Laminar flow of a conducting fluid with constant properties entering a semi-infinite flat duct with a transverse applied magnetic field is considered.The fluid is assumed to enter the duct with a uniform velocity profile.The duct walls are nonconducting and a variable external resistance connects the two end plates which are displaced to infinity. The velocity and pressure distributions are then determined for the region between the inlet and fully developed flow. A method developed by Schlichting is used wherein the flow field is divided into tiuo sections and an appropriate analysis utilized in each. In the section near the inlet a boundary-layer formulation of equations is used and a solution developed in a series stream function with Blasius functions as coefficients.When this solution becomes unwieldy, an exponential velocity deviation from the fully developed flow is assumed and joined to the boundary-layer solution to complete the description of the flow. R EIECENTLY, attention has been directed toward magnetohydrodynamic power generation. This interest stems from both the more direct method of energy conversion together with the possibility of increased operating temperatures and the accompanying increases in thermal efficiency. A model generator is shown in Fig. 1 as a semi-infinite, nonconducting flat duct with normal transverse applied magnetic field, B0, and the conducting fluid entering the duet with a uniform velocity, j/o. There is an external variable resistance connecting the two perfectly conducting end plates (electrodes) which are displaced to infinity at each side of the duct, and which control the amount of current in the generator circuit. Chang and Lundgren [l], 2 in the full}' developed flow case, consider the duct walls to be of variable con-1 This paper is based on an MS thesis submitted by R. M. Roidt to the Mechanical Engineering Department of the University of Pittsburgh. . ductivity and the circuit is then completed in these walls. The results thus obtained are the same as those obtained in this paper when flow is fully developed. The present investigation undertakes the description of the velocity and pressure developments in the entrance region of such a duct.The analysis is patterned after a method developed by Schlichting [2] for nonmagnetic flow, in which case the flow field is divided into two sections; flow near the inlet or upstream section, and aFig. 1 Geometry of duct-entrance region 'Nomenclaturea -duct half-width, a = s/2 u, = fully developed velocity X = eigenvalue B = magnetic field intensity U = potential flow velocity V = kinematic viscosity e = electric field magnitude factor, V = 2/-component of velocity P = fluid density Eo = -eii0B0 w = z-component of velocity a = electrical conductivity E = electric field strength z = direction component normal to x = Blasius stream function fn = Blasius coefficient, functions of rj and y as shown in Fig. 1. = deviation velocity function j = electrical current density y = direction component measured Tw = wall shear stress M = H...
A tracer gas is injected into a single subchannel of a large air flow model of a reactor rod bundle. Axial variations in the tracer flux are determined by sampling at two downstream positions in both the injection subchannel and those adjacent to it. This information, with measured subchannel area changes, is used to calculate crossflows and the turbulent eddy diffusion coefficient. The latter number agrees with the results of other investigators in regular pipe flows. Also determined are distributional factors which would be required for modeling the transport equations, for this particular scalar distribution, with a typical lumped parameter computer code.
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