Summary
Fluid motion generated by a long vertical hot plate in the presence of an externally applied magnetic field is investigated when radiative transfer is important. Even though the velocities involved are small, this paper takes compressibility into effect owing to the extreme heat encountered in radiation problems. Thus the viscosity (μ) and the thermal conductivity (K) are assumed to vary with the temperature (T). In this paper we takeμαT n while the Prandtl number (Pr) which is defined in terms of the specific heat at constant pressure (c p) byPr=μc p/K is constant. Assuming a general differential approximation for the radiative flux, the asymptotic problem, valid far away from the tips of the plate, is reduced to a set of nonlinear coupled ordinary differntial equations. Solution to this problem is discussed quantitatively.
Zusammenfassung
Es wird die Bewegung eines Fluids entlang einer heißen vertikalen Platte untersucht in Gegenwart eines außen angebrachten Magnetfeldes, im Falle daß die Strahlung wichtig ist. Obwohl die Geschwindigkeiten klein sind, werden in dieser Arbeit Kompressibilitätseffekte berücksichtigt, da bei Strahlungsproblemen hohe Temperaturen auftreten. Die Zähigkeitμ und der WärmeleitungskoeffizientK werden mit der Temperatur veränderlich angenommen, mitμ∼T n, und der Prandtl-ZahlPr=μc p/K konstant. Für den Strahlungsfluß wird eine allgemeine différentielle Form angenommen, und das asymptotische Problem, gültig in einigem Abstand von den Plattenenden, wird auf ein System von nichtlinearen gekoppelten gewöhnlichen Differentialgleichungen reduziert. Die Lösung des Problems wird quantitativ diskutiert.
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Bestman, A.R. Compressibility effect on laminar convection to a radiating gas past a vertical plate. Z. angew. Math. Phys. 36, 767–774 (1985). https://doi.org/10.1007/BF00960388
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DOI: https://doi.org/10.1007/BF00960388