Summary
Similar solutions of the equations describing the thermal boundary layer of a micropolar fluid on a plane wall are found to exist for the stagnation point flow when the wall temperature variation is parabolic. The two types of boundary conditions used for microrotation are: (a) the relative spin of the particles on the boundary is related to the skew symmetric part of the stress on the boundary by a parameter which is a measure of the concentration of microelements, and (b) the couple stress on the boundary is related to the relative spin of the particles on the boundary by a friction factor which accounts for the rotational slip of the fluid along the boundary. The velocity, microrotation and temperature fields have been presented graphically for various values of the boundary condition parameters. The skin friction coefficient, wall couple stress coefficient, displacement and momentum thicknesses and rate of heat transfer have been tabulated. A comparison with the corresponding results for a Newtonian fluid has been made.
Zusammenfassung
Es werden ähnliche Lösungen der Gleichungen, die die thermische Randschicht eines mikropolaren Fluids längs einer ebenen Wand beschreiben, für die Staupunktsströmung bei parabolischer Änderung der Wandtemperatur gefunden. Zwei Typen von Randbedingungen werden für die Mikrorotation verwendet: (a) Der relative Spin der Teilchen am Rand ist verknüpft mit dem schiefsymmetrischen Anteil der Spannungen am Rand über einen Parameter, der ein Maß für die Konzentration der Mikroelemente darstellt. (b) Die Momentenspannung an der Berandung ist mit dem relativen Spin der Teilchen am Rand mit einem Reibungsfaktor verknüpft, der den Drehslip des Fluids längs der Berandung beschreibt. Die Geschwindigkeits-, Mikrorotations- und Temperaturfelder werden graphisch für verschiedene Werte des Parameters für die Randbedingungen dargestellt. Der Wandreibungskoeffizient, der Koeffizient der Wandmomentenspannung, Verschiebung und Impulsflußdicke und die Wärmeübergangsrate werden tabelliert. Ein Vergleich mit den entsprechenden Ergebnissen der Newtonschen Flüssigkeit wird angestellt.
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Ramachandran, P.S., Mathur, M.N. Heat transfer in the stagnation point flow of a micropolar fluid. Acta Mechanica 36, 247–261 (1980). https://doi.org/10.1007/BF01214635
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DOI: https://doi.org/10.1007/BF01214635