Statistical Analyses of Ozone Trends in Calgary, Alberta: An Application of Multivariate Geostatistics

Course Outcomes

Semester May 2013CLO1Explain the theoretical aspect of momentum, mass and energy transportCLO2Apply mathematical and numerical methodology in analyzing momentum transfer problemCLO3Apply mathematical and numerical methodology in analyzing heat transfer problemCLO4Apply mathematical and numerical methodology in analyzing mass transfer problemCLO5Analyze and solve transport phenomena using Computational Fluid Dynamics (CFD) tools.2316. Explain the principles of heat transferExplain Fouriers law of heat conductionEstimate thermal conductivityExplain Convective Energy FluxExplain Molecular Work FluxExplain the combined energy Flux

Lesson outcomes4Energy an be transmitted byConduction ConvectionRadiation Conduction :- Molecular energy transport due to the motion of the constituent molecules.Convection :- Energy transport due to the bulk motion of the fluid and depends on the density of the fluid.Radiation :- Unlike conduction and convection does not require material medium to be transmitted.

Principles of Energy Transport5 Fouriers Law of Heat Conduction

A solid slab between two parallel platesIt is found that for sufficiently small values of T the following relation holds:

The rate of heat flow per unit area is proportional to the temperature decrease over the distance 6In differential form

One- dimensional form of the Fouriers Law of Heat conduction Fouriers Law of Heat ConductionFouriers Law of Heat conduction :- The heat flux by conduction is proportional to the temperature gradient. If the temperature varies in all three directions in Cartesian coordinate:

Three- dimensional form of the Fouriers Law.7In cylindrical coordinates:

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When thermal conductivity data for a particular compound cannot be found an estimate by can be made using the corresponding state principle. Estimation of Thermal Conductivity9ProcedureWhen k1 is known at some T1 and P1 and k at some other temperature T and pressure P is required.Determine kr1 from Tr1, Pr1Determine kc

Determine kr from Tr, PrDetermine k

Estimation of Thermal Conductivity10Second approach/ using low density regionThe Chapman-Enskog formula for the thermal conductivity of a monoatomic gas at low density and temperature T

k [=] cal/cm.s.K T [=] K [=] k (collision integral for thermal conductivity)dimensionless

Estimation of Thermal Conductivity11Example Compute the thermal conductivity of Ne at 1 atm and 373.2K.

SolutionFrom Table E.1 the Lennard-Jones constant for Ne are =2.789 and \ = 35.7K its molecular weight is 20.18.At T=373.2K T/ = 373.2/35.7 = 10.45From Table E.2 k = y=0.821

Estimation of Thermal Conductivity12Thermal diffusivity:- In addition to thermal conductivity thermal diffusivity is also commonly used.

The Prandtl Number (Pr) is used to measure the relative ease of momentum and energy transport in flow systems. Estimation of Thermal Conductivity13Convective Energy Transport :- Energy transport due to the bulk motion of the fluid.

Convective Energy TransportThe convective energy flux through a surface area perpendicular to:

Kinetic energy per unit volume

Internal energy per unit volume14 Work Associated With Molecular TransportThe rate of work per unit area due to molecular stress, , can be expressed as follows:

The total molecular stress can be split into two parts as follows:

Splitting the molecular stress we get15 Combined energy flux vector

The combined energy flux is the sum of the(a)the rate of heat transport per unit area by molecular mechanism (b) convective energy flux (c) rate of doing work per unit area by molecular mechanism

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Combined energy flux vector17Explain the principles of Energy TransportExplain Fouriers law of heat conductionEstimate thermal conductivityExplain Convective Energy FluxExplain Molecular Work FluxExplain the combined energy Flux

Lesson outcomes