Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. I. Semi-infinite slab approximations

• DOI: 10.1063/1.4901309
• Publication Date: 2014-11-25T01:30:55Z
• Authors: M. van Berkel; H. J. Zwart; N. Tamura; G. M. D. Hogeweij; S. Inagaki; M. R. de Baar; K. Ida
• Keywords: Dimensionless quantity; Approximations of π; Slab; Harmonic

In this paper, a number of new approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For purpose, harmonic components heat waves induced by localized deposition modulated power used. The based on semi-infinite slab equation. main result is approximation χ under influence V τ phase two harmonics making less sensitive calibration errors. To understand why can well geometry, relationships between transport models geometry studied. addition, relationship amplitude with respect their derivatives, used χ, discussed. results presented terms relative error for different derived values frequency, coefficients, dimensionless radius. show significant region which V, be estimated well, but also regions large. Also, it shown that some compensation necessary On other hand, errors resulting from simplified assumptions discussed showing estimating realistic infinite domains will difficult practice. This paper first part (Part I) series three papers. Part II III, directly domain (outward propagating pulses) inward pulses domain, respectively, treated.