Let us consider a fully developed flow in a duct with rectangular cross-section as shown in Fig. 3.1. An electrically conducting fluid is driven through the duct by a constant pressure gradient and flows with unidirectional velocity \(v = u\hat x\). The duct and the fluid are exposed to an externally applied magnetic field B. Walls on which the magnetic field has a normal component are called the Hartmann walls, whereas the walls tangential to the field are called the side walls.
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