For situations in which the speed of thermal propagation cannot be considered infinite, a hyperbolic heat conduction equation is typically used to analyze the heat transfer. The conventional hyperbolic heat conduction equation is not consistent with the second law of thermodynamics, in the context of nonequilibrium rational thermodynamics. A modified hyperbolic type heat conduction equation, which is consistent with the second law of thermodynamics, is investigated in this paper. To solve this equation, we introduce a numerical scheme from the field of computational compressible flow. This scheme uses the characteristic properties of a hyperbolic equation and has no oscillation. By solving a model problem, we show that the conventional hyperbolic heat conduction equation can give physically wrong solutions (temperature less than absolute zero) under some conditions. The modified equation does not display these erroneous results. However, the difference between results of these two models is negligible except under extreme conditions.

Abstract. An exact solution is presented of fully developed, laminar flow between inclined parallel plates with a uniform wall heat flux boundary condition. The flow is downward and the heat flux is into the channel, so that natural convection opposes the forced flow. The solution depends on the two parameters P1 = Gr sin O/Re and P2 = Gr cos O/Re 2 Pr. Four different flow reversal regimes are observed: 1) no reversal, 2) top reversal, 3) bottom reversal, and 4) top and bottom reversal. Velocity profiles, temperature profiles, wall friction, and Nusselt numbers are presented. Despite the simplicity of the problem which has been analyzed, it does display some features which have been observed in real mixed convection flows, such as flow reversal and nonmonotonic dependence on tilt angle. Berechnung der roll entwickelten entgegengesetzt geriehteten Misch-Konvektion zwischeu geneigten parallelen PlattenZusammenfassung. Es wird eine exakte L6sung ftir voll entwickelte laminare Str6mung zwischen geneigten parallelen Platten mit einheitlichem Wand-Wfirmestrom als Randbedingung dargestellt. Die Str6mung ist abwfirts gerichtet und der Wfirmestrom fiihrt in den Kanal, so daB die freie Konvektion der erzwungenen entgegengesetzt gerichtet ist. Die L6sung hfingt yon den beiden Parametern P1 = Gr sin O/Re und P2 = Gr cos O/Re 2 Pr ab. Vier verschiedene Bereiche der Str6mungsumkehr wurden betrachtet: 1) keine Richtungsumkehr, 2) Umkehr an der Oberseite, 3) Umkehr an der Unterseite und 4) Umkehr an Ober-und Unterseite. Es wurden Geschwindigkeits-und Temperaturprofile, Wandreibung und Nusselt-Zahlen dargestellt. Trotz der Einfachheit des analysierten Problems werden einige Dinge dargestellt, welche in realer gemischter Konvektion untersucht wurden, so z. B. Str6mungsumkehr und die nicht-monotone Abhfingigkeit yore Schr/igungswinkel.

No abstract

Heat generated during grinding may cause thermal damage to the workpiece and wheel. To avoid this, grinding fluids are often used, but their effects are not well understood. A simple analytical model of the convective heat transfer between the wheel and workpiece surfaces and the grinding fluid is described. The model predicts the convective heat transfer coefficient at the workpiece surface, the fraction of energy entering the workpiece, and the workpiece surface temperature. Despite its simplicity, the model shows remarkable agreement with published data for conventional and creep feed grinding conditions.

No abstract