SUMMARYThe laminar, incompressible, three-dimensional, fully developed viscous ow of a non-conducting biomagnetic uid in a impermeable rectangular duct is numerically studied in the presence of an applied magnetic ÿeld. It is assumed that the magnetic ÿeld strength is su ciently strong to saturate the bio uid and the magnetization is given as a function of the magnetic ÿeld intensity. The system of the partial di erential equations, resulting after the introduction of appropriate non-dimensional variables, is solved applying an e cient numerical technique based on a pressure-linked pseudotransient method on a common grid. Results concerning the existence and the uniqueness of the solution, are also given. The obtained results, for di erent values for the parameters entering into the problem under consideration, show that the ow is appreciably in uenced by the presence of the magnetic ÿeld.

SUMMARYA new numerical method is presented for the solution of the Navier-Stokes and continuity equations governing the internal incompressible ows. The method denoted as the CVP method consists in the numerical solution of these equations in conjunction with three additional variational equations for the continuity, the vorticity and the pressure ÿeld, using a non-staggered grid. The method is used for the study of the characteristics of the laminar fully developed ows in curved square ducts. Numerical results are presented for the e ects of the ow parameters like the curvature, the Dean number and the stream pressure gradient on the velocity distributions, the friction factor and the appearance of a pair of vortices in addition to those of the familiar secondary ow. The accuracy of the method is discussed and the results are compared with those obtained by us, using a variation of the velocity-pressure linked equation methods denoted as the PLEM method and the results obtained by other methods.

The incompressible fully developed laminar flow in a helically duct of square cross section is studied expressing the governing equations in terms of an orthogonal coordinate system. Numerical results are obtained with the described continuity, vorticity, and pressure (CVP) numerical method using a colocation grid for all variables. Since there are not approximations, the interaction effects of curvature, torsion and axial pressure gradient on the velocity components and the friction factor are presented. The results show that the torsion deforms substantially the symmetry of the two centrifugal vortices of the secondary flow, which for large values of torsion combined with small curvature tend to one vortex covering the whole cross section. The friction factor decreases for torsion in the range 0 to 0.1 and increases as the torsion increases further, a behavior which is more profound as the Dean number increases. Our results are stable for the calculated Dean numbers.

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The fully developed forced convective heat transfer flow in a curved square duct is studied, under a constant uniform wall temperature axially and peripherally. The continuity and momentum equations are solved with a new numerical-variational method denoted the CVP method. The method uses a nonstaggered grid for all primitive variables without introducing spurious oscillations in the solutions. Numerical results are presented for the effects of the curvature, the Dean number and the stream pressure gradient, on the velocity, the temperature, the friction factor, and the Nusselt number for fluids with Prandtl numbers 0.7 and 7. The accuracy of the method is discussed, and the results are in close agreement with those obtained by other methods.