K.J. De Witt

Momentum and heat transfer on a continuous moving surface in a power law fluid

This analysis examines the momentum and heat transfer occurring in the laminar boundary layer on a continuously moving and stretching two-dimensional surface in a non-Newtonian power law fluid. The Merk-Chao series expansion is used to generate ordinary differential equations from the partial differential momentum equation in order to obtain universal velocity functions. For the problem of combined momentum and heat transfer in the boundary layer of the moving sheet, a general power series is used to describe the fluids velocity and temperature. Examples for a non-linear surface velocity and a linearly stretching surface velocity are provided.

Momentum and Heat Transfer on a Continuous Moving Surface

Determination du transfert de chaleur et de quantite de mouvement dans la couche limite laminaire sur une surface mobile avec une vitesse de surface arbitraire et une temperature de surface non uniforme

Momentum and heat transfer in a power-law fluid with arbitrary injection/suction at a moving wall

Abstract The momentum and heat transfer in the laminar boundary layer of a non-Newtonian power-law fluid flowing over a flat plate, which is moving in the direction opposite to the uniform main stream, and with arbitrary fluid injection/suction along the plate surface, are analyzed. The partial differential equations are decomposed into a sequence of ordinary differential equations using the Merk–Chao series to obtain universal velocity and temperature functions that are independent of the fluid injection/suction distribution profile. Results are tabulated as a function of the problem parameters. Friction coefficients and Nusselt numbers are calculated for constant fluid injection/suction along the plate.

Pulsatile flow through a bifurcation with applications to arterial disease

Abstract Fatty streaks and fibrous plaques are known to be localized in bends, junctions, and branches of the large arteries, suggesting a significant role for fluid mechanics in the genesis of arterial disease. Various mechanisms have been proposed in the literature based on the known occurrence of eddies and high surface traction. For the purpose of helping in the evaluation of these mechanisms, the flow behavior in a bifurcation was chosen for study. The equations of continuity and motion were solved using the marker and cell numerical technique for the two-dimensional, periodic flow of a Newtonian fluid through a horizontal, bifurcating, rigid channel. Both regions of eddying at the outer wall and of high shear stress at the inner wall were shown by the calculations for both steady and pulsatile flows. The eddies disappeared completely during a portion of each cycle for pulsatile flow.

Mixed convection to power-law fluids from two-dimensional or axisymmetric bodies

Abstract Momentum and heat transfer in mixed-convective, power-law fluid flow over arbitrarily shaped two-dimensional or axisymmetric bodies are examined theoretically. The Merk-Chao series expansion technique, with three mixed convection parameters, is used for the analysis. Solutions to the governing equations are obtained as universal functions which are independent of the geometry of the problem. Using the wall derivatives of these universal functions, results are given for the flow over the flat plate, the horizontal circular cylinder and the sphere. The results are compared with the literature for the limiting cases of forced and natural convection.

The final approach to steady state in nonsteady stagnation point heat transfer

SummaryThe thermal response of a laminar boundary layer flow near a stagnation point due to step wall temperature change is investigated when the elapsed time is large. The final approach to the steady state temperature field is shown to be characterized by exponential decay with time of perturbations from the steady state. The characteristic factors appearing in the exponents arise from the solution of an eigenvalue problem in ordinary linear differential equations. Results are presented for Prandtl numbers of 0.01 to 100 for two dimensional stagnation flow and 0.1 to 10 for axisymmetrical stagnation flow.

Investigation of oxygen transfer to slime as a surface reaction

Abstract Trickling filters are essentially contacting devices which facilitate the adsorption of oxygen and organic material in waste water by a slime layer consisting of a gelatinous matrix interspersed with microorganisms. From a mechanistic viewpoint, therefore, the trickling filter is analogous to a fixed bed catalytic reactor. The characteristics of the catalytic surface, namely, the slime layer, are the major differences. Most of the previous studies on trickling filter analysis based on the above viewpoint have utilized a simple vertical wall or an inclined plane as the physical model. In this study, a circular tube containing flowing liquid forms the basis of the mathematical model permitting the determination, by use of experimental macroscopic data, of the reaction rate between dissolved oxygen and a thin layer of microorganisms attached to the wall within the system. The mathematical analysis assumes that both mass transfer and chemical reaction are important in the overall oxygen consumption process. The experimental data, based on the mathematical model, show that in a continuous flow, steady state system the reaction kinetics between dissolved oxygen and the attached thin layer of microorganisms does not depend on the dissolved oxygen concentration, and thus is kinetically zero order. This has been experimentally shown previously only for suspended cultures of bacteria and for the first time has been verified for slime beds.

MASS TRANSFER TO A DROPLET WITH A FIRST-ORDER CHEMICAL REACTION

The steady-state mass transfer to a droplet with a first-order chemical reaction is i nvestigated as a function of the Damkohler number (Da11) for the special case of very high Peclet number flow. The flow field in the droplet employed in this work is Hills spherical vortex. The resistance to mass transfer is assumed to occur inside the droplet with negligible resistance to mass transfer in the continuous phase.

The transient motion of a spherical fluid droplet

Abstract A numerical method is developed for investigation of the unsteady motion of a spherical fluid droplet under the influence of gravity. This study extends previous work valid for creeping flow to moderate Reynolds number. The unsteady flow fields inside and outside of the fluid sphere are described by the two-dimensional, axisymmetric Navier-Stokes equations in the form of vorticity and stream function, along with the equation of motion of the droplet. The governing equations are approximated by a central difference and a second-order upwind difference, and are solved iteratively using the Gauss-Siedel and secant methods. Numerical results of the time-dependent vorticity, stream function and drop velocity are presented for a water droplet moving through air and for an air bubble rising in water. The steady state drop velocity and the drag coefficient at various Reynolds numbers are examined, and they are shown to agree very well with previous results.

Numerical prediction of cold turbulent flow in combustor configurations with different centerbody flame holders

A numerical study of cold turbulent flow in a combustor containing a centerbody flame holder is presented in this paper. The axisymmetric Navier-Stokes equations incorporating a k - e turbulence model were solved in a nonorthogonal curvilinear coordinate system. The finite volume method, applied to a staggered grid system, was used to discretize the differential equations. These finite differenced equations were then solved iteratively utilizing the SIMPLE algorithm. Solutions were obtained for two combustor duct geometries with various centerbody flame holders which included a disk, a cone and a sphere. The extent of mixing due to these bodies was evaluated. A comparison with previously obtained experimental data yielded moderately good agreement.