Magnetohydrodynamic Effects On Mixed Convection Flows In Channels And Ducts

This work focuses on magnetohydrodynamic (MHD) mixed convection flow of electrically conducting fluids enclosed in simple 1D and 2D geometries in steady periodic regime. In particular, in Chapter one a short overview is given about the history of MHD, with reference to papers available in literature, and a listing of some of its most common technological applications, whereas Chapter two deals with the analytical formulation of the MHD problem, starting from the fluid dynamic and energy equations and adding the effects of an external imposed magnetic field using the Ohm's law and the definition of the Lorentz force. Moreover a description of the various kinds of boundary conditions is given, with particular emphasis given to their practical realization. Chapter three, four and five describe the solution procedure of mixed convective flows with MHD effects. In all cases a uniform parallel magnetic field is supposed to be present in the whole fluid domain transverse with respect to the velocity field. The steady-periodic regime will be analyzed, where the periodicity is induced by wall temperature boundary conditions, which vary in time with a sinusoidal law. Local balance equations of momentum, energy and charge will be solved analytically and numerically using as parameters either geometrical ratios or material properties. In particular, in Chapter three the solution method for the mixed convective flow in a 1D vertical parallel channel with MHD effects is illustrated. The influence of a transverse magnetic field will be studied in the steady periodic regime induced by an oscillating wall temperature. Analytical and numerical solutions will be provided in terms of velocity and temperature profiles, wall friction factors and average heat fluxes for several values of the governing parameters. In Chapter four the 2D problem of the mixed convective flow in a vertical round pipe with MHD effects is analyzed. Again, a transverse magnetic field influences the steady periodic regime induced by the oscillating wall temperature of the wall. A numerical solution is presented, obtained using a finite element approach, and as a result velocity and temperature profiles, wall friction factors and average heat fluxes are derived for several values of the Hartmann and Prandtl numbers. In Chapter five the 2D problem of the mixed convective flow in a vertical rectangular duct with MHD effects is discussed. As seen in the previous chapters, a transverse magnetic field influences the steady periodic regime induced by the oscillating wall temperature of the four walls. The numerical solution obtained using a finite element approach is presented, and a collection of results, including velocity and temperature profiles, wall friction factors and average heat fluxes, is provided for several values of, among other parameters, the duct aspect ratio. A comparison with analytical solutions is also provided, as a proof of the validity of the numerical method. Chapter six is the concluding chapter, where some reflections on the MHD effects on mixed convection flow will be made, in agreement with the experience and the results gathered in the analyses presented in the previous chapters. In the appendices special auxiliary functions and FORTRAN program listings are reported, to support the formulations used in the solution chapters.