Problem 4. Consider a planar microchannel of width h, as shown (it is actually very long...

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Problem 4. Consider a planar microchannel of width h, as shown (it is actually very long in the x direction and open at both ends). A rectangular coordinate system with its origin positioned at the center of the microchannel is used in this study. The microchannel is filled with a weakly conductive solution. Applying electric current across the two conductive walls and placing the entire device in a constant magnetic field result in a Lorentz force of JB in the unit of Pa/m in the x direction. The flow driven by the Lorentz force can be described by the continuity and momentum equations, expect that the x component momentum equation has the Lorentz force term on the right-hand side. Assuming that the flow is fully developed, incompressible fluid, 2-D flow, and zero pressure gradient, derive the expression for the velocity field. h y Conductive wall TNH. Conductive wall X //// Problem 4. Consider a planar microchannel of width h, as shown (it is actually very long in the x direction and open at both ends). A rectangular coordinate system with its origin positioned at the center of the microchannel is used in this study. The microchannel is filled with a weakly conductive solution. Applying electric current across the two conductive walls and placing the entire device in a constant magnetic field result in a Lorentz force of JB in the unit of Pa/m in the x direction. The flow driven by the Lorentz force can be described by the continuity and momentum equations, expect that the x component momentum equation has the Lorentz force term on the right-hand side. Assuming that the flow is fully developed, incompressible fluid, 2-D flow, and zero pressure gradient, derive the expression for the velocity field. h y Conductive wall TNH. Conductive wall X ////