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Data are reported for heat transfer from water to melting ice spheres and for mass transfer in the case of dissolving spheres of pivalic acid suspended in water agitated in a stirred vessel.The transport coefficients are found to depend on agitator power input but not on agitator design, in agreement with the Kolmogoroff theory. These experimental results are used with others in the literature to develop a correlation involving Nusselt and Prandtl or Schmidt numbers together with a dimensionless group involving agitation power. The correlation is essentially independent of solid-liquid density ratio in the ranqe 0.8 to 1.25, and in this range the gravity group also appears to be unimportant.Particles or drops suspended in agitated liquids are employed in various chemical processes, including crystallization, solvent extraction, polymerization, slurry catalysis, and direct-contact heat exchange. In many cases the size of the process equipment is directly related to the rate of mass or heat transfer between the particles and the liquid. Though numerous studies of the transport rates in such systems have been reported, the large number of variables involved has made it difficult to develop a full understanding of the physics of the processes of interest. Evidently the physical properties of both phases are important, as well as the nature of the turbulence in the liquid, as determined by the type of agitation and the geometry of the system.Perhaps the most widely used method of estimating transport rates in such systems is that based on the work of Harriott (12). Hariott suggested that the transport rates in a stirred tank can be estimated as a multiple of the transport which would result if the particles fell through a stagnant medium at their terminal velocity. There are, however, no reliable methods of predicting this multiple. KOLMOGORBFF'S THEORYSeveral investigators (8, 21,27) have suggested that KolmogoroFs theory of isotropic turbulence may be applied to a stirred liquid in turbulent motion and, therefore, that the transport results can be correlated with the agitation power per unit volume. However, no satisfactory correlation of transport data based upon these ideas has been developed.Kolmogoroff's theory postulates that turbuleiice results in a continuous inertial transfer of kinetic energy from the larger eddies to smaller and smaller eddies, finally resulting in viscous dissipation of the energy by the smallest eddies in the dissipation range. In a stirred tank, the impeller continually creates eddies described by a certain size and frequency distribution and also by a certain geometric orientation. The largest eddies are of the order of the size of the container and constitute the bulk flow. These large eddies transfer energy to smaller and smaller eddies through inertial interaction. As the kinetic energy is transferred from large to small eddies, the geometric orientation is lost. The large eddies interact to produce more random smaller ones and eventually, if sufficient interaction takes place, all ...

A finite-difference method is presented for solving three-dimensional transient heat conduction problems. The method is a modification of the method of Douglas and Rachford which achieves the higher-order accuracy of a Crank-Nicholson formulation while preserving the advantages of the Douglas-Rachford method: unconditional stability and simplicity of solving the equations a t each time level. Although the method has not yet been applied, the analysis in this paper suggests that it will prove to be the most efficient method yet proposed for the numerical integration of three-dimensional transient heat conduction problems.Transient heat conduction problems in three dimensions represent a class of problems of great importance in many fields of engineering and science today. When the need for a numerical solution of such a problem arises, the requirements of computing time and of storage capacity often tax the capabilities of today's largest digital computers. Thus the need for more efficient finite-difference methods for solving such problems is an ever-constant one.The differential equation describing transient heat conduction in an isotropic medium of constant thermal conductivity and volumetric heat capacity is where the time scale has been normalized to include the thermal diffusivity. Three well-known finite-difference approximations to Equation (1) A.1.Ch.E. JournalConsider the following finite-difference approximation to Equation (1): A22(T*Z.,.k.m+l) + A2#(T'#,,*,fJIn Equation (6) the unknown values T*,,j,s,n+l appear only in the time difference and in the x-direction differerne. Thus only T' values along a row parallel to the x-axis are related by a system of simultaneous equations. In contrast to the solution of Equations ( 3 ) and ( 4 ) , Equation ( 6 ) requires the solution of many small, independent systems of simultaneous equations instead of one large system relating all T* values within the three-dimensional region. Furthermore each system is tridiagonal, and a very efficient method for solving the tridiagonal system without iteration is well known (1, 5, 6).If Equation (6)