Mixed convection hydromagnetic flow in a rotating channel with Hall and wall conductance effects

Heat transfer—A review of 1969 literature

An analysis of the fully-developed MHD free convective flow between two vertical, electrically conducting plates has been carried out. The effects of the external circuit, heat sources and modified boundary conditions on the temperature at the non-perfect thermally conducting plates have been studied. The nonlinear integro-differential equations, governing the flow, have been solved by perturbation method. Velocity and temperature profiles have been shown on graphs and the numerical values of other quantities are entered in tables. It is observed that the flow is stable at small values ofM, the Hartmann number, whereas at large values ofM, an increase inΦ
1 (the thermal conductance ratio) or λ (line heat source) leads to an instability of the flow. However, instability of the flow may be avoided by selecting the plates of high electrical conductivity.

MHD free convective flow in a vertical channel

Convection in ferromagnetic fluid due to magnetocaloric effect

The combined natural and forced convection fully developed flow and heat transfer of an electrically conducting fluid with and without temperature dependent heat sources in a vertical channel has been studied under the influence of transverse applied magnetic field and external circuit. The two plane walls of the channel are having the same temperature gradient along their lengths but both are art different temperatures. The system of non-linear integro-differential equations have been solved by an iteration method and the shearing stress and Nusselt number at the walls have been calculated. It has been found that the temperature dependent heat sources impose oscillatory behaviour on the temperature profiles and the heat transfer between the wall and the adjacent fluid changes its direction for different ranges of values of the heat source per unit volume. The magnetic field reduces the velocity but increases the temperature and the presence of linear variation of the wall temperature helps in cooling the walls.



In der vorliegenden Arbeit werden die in einem vertikalen Kanal verlaufende vollentwickelte laminare Konvektionsstromung einer elektrisch leitenden Flussigkeit, die der Wirkung eines magnetischen Querfeldes und eines auseren Stromkreises unterworfen ist, und die sich dabei vollziehende Warmeubertragung untersucht, wobei noch Warmequellen vorhanden sein konnen. Die beiden ebenen Wande des Kanals haben verschiedene Temperaturen aber in Langsrischtung denselben Temperaturgradienten. Das den Vorgang beherrschende System von Integrodifferentialgleichungen wird iterativ gelost, und es werden die Schubspannung und die Nusselt-Zahl-an den Wanden berechnet. Es zeigt sich, das die Warmequellung temperaturabhangig ist und an den Temperaturprojilen ein oszillatorisches Verhalten bewirkt und das der Warmeubergang zwischen Wand und angrenzender Flussigkeit in Abhangigkeit von den Werten der Warmequellergiebigkeit seine Richtung andert. Das Magnetfeld reduziert die Geschwindigkeit, last aber die Temperatur anwachsen, und durch eine lineare Anderung der Wandtemperatur last sich eine Kuhlung der Wande erreichen.

U. N. Das

Papers

Combined Natural and Forced Convection Hydromagnetic Flow in Vertical Channels