Determines ratio of ﬂuid/HT BL thickness Determines ratio of ﬂuid/MT BL thickness Pr = ν/α = µcp /k Pr = ν/D = µ/ρD Nusselt Number M.T. Nusselt (Sherwood) Number Ratio of lengthscale to thermal BL thickness Ratio of lengthscale to diﬀusion BL thickness Used to calculate heat transfer coeﬃcient h Used to calculate mass transfer coeﬃcient hD Nu = hL/kf luid Nu = hD L/Df luid Grashof Number Ratio of natural convection buoyancy force to viscous force Controls the ratio of lengthscale to natural convection boundary layer thickness Gr = gβΔT L3 /ν 2 Gr = gβC ΔCL3 /ν 2 Peclet Number Ratio of convective to diﬀusive heat/mass transport in a ﬂuid Used to determine plug ﬂow/perfect mixing (CSTR) continuous ﬂow model validity Pe = RePr = U L/α Pe = RePr = U L/D Rayleigh Number Ratio of natural convective to diﬀusive heat/mass transport Determines the transition to turbulence Ra = GrPr = gβΔT L3 /να Ra = GrPr = gβC ΔCL3 /νD

Summary of Dimensionless Numbers

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