Mariano López de Haro

Minimization of entropy generation by asymmetric convective cooling

The uniform internal heating of a solid slab and the viscous flow between two parallel walls, are used to illustrate the possibility of minimizing the global entropy generation rate by cooling the external surfaces convectively in an asymmetric way. The known analytic expressions for the temperature field, in the first case, and the velocity and temperature fields, in the second case, are used to calculate the global entropy generation rate explicitly. In dimensionless terms, this function depends on the dimensionless ambient temperature and convective heat transfer coefficients (Biot numbers) of each surface which, in general, are not assumed to be the same. When the Biot numbers for each surface are equal, the entropy generation rate shows a monotonic increase. However, when the Biot numbers are different this function displays a minimum for specific cooling conditions.

Equation of state of a multicomponent d-dimensional hard-sphere fluid

A simple recipe to derive the compressibility factor of a multicomponent mixture of d-dimensional additive hard spheres in terms of that of the one-component system is proposed. The recipe is based (i) on an exact condition that has to be satisfied in the special limit where one of the components corresponds to point particles; and (ii) on the form of the radial distribution functions at contact as obtained from the Percus—Yevick equation in the three-dimensional system. The proposal is examined for hard discs and hard spheres by comparison with well-known equations of state for these systems and with simulation data. In the special case of d = 3, our extension to mixtures of the Carnahan—Starling equation of state yields a better agreement with simulation than the already accurate Boublik—Mansoori—Carnahan—Starling—Leland equation of state.

Entropy generation analysis of magnetohydrodynamic induction devices

Magnetohydrodynamic (MHD) induction devices such as electromagnetic pumps or electric generators are analysed within the approach of entropy generation. The flow of an electrically-conducting incompressible fluid in an MHD induction machine is described through the well known Hartmann model. Irreversibilities in the system due to ohmic dissipation, flow friction and heat flow are included in the entropy-generation rate. This quantity is used to define an overall efficiency for the induction machine that considers the total loss caused by process irreversibility. For an MHD generator working at maximum power output with walls at constant temperature, an optimum magnetic field strength (i.e. Hartmann number) is found based on the maximum overall efficiency.

Contact values of the radial distribution functions of additive hard-sphere mixtures in d dimensions: A new proposal

The contact values gij(σij) of the radial distribution functions of a d-dimensional mixture of (additive) hard spheres are considered. A “universality” assumption is put forward, according to which gij(σij)=G(η,zij), where G is a common function for all the mixtures of the same dimensionality, regardless of the number of components, η is the packing fraction of the mixture, and zij=(σiσj/σij)〈σd−1〉/〈σd〉 is a dimensionless parameter, 〈σn〉 being the nth moment of the diameter distribution. For d=3, this universality assumption holds for the contact values of the Percus–Yevick approximation, the scaled particle theory, and, consequently, the Boublik–Grundke–Henderson–Lee–Levesque approximation. Known exact consistency conditions are used to express G(η,0), G(η,1), and G(η,2) in terms of the radial distribution at contact of the one-component system. Two specific proposals consistent with the above-mentioned conditions (a quadratic form and a rational form) are made for the z dependence of G(η,z). For one-dim...

Optimization analysis of an alternate magnetohydrodynamic generator

The production of electric power through the oscillatory motion of an electrically conducting fluid in a continuous electrode Faraday generator is considered. The performance of this alternate magnetohydrodynamic (MHD) generator is analyzed using the conventional isotropic electrical efficiency and an overall second law efficiency, based on the global entropy generation rate. The velocity, electric current density and temperature fields for the oscillatory Hartmann flow are calculated in order to assess, in terms of the entropy generation rate, the dissipative phenomena caused by fluid friction, Joule heating and heat transfer in the MHD generator. The overall second law efficiency is used to determine optimum operation conditions that minimize process irreversibilities.

Structure of multi-component hard-sphere mixtures

A method to obtain (approximate) analytical expressions for the radial distribution functions and structure factors in a multi-component mixture of additive hard spheres is introduced. In this method, only contact values of the radial distribution function and the isothermal compressibility are required and thermodynamic consistency is achieved. The approach is simpler than but yields equivalent results to the Generalized Mean Spherical Approximation. Calculations are presented for a binary and a ternary mixture at high density in which the BoublikMansoori-Carnahan-Starling-Leland equation of state is used. The results are compared with the Percus-Yevick approximation and the most recent simulation data.

Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular-dynamics simulations.

Following the work of Leutheusser [Physica A 127, 667 (1984)], the solution to the Percus-Yevick equation for a seven-dimensional hard-sphere fluid is explicitly found. This allows the derivation of the equation of state for the fluid taking both the virial and the compressibility routes. An analysis of the virial coefficients and the determination of the radius of convergence of the virial series are carried out. Molecular-dynamics simulations of the same system are also performed and a comparison between the simulation results for the compressibility factor and theoretical expressions for the same quantity is presented.

RADIAL DISTRIBUTION FUNCTIONS FOR A MULTICOMPONENT SYSTEM OF STICKY HARD SPHERES

A method to obtain (approximate) analytical expressions for the radial distribution functions and structure factors in a multicomponent system of sticky hard spheres is introduced. In its simplest implementation, the method yields the Percus–Yevick approximation. In the next order, only contact values of the cavity functions and the isothermal compressibility are required. Some tentative strategies to determine the input values are discussed. Illustrative examples following these strategies, in which the radial distribution functions and structure factors are computed, are also presented.

A branch-point approximant for the equation of state of hard spheres.

Using the first seven known virial coefficients and forcing it to possess two branch-point singularities, a new equation of state for the hard-sphere fluid is proposed. This equation of state predicts accurate values of the higher virial coefficients, a radius of convergence smaller than the close-packing value, and it is as accurate as the rescaled virial expansion and better than the Pade [3/3] equations of state. Consequences regarding the convergence properties of the virial series and the use of similar equations of state for hard-core fluids in d dimensions are also pointed out.

Virial series for fluids of hard hyperspheres in odd dimensions

A recently derived method [R. D. Rohrmann and A. Santos, Phys. Rev. E 76, 051202 (2007)] to obtain the exact solution of the Percus-Yevick equation for a fluid of hard spheres in (odd) d dimensions is used to investigate the convergence properties of the resulting virial series. This is done both for the virial and compressibility routes, in which the virial coefficients B(j) are expressed in terms of the solution of a set of (d-1)/2 coupled algebraic equations which become nonlinear for d>/=5. Results have been derived up to d=13. A confirmation of the alternating character of the series for d>/=5, due to the existence of a branch point on the negative real axis, is found and the radius of convergence is explicitly determined for each dimension. The resulting scaled density per dimension 2eta(1/d), where eta is the packing fraction, is wholly consistent with the limiting value of 1 for d-->infinity. Finally, the values for B(j) predicted by the virial and compressibility routes in the Percus-Yevick approximation are compared with the known exact values [N. Clisby and B. M. McCoy, J. Stat. Phys. 122, 15 (2006)].