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Pressure loss is one of the significant parameters in designing pipe bends. In this paper, the pressure distribution and pressure losses induced by turbulent flows in a circular cross-sectioned piping elbow with or without guide vane were simulated. The flow distribution in the piping elbow was simulated by the k- model using control volume method. The main objective of this study is to characterize the effect of changing the angle of pipe bend and Reynolds number on the flow separation of single-phase turbulent flow through numerical simulation. Results were validated by other experimental results and then loss coefficient was calculated in different angles from 45 to 135-degree pipe bend in various radius ratios with or without guide vane. Despite the fact that increasing pipe angle increased the pipe bend loss coefficient, using guide vane in the pipe elbow decreased this coefficient. In the radius ratio 1.5 with one guide vane, the loss coefficient of the pipe bends decreased by 50 percent in all degrees. Results revealed that the use of two vanes in pipe bend is more effective on the reduction of elbow pressure losses. Moreover, two guide vanes can decrease loss coefficient more than 50 percent. Also, the results indicated that loss coefficient decreased by increasing Reynolds number.

Deformation of thin viscous liquid films exposed to a transverse thermal gradient results in Bénard–Marangoni instability, which would lead to the formation of micro- and nano-sized features. Linear and nonlinear analyses are performed to investigate the thermally induced pattern formation in shear thinning and shear thickening liquid films. The so-called thin film (TF) equation is re-derived to include viscosity variations using the power-law (PL) model. The characteristic wavelength for the growth of instabilities is found using a linear stability analysis of the PL-TF equation. A finite-difference-based discretization scheme and adaptive time step solver are used to solve the PL-TF equation for the nonlinear numerical model. The results show that the rheological property affects the timescale of the process and the size and final shape of the formed features. The fastest growth pillar reaching the top substrate in a shear thickening fluid is shorter than both the shear thinning and the Newtonian fluid cases. Moreover, morphological changes between patterns of shear thinning and shear thickening fluids are correlated with local viscosity variations. The number of formed pillars considerably increases with the increasing flow behavior index. The existing model also predicts the formation of pillars and bicontinuous structures at very low and high filling ratios.

In this paper, the effects of the thicknesses and locations of two rectangular heaters, located on the bottom and one side of on an enclosure, on mixed convection of nanofluid flows in a lid-driven cavity are numerically investigated. The enclosure is simultaneously heated partially by these two heaters which have similar or different thicknesses and also filled with different nanofluids containing nanoparticles of Cu, Ag, Al2O3, and TiO2 within the base fluid of water. A finite volume approach by the SIMPLE algorithm is used to solve the governing equations. The effects of different Rayleigh numbers (103≤Ra≤106), Reynolds numbers (1≤Re≤1000), solid volume fractions (0≤ϕ≤0.2), heater lengths (0.2≤B≤0.6), heater locations (0.25≤D≤0.75) and heater thicknesses (0.1≤t≤0.3) on the streamlines, isotherms and the average Nusselt number along two heaters are studied accurately. Also, variations of average Nusselt number of two heaters are considered whenever one heater is fixed and the other heater moves along on the wall. Moreover, variations of the length of one heater on the average Nusselt number are also studied whenever the length of the other heater is fixed. In addition, variations of the thickness of one heater on the average Nusselt number are studied whenever the thickness of the other heater is fixed.

This study focuses on a detailed analysis of thermally induced Benard convection, thermocapillary instability, and interfacial deformation of a nanofilm. The dynamics, instability, and morphological evolution of a thin liquid film investigated using a volume of fluid (VOF) numerical scheme that incorporates the Marangoni stress to model the gas–liquid interface deformation. The results obtained from VOF are then compared with those of the “thin-film” model in many cases to find an accurate model for predicting the characteristic wavelength for the growth of instabilities. We also present a correlation to predict the relation between the characteristic wavelength found by VOF numerical results and the analytical linear stability analysis predictions. This is followed by examining the protrusion width and the distance between the protrusions on the structures’ final shape and interface evolution time. Finally, linear theoretical relations for the formation of secondary pillars are presented based on the width of protrusions, their separation distance, and the inverse filling ratio. The results show that the number of pillars increases when the width and distance between two protrusions are greater than a critical value.

The underlying mechanism of thermal induced patterning is investigated using a numerical phase-field model. Research on the subject has been mostly restricted to lubrication approximation, which is only valid for the cases that the initial film thickness is smaller than the characteristic wavelength of induced instabilities. Since the long-wave approximation is no longer valid in the later stages of pattern evolution, we employed the full governing equations of fluid flow and the thermally induced Marangoni effect to track the interface between the polymer film and the air bounding layer. Conducting a systematic study on the impact of influential parameters, we found that an increase in the temperature gradient, thermal conductivity ratio, and initial thickness of the thin film resulted in shorter processing time and faster pattern formation. Additionally, the contact angle between the polymer film and the bounding plates showed a significant effect on the shape of created features. Compared to the reported experimental observation by Dietzel and Troian [“Mechanism for spontaneous growth of nanopillar arrays in ultrathin films subject to a thermal gradient,” J. Appl. Phys. 108, 074308 (2010)], our numerical modeling provided a more accurate prediction of the characteristic wavelength against the linearized model currently used in the literature. The numerical findings in this study provide valuable insight into thermal-induced patterning, which can be a useful guide for future experimental works.

In this paper, entropy generation induced by natural convection of cu-water nanofluid in rectangular cavities with different circular corners and different aspect-ratios were numerically investigated. The governing equations were solved using a finite volume approach and the SIMPLE algorithm was used to couple the pressure and velocity fields. The results showed that the total entropy generation increased with the increase of Rayleigh number, irreversibility coefficient, aspect ratio or solid volume fraction while it decreased with the increase of the corner radius. It should be noted that the best way for minimizing entropy generation is decreasing Rayleigh number. This is the first priority for minimizing entropy generation. The other parameters such as radius, volume fraction, etc are placed on the second priority. However, Bejan number had an inverse trend compared with total entropy generation. As an exception, Bejan number and total entropy number had the same trend whenever solid volume fraction increased. Moreover, Nusselt number increased as Rayleigh number, solid volume fraction or aspect ratio increased whereas it decreases with the increase of corner radius.

This article numerically studies entropy generation due to natural convection in a rectangular cavity with circular corners. In this work, in order to solve the governing equations, an explicit finite-volume procedure and a time-marching method are utilized. Also, instead of the conventional algorithms of SIMPLE, SIMPLEM, and SIMPLEC, an artificial compressibility technique is applied for coupling the continuity to the momentum equations. Entropy generation, as a representation of irreversibility and efficiency loss in engineering heat transfer processes, is analyzed in detail. In this work, effects of the radius of walls corner, Rayleigh number, and distribution ratio on total entropy generation, Nusselt number, and Bejan number are also evaluated. The results show that entropy generation decreases with the increase of the radius of the walls’ corner and increases with the increase of Rayleigh number, aspect ratio, and irreversibility ratio.

The numerical analysis of heat transfer of laminar nanofluid flow over a flat stretching sheet is presented. Two sets of boundary conditions (BCs) are analyzed, i.e., a constant (Case 1) and a linear streamwise variation of nanoparticle volume fraction and wall temperature (Case 2). The governing equations and BCs are reduced to a set of nonlinear ordinary differential equations (ODEs) and the corresponding BCs, respectively. The dependencies of solutions on Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt are studied in detail. The results show that the reduced Nusselt number and the reduced Sherwood number increase for the BCs of Case 2 compared with Case 1. The increases of Nb, Nt, and Le numbers cause a decrease of the reduced Nusselt number, while the reduced Sherwood number increases with the increase of Nb and Le numbers. For low Prandtl numbers, an increase of Nt number can cause to decrease in the reduced Sherwood number, while it increases for high Prandtl numbers.