Hartmann flow in annular channels. Part 2. Numerical solutions for low to moderate Hartmann numbers

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Abstract
Flow of a conducting fluid along the annular channel between two non-conducting circular cylinders is examined by a numerical method for concentric and eccentric cases. Solutions have been obtained for Hartmann numbers ranging from 0·1 to 40 and, for some of these, details of velocity distribution and of induced current are given. The results obtained enable the development of the patterns of velocity and of current flow to be traced as the Hartmann number increases. The details of the development of the current flow patterns for eccentric cylinders are particularly interesting and are discussed in detail. At the higher values of Hartmann number studied the solutions are in excellent agreement with the results of Todd's (1967) high Hartmann number analysis and it is possible to determine at what value of Hartmann number Todd's analysis becomes applicable within a specified accuracy. The effect of eccentricity of the cylinders on the flow rate at a fixed pressure gradient is shown to diminish rapidly with increasing Hartmann number. The net flow of current around the annulus, which occurs when the cylinders are eccentric, has a maximum value for each case studied at a Hartmann number of 3, approximately.