A Similarity Solution with Two-Equation Turbulence Model for Computation of Turbulent Film Condensation on a Vertical Surface

In this paper, we presented a similarity solution for turbulent film condensation of stationary vapor on an isothermal vertical flat plate. In this method, some similarity transformations are employed and the set of governing partial differential equations (PDE) of conservation together with transport equations of turbulent kinetic energy and dissipation rate are transformed into a set of ordinary differential equations (ODE). Calculated data for the flow field, velocity profile, wall shear stress, condensate film thickness, turbulent kinetic energy, rate of dissipation, and heat transfer properties are discussed. The effect of Prandtl (Pr) number was also investigated in a wide range of variations. The obtained results showed that at high Prandtl numbers, the velocity profile becomes more uniform across the condensation film and therefore, the kinetic energy of turbulence is reduced. Furthermore, the effect of change in Pr is negligible at high Pr numbers and consequently, the flow parameters have no significant change in this range. The friction coefficient changes linearly through the condensation film and the slope of friction lines diminishes slightly by the Pr number. The rate of turbulent kinetic energy increases linearly from the wall up to about 20% of condensate film, then rises asymptotically and converges to a constant value near the liquid-vapor interface. Also, the rate of turbulent dissipation grows linearly up to 40% of condensate film thickness and then increases slightly while it oscillates

Power Law Nanofluid through Tapered Artery based on a ‎Consistent Couple Stress Theory

Based on couple stress theory, this study investigated non-Newtonian power-law nanofluid flows in converging, non-tapered, and diverging arteries. In addition to excluding gravity effects artery, geometry included mild stenosis. The momentum equation is solved via the Galerkin method, and the results are compared with experimental and classical findings. Although the power-law couple stress theory’s relations are first used in the analysis of non-Newtonian blood flow, the results of this theory are far more consistent with experimental results than classical results. Comparison of the results of the study of blood flow velocity profiles in a non-tapered artery without stenosis by the mentioned theory with experimental and classical theory results shows the difference in velocity at the center of the artery between the experimental results and the results of the classical theory is 36%, while this value has been reduced to 14% for the results of the couple stress theory. The variations in velocity profile with the power-law index (n=0.8 and n=0.85) and the dimensionless Darcy number (Da=10-10 and Da=10-7) in all three geometries indicated a flat velocity distribution with the increase in the power-law index while increasing the velocity profile with increased Darcy number. Mass transfer and energy equations are solved using the extended Kantorovich method. The solution convergence is evaluated, and the influence of parameters such as Prandtl number, Schmidt number, and dimensionless thermospheric and Brownian parameters on concentration and temperature profiles is obtained

Development of the Couple Stress Relationships for the Power Law Fluid and the Solution of Flow in Ceramic Tape Casting Process

The absence of characteristic material length in the Navier-Stokes equations has led to the development of different couple stress theories. In the present study, for the first time, the relations of a couple stress theory are extended to power-law fluids. Moreover, considering the significance of the length scale in nano- and micromechanics, the relations of the extended theory were applied to Newtonian and power-law fluids in tape casting of ceramics. The obtained velocity was used to calculate the volumetric flow rate as well as the thickness of the ceramic tape. A comparison between the results of the Newtonian fluid and the analytical and experimental results indicated a close agreement between the present results and the results of other studies. Moreover, the tape thickness was obtained for different length scales (L) by numerically solving the velocity relations obtained for the non-Newtonian fluid. Also, the impact of casting speed on the tape thickness was shown for four power-law fluids assuming L=0.35

Entropy analysis on convective film flow of power-law fluid with nanoparticles along an inclined plate

Entropy generation in a two-dimensional steady laminar thin film convection flow of a non-Newtonian nanofluid (Ostwald-de-Waele-type power-law fluid with embedded nanoparticles) along an inclined plate is examined theoretically. A revised Buongiorno model is adopted for nanoscale effects, which includes the effects of the Brownian motion and thermophoresis. The nanofluid particle fraction on the boundary is passively rather than actively controlled. A convective boundary condition is employed. The local nonsimilarity method is used to solve the dimensionless nonlinear system of governing equations. Validation with earlier published results is included. A decrease in entropy generation is induced due to fluid friction associated with an increasing value of the rheological power-law index. The Brownian motion of nanoparticles enhances thermal convection via the enhanced transport of heat in microconvection surrounding individual nanoparticles. A higher convective parameter implies more intense convective heating of the plate, which increases the temperature gradient. An increase in the thermophoresis parameter decreases the nanoparticle volume fraction near the wall and increases it further from the wall. Entropy generation is also reduced with enhancement of the thermophoresis effect throughout the boundary layer