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Heat Transfer Handbook part 135

Heat Transfer Handbook part 135. The Heat Transfer Handbook provides succinct hard data, formulas, and specifications for the critical aspects of heat transfer, offering a reliable, hands-on resource for solving day-to-day issues across a variety of applications. | 1338 MICROSCALE HEAT TRANSFER Using the relaxation time approximation and Boltzmann transport equation expressions for the electrical and thermal conductivity have been derived in terms of a relaxation time eqs. 18.63 and 18.67 . Becauee both quantities are rented linearly to the relaxation time their ratio is independent of the relaxation time K 1 n2kln 2EF vj.r n2 kB V - - m - I.T 18.68 where eq. 18.21 is used oar the etectton hett oppach. This resutt known as the Wiedemann-Franz law relates the electrical conductivity to the thermal conductivity for metals at all but very low temperature. The proportionality constant is known as the Lorentz number L - K - - 2.45 x 10-8 W Q K2 18.69 oT 3 e 18.3.3 Molecular Approach Recent advances in computational capabilities have increased interest in molecular approaches to solving microscale heat transfer problems. These approaches include lattice dynamic approaches Tamura et al. 1999 molecular dynamic approaches Voltz and Chen 1999 I.ukos et a. 2000 and Monte Crato 811 3110 KlisOter et al. 1988 Woolard et al 1993 . In lattice dynamiaal aalsurrtions flee tons rre asuumed to be at their equilibrium positions andthe intermolecular forces are modeledusing appropriate expressions for the types of bonds present. This technique can be very effective in calculating phonon dispersion relations Tamura et al. 1999 and has also been applied to catenating interface properties Young and MT S1 1999 . Ii is difficult however to take into account defects and grain boundaries. The molecular dynamics approach is very similar however more emphasis placed on modeilng the interatoa tic potential and tee ssumn 1 o no of a rigid 013x1.111110 rtiuc-ture is no longer imposed Chou et ah 1999. Most morecur e donutes nperrccnas have utilized hee Lennard-Joeas potential r 40 18.70 where is a measure of the strength of the attractive forces and rc is a measure of the radius of the repulsive core. Basically the ions attract each other with a potential that