Genera Zized Variationa I Prhcz $ Zes for Convective Heat Transfer and Irreversz ’ b k Thermodynamics
Variational principles for convective heat transfer are extended to nonhomogeneous fluids and to fluids with thermal expansion. The results apply to nonlinear problems with temperature dependent properties. The context is restricted to heat transfer but the derivation and a discussion of the physics brings out the general validity of the variational principles for a large category of irreversible processes.
New Methods in Heat Flow Analysis With Application to Flight Structures
New methods are presented for the analysis of transient heat flow in complex structures, leading to drastic simplifications in the calculation and the possibility of including nonlinear and surface effects. These methods are in part a direct application of some general variational principles developed earlier for linear thermodynamics.1-3 They are further developed in the particular case of purely thermal problems to include surface and boundary-layer heat transfer, nonlinear systems with temperature-dependent parameters, and radiation. The concepts of thermal potential, dissipation function, and generalized thermal force are introduced, leading to ordinary differential equations of the Lagrangian type for the thermal flow field. Because of the particular nature of heat flow phenomena, compared with dynamics, suitable procedures must be developed in order to formulate each problem in the simplest way. This is done by treating a number of examples. The concepts of penetration depth and transit time are introduced and discussed in connection with onedimensional flow. Application of the general method to the heating of a slab, with temperature-dependent heat capacity, shows a substantial difference between the heating and cooling processes. An example of heat flow analysis of a supersonic wing structure by the present method is also given and requires only extremely simple calculations. The results are found to be in good agreement with those obtained by the classical and much more elaborate procedures.
Refinement of crystal structure parameters using convergent‐beam electron diffraction: the low‐temperature phase of SrTiO3
The method to refine crystal structure parameters (atom positions and Debye–Waller factors) using convergent-beam electron diffraction (CBED), which is applicable to crystal structure analysis of a small specimen area down to a few nm in diameter, is studied. The line profiles of higher-order Laue-zone reflections are recorded using imaging plates. Theoretical intensities are calculated based on the dynamical theory of electron diffraction with the aid of the generalized Bethe approximation to shorten calculation time. The structural parameters are determined by fitting the experimental profiles with the theoretical ones using a nonlinear least-squares method. The present method has been applied to the low-temperature phase of SrTiO3. The structural parameter or the rotation angle of the oxygen octahedron has been determined to be \varphi = 1.12 (4)°, which shows good agreement with that obtained from electron spin resonance experiments.