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A mathematical model of the plate heat exchanger (PHE) cooling unit has been developed and solved using a digital computer. The equations of temperature distribution on each plate in a counterflow PHE cooling unit are derived using an energy balance analysis. The results are presented in the form of numerical values of the “overall effectiveness” of the heat exchanger. Factors affecting the effectiveness of the PHE cooling units have been investigated. The change of temperatures and humidity ratios of the air flows in the heat exchanger are also analyzed. Finally, the high performance of the PHE cooling unit is explained by introducing the concept of “enthalpy potential.” This unit is of particular interest as a component in solar-assisted cooling systems.

The coupled elastic and hydrodynamic equations describing the transient behavior of a low capacity lubricant pumping and sealing device known as an oil pumping ring assembly have been solved numerically for both isothermal and adiabatic conditions in the lubricant film. Results show the transient behavior of the pressure, viscosity and temperature fields in the lubricant film, stresses developed in the pumping ring, and the amount of fluid pumped. A performance analysis over a limited range of component dimensions is also presented.

Packed towers can be used for solar regeneration of aqueous solutions and dehumidification of air using aqueous solutions. These processes involve simultaneous heat and mass transfer with heat effects. In order to design a packed tower for aqueous solution-air contacting operations, heat and mass transfer coefficients for each phase are required. For the present study, aqueous calcium chloride solution is used; ceramic Raschig rings and Berl saddles are used as the packing material. In this paper air phase transfer coefficients are correlated with flow rates of air and liquid and the temperature of air, whereas liquid phase coefficients are correlated with rates of air and liquid flow, and the temperature and concentration of the liquid.

Heat and mass transfer analysis between a desiccant-air contact system in a packed tower has been studied in application to air dehumidification employing liquid desiccant, namely calcium chloride. Ceramic 2 in. Raschig rings are used as the packing material. To predict the tower performance, a steady-state model which considers the heat and mass transfer resistances of the gas phase and the mass transfer resistance of the liquid phase is developed. The governing equations are solved on a digital computer to simulate the performance of the tower. The various parameters such as the effect of liquid concentration and temperature, air temperature and humidity and the rates of flow of air and liquid affecting the tower performance have been discussed.

The vorticity-streamfunction formulation is implemented on the control-volume-based finite-element method (CVFEM). The key contribution of this work is the formulation of the wall vorticity, which allows successful modeling of fluid flow problems with irregular boundaries. The resulting algorithm exhibits the desirable qualities of consistency, accuracy, and stability.

The effects of free thermal expansion on the performance of infinitely wide slider bearings are investigated and several numerical examples are computed which show conclusively that thermal expansion is the fundamental cause of hydrodynamic lubrication of radially grooved initially parallel thrust bearings. In addition, thermal expansion is a likely explanation for the performance of centrally pivoted lilting pad thrust bearings.

An iterative method of calculating the steady-state pressure and temperature distributions in the fluid film for infinitely wide slider bearings is presented. The bearing profile is assumed to be quite general, rendering the method particularly applicable to problems involving thermal or elastic distortion. The viscosity of the lubricant is regarded as a function of temperature and pressure; the density as a function of temperature only. The inertia terms are retained in the simplified Navier-Stokes equation and the energy equation includes the compression work term. Heat transfer between the bearing surfaces and the fluid film are accounted for. Several numerical examples are evaluated and compared with existing solutions. The solution presented is believed to be the most complete to date. A subsequent paper will deal with the effect of thermal distortions of similar geometrical arrangements described herein.

Flow of a fluid through a parallel channel is one of the simplest types of flow. However, the equations of flow and energy are far from simple and can only be solved in a closed form in the simplest cases when nonlinear effects such as the inertia and convective terms can be neglected (i.e., for zero Reynolds number) and when the energy and momentum equations are uncoupled. A numerical iterative method is described in which the coupled momentum and energy equations are solved when the viscosity, thermal conductivity and specific heat are functions of temperature, and the density a function of temperature and pressure; inertia terms are retained in the momentum equation and the convective terms, compression work term and the predominant dissipation term retained in the energy equation. Results are obtained for a variety of boundary temperatures up to about 2400 deg F and the effect of variable fluid properties and various terms in the energy and momentum equation are shown.

The problem of the stepped-thrust bearing is considered but, whereas normally volumetric continuity is assumed, the equations are solved assuming mass continuity; i.e., the variation of density is also considered as well as the effect of the stepped discontinuity on the load-carrying capacity and the coefficient of friction. Computed theoretical curves illustrate the importance of the density on the operation of this bearing and, in part, explain results already published.

Previously, solutions of the problem of the Rayleigh-type bearing with a step which is not straight have involved the use of the electrolytic tank or the use of relaxation methods, both of which are somewhat inconvenient as compared with the approximate analytical method described in this paper. The solution of the derived differential equation is in the form of a convergent infinite series, but for rapid computation it is shown that an economized series (the τ method for the solution of linear differential equations) yields results of high accuracy.

Analytical investigation into the stepped thrust bearing was first carried out by Lord Rayleigh, whose solution neglected side leakage. More recently Archibald has presented a solution with side leakage not neglected but limited by the step being straight across the bearing surface perpendicular to the direction of motion. This paper gives an alternative solution, using relaxation methods, which is applicable to any shape of the step. Results show that the load capacity of the completely internal step is much greater than that for the simple tilting slider.