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TransportPropLect28ME501F2011

# TransportPropLect28ME501F2011 - Purdue University ME 501...

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Patterned Border Template 1 Purdue University School of Mechanical Engineering ME 501: Statistical Thermodynamics Lecture 28: Fundamentals of Molecular Transport Prof. Robert P. Lucht Room 2204, Mechanical Engineering Building School of Mechanical Engineering Purdue University West Lafayette, Indiana [email protected] , 765-494-5623 (Phone) November 21, 2011

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Patterned Border Template 2 Purdue University School of Mechanical Engineering Lecture Topics • Perturbation analysis of molecular transport: calculation of property fluxes for pure monatomic gases. • Calculation of transport properties from the property fluxes. • Rigorous transport theory. • Dimensionless transport parameters. • Collision integrals and the Lennard-Jones potential.
Patterned Border Template 3 Purdue University School of Mechanical Engineering Perturbation Analysis of Molecular Transport • Consider molecular transport of microscopic properties in the z- direction. We will focus on the velocity group with the z- component of velocity between V z and V z + dV z and with speeds between V and V + dV. In this medium particles travel an average distance between collisions. The plane shown above the x-y plane is the planes where we expect the next collision for the velocity group of interest.

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Patterned Border Template 4 Purdue University School of Mechanical Engineering Perturbation Analysis of Molecular Transport • At steady state the number of particles crossing the x-y plane in the + z direciton is the same as in the – z direction. The lower plane shown is where we expect the next collision for the velocity group with the z-component of velocity between - V z and –( V z + dV z ) . The net flux of particles due to the two velocity groups will sum to zero for a medium with an isotropic (MB) velocity distribution.
Patterned Border Template 5 Purdue University School of Mechanical Engineering Perturbation Analysis of Molecular Transport • Because the net particle flux across the x-y plane is zero, there will be no transport of a microscopic property P ( z ) unless there is a gradient in this property in the z -direction. We apply the Taylor’s series expansion:   0c o s dP Pz P dz  • The net particle flux across the x-y plane due to the velocity group ( V x +dV x , V y +dV y , V z +dV z ) is given by  zz x y nV f Vd V

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Patterned Border Template 6 Purdue University School of Mechanical Engineering Perturbation Analysis of Molecular Transport • The differential net flux of the property P ( z ) across the x-y plane due to the velocity group ( V x +dV x , V y +dV y , V z +dV z ) is given by: • The net flux across the x-y
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TransportPropLect28ME501F2011 - Purdue University ME 501...

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