Search Results (80)

The aim of this study was to analyze the simulation effect of heterogeneous resistance in the municipal sludge-transportation pipeline using the modified Turian-Yuan model. The simulation results of the modified Turian-Yuan model were investigated using five samples of sludge with different volumetric concentrations (0.92%, 1.76%, 2.12%, 2.45%, and 2.98%, respectively); these were compared with those of the Hazen-Williams model and the Darcy-Weisbach model. The results showed that the simulation accuracy of the modified Turian-Yuan model was higher than the results of the others under different volumetric sludge concentrations. Meanwhile, the accuracy of the modified Turian-Yuan model was less affected by the sludge concentration, indicating that the stability of this model was high. In addition, the simulation results of the modified Turian-Yuan model are all better than the level of measured values; this means that the model is relatively safe but may lead to an increase in capital and operational costs. The possible reason for this phenomenon may be the reduction in sludge particle sizes due to shear frictions and the tendency of sludge particles to be spherical in shape. Full article

This study focuses on understanding the bioconvection in Jeffery–Hamel (JH) flow, which has valuable applications in areas like converging dies, hydrology, and the automotive industry, which make it a topic of practical importance. This research aims to explore Homogeneous–Heterogeneous (HH) chemical reactions in a magnetic Darcy–Forchheimer model with bioconvection in convergent/divergent channels. To analyze the role of porosity, the Darcy–Forchheimer law is applied. The main system of equations is simplified through similarity transformation into ordinary differential equations solved numerically with the help of the NDSolve technique. The results, compared with previous studies for validation, are presented through graphs and tables. The study reveals that in divergent channels, the velocity decreases with higher solid volume fractions, while in convergent channels, it increases. Furthermore, various physical parameters, such as the Eckert number and porosity parameter, increase skin friction in divergent channels but decrease it in convergent channels. These findings suggest that the parameters investigated in this study can effectively enhance homogeneous reactions, providing valuable insights for practical applications. Full article

Determining the friction coefficients for uniform flows over very rough bottoms is a long-standing problem in open-channel hydraulics and river engineering. This experimental study presents measurements of the surface deformation as well as Darcy–Weisbach and Manning friction coefficients for steady, turbulent (6058 $\le \mathcal{R}e\le$ 28,502), and subcritical flows (0.14 $\le \mathcal{F}r\le$ 0.52) over large roughness elements, where $\mathcal{F}r$ and $\mathcal{R}e$ denote the Froude and Reynolds numbers, respectively. The experiments were conducted in a rectangular, inclined flume with a train of half-cylinders mounted on the bed, with radii in the range 20 mm $\le a\le$ 50 mm. These obstacles yield a relative submergence 1.45 $\le h_N/a\le$ 4.41 and a constant spacing ratio $e/a=12.8$ across all experimental runs, where $h_N$ and e denote the normal flow depth and the center-to-center spacing between cylinders, respectively. The relative amplitude of the surface profiles, ($\Delta h/a$), was analyzed and found to correlate strongly with $h_N/a$, $\mathcal{R}e$ and $\mathcal{F}r$. The results reveal very high values of the Darcy friction factor, f, which follows scaling laws of the form ${f\propto (h_N/a)}^{\widehat{n}}$, with $\widehat{n}<0$, independent of a, and ${f\propto \mathcal{R}e}^{\beta }$, where $\beta <0$ is closely linked to a. Scaling relationships for the Manning roughness coefficient, (n), were also investigated and are reported herein. Full article

The use of solar energy is a promising solution to reduce dependence on fossil fuels. Flat-plate collectors (FPCs) are commonly employed to harness solar energy, but their performance is often limited by thermal resistance, surface deterioration, and inefficient heat dissipation. This study investigates the performance enhancement of an FPC integrated with porous copper foam through numerical simulations. The porous foam increases surface area and improves heat transfer by creating a complex flow path for the working fluid. Key parameters such as the porous foam height ratio (S), Darcy number (Da), and volumetric flow rate ($\dot{V}$) are analysed to determine their impact on thermal performance. The results indicate that a maximum Nusselt number (Nu) of 28.85 and an outlet temperature of 306.81 K is obtained for S = 1. A decrease in Da from 10⁻² to 10⁻⁶ and an increase in $\dot{V}$ from 0.25 L/min to 1 L/min enhance the Nu by 5.7% and 8.8%, respectively. The friction factor (f) increases with increases in S, a decrease in Da and an increase in $\dot{V}$. The performance evaluation criteria (PEC) are obtained to be maximum at S = 0.4, Da = 10⁻² and $\dot{V}$ = 0.25 L/min. These findings demonstrate the potential of porous copper foam in improving FPC efficiency. Full article

This study investigates the steady, two-dimensional boundary layer flow of a Casson fluid over an inclined nonlinear stretching surface embedded within a Forchheimer porous medium. The governing partial differential equations are transformed into a set of ordinary differential equations through similarity transformations. The analysis incorporates the effects of an external uniform magnetic field, gravitational forces, thermal radiation modeled by the Rosseland approximation, and first-order homogeneous chemical reactions. We consider several dimensionless parameters, including the Casson fluid parameter, magnetic parameter, Darcy and Forchheimer numbers, Prandtl and Schmidt numbers, and the Eckert number to characterize the flow, heat, and mass transfer phenomena. Analytical solutions for the velocity, temperature, and concentration profiles are derived under simplifying assumptions, and expressions for critical physical quantities such as the skin friction coefficient, Nusselt number, and Sherwood number are obtained. Full article

Topography is an important factor that impacts the hydrological processes on sloping farmlands. Yet, few studies have reported the combined influences of slope gradient and slope position on infiltration characteristics and hydrodynamic parameters on sloping croplands in purple soil regions, an important area for agricultural productivity in Southwest China. Here, laboratory-simulated rainfall experiments were conducted in a steel trough (5 m long, 2 m wide, and 0.45 m deep), and rainfall lasted for 1 h at a rate of 90 mm h⁻¹ to examine the variations in the infiltration rates and hydrodynamic parameters under varying slope gradients (i.e., 3°, 6°, 10°, 15°, 21°, and 27°) and slope positions (i.e., upper, middle, and lower), and explore the relationships between the infiltration rate and the soil detachment rate. The results showed that the infiltration rate decreased gradually with duration rainfall and ultimately approached a steady state in the six slope treatments. Cumulative infiltration ranged from 15.54 to 39.32 mm during rainfall, and gradually reduced with the increase of slope gradient. The Horton’s model outperforms other models for predicting the infiltration rate with an R² value of 0.86. Factors such as Darcy–Weisbach friction, flow shear force, Manning friction coefficient, unit energy, and runoff depth varied in the following order: upper slope > middle slope > lower slope, whilst the Reynolds number and Froude number gradually increased along the slope transect from the upper to lower slope positions. A significant linear function was fitted between the soil detachment rate and the infiltration rate at the gentle slopes (3°, 6°, 10°), whereas an exponential relationship was observed at the steep slopes (15°, 21°, and 27°). Observation also suggested that 15° was the critical slope gradient of sediment detachment, infiltration characteristics, and hydrodynamic parameters. Our results provide theoretical insight for developing models that predict the impacts of topographic factors on hydrological characteristic and soil erosion in hilly agricultural landscapes of purple soil fields. Full article

Suitable friction groups are provided for solving three typical hydraulic problems. While the friction group based on viscous forces is used for calculating the pressure drop or head loss in pipes and open channels, commonly referred to as the Type 1 problem in hydraulic engineering, additional friction groups with similar behaviors are introduced for calculating steady flow discharge as the Type 2 problem and, for estimating hydraulic diameter as the Type 3 problem. Contrary to the viscous friction group, the traditional Darcy–Weisbach friction factor demonstrates a negative correlation with the Reynolds number. This results in curves that slope downward from small to large Reynolds numbers on the well-known Moody chart. In contrast, the friction group used here, based on viscous forces, establishes a more appropriate relationship. In this case, the friction and Reynolds number are positively correlated, meaning that both increase or decrease simultaneously. Here, rearranged diagrams for all three mentioned problems show similar behaviors. This paper compares the Moody diagram with the diagram for the viscous force friction group. The turbulent parts of both diagrams are based on the Colebrook equation, with the newly reformulated version using the viscous force friction group. As the Colebrook equation is implicit with respect to friction, requiring an iterative solution, an explicit solution using the Lambert W-function for the reformulated version is offered. Examples are provided for both pipes and open channel flow. Full article

Accurate prediction of the friction factor is fundamental for designing and calibrating fluid transport systems. While the Colebrook–White equation is the benchmark for precision due to its physical basis, its implicit nature hinders practical applications. Explicit correlations like Churchill’s equation are commonly used but often sacrifice accuracy. This study introduces two novel modifications to Churchill’s equation to enhance predictive capabilities. Developed through a rigorous analysis of 240 test cases and validated against a dataset of 21,000 experiments, the proposed Churchill B(Re) and Churchill B(V,ε) models demonstrate significantly improved accuracy compared to the original Churchill equation. The development of these functions was achieved through generalized reduced gradient (GRG) nonlinear optimization. This optimized equation offers a practical and precise alternative to the Colebrook–White equation. The mean relative errors (MRE) for the modified models, Churchill B(Re) and Churchill B(V,ε), are 0.025% and 0.807%, respectively, indicating a significant improvement over the original equation introduced by Churchill in 1973, which exhibits an MRE of 0.580%. Similarly, the mean absolute errors (MAE) are 0.0008% and 0.0154%, respectively, compared to 0.0291% for the original equation. Beyond practical applications, this research contributes to a deeper understanding of friction factor phenomena and establishes a framework for refining other empirical correlations in the field. Full article

The main objective of this study is to explore the inventive conception of the magnetohydrodynamic flow of a hybrid nanofluid over-porous stretching/shrinking sheet with the effect of radiation and mass suction/injection. The hybrid nanofluid advances both the manufactured nanofluid of the current region and the base fluid. For the current investigation, hybrid nanofluids comprising two different kinds of nanoparticles, aluminium oxide and ferrofluid, contained in water as a base fluid, are considered. A collection of highly nonlinear partial differential equations is used to model the whole physical problem. These equations are then transformed into highly nonlinear ordinary differential equations using an appropriate similarity technique. The transformed differential equations are nonlinear, and thus it is difficult to analytically solve considering temperature increases. Then, the outcome is described in incomplete gamma function form. The considered physical parameters namely, magnetic field, Inverse Darcy number, velocity slip, suction/injection, temperature jump effects on velocity, temperature, skin friction and Nusselt number profiles are reviewed using plots. The results reveal that magnetic field, and Inverse Darcy number values increase as the momentum boundary layer decreases. Moreover, higher values of heat sources and thermal radiation enhance the thermal boundary layer. The present problem has various applications in manufacturing and technological devices such as cooling systems, condensers, microelectronics, digital cooling, car radiators, nuclear power stations, nano-drag shipments, automobile production, and tumour treatments. Full article

The principal objective of the study is to examine the impact of thermal radiation and entropy generation on the magnetohydrodynamic hybrid nano-fluid, Al₂O₃/H₂O, flow in a Darcy–Forchheimer porous medium with variable heat flux when subjected to an electric field. Investigating the impact of thermal radiation and non-uniform heat flux on the hybrid nano-liquid magnetohydrodynamic flow in a non-Darcy porous environment produces novel and insightful findings. Thus, the goal of the current study is to investigate this. The non-linear governing equation can be viewed as a set of ordinary differential equations by applying the proper transformations. The resultant dimensionless model is numerically solved in Matlab using the $bvp4c$ command. We obtain numerical results for the temperature and velocity distributions, skin friction, and local Nusselt number across a broad range of controlling parameters. We found a significant degree of agreement with other research that has been compared with the literature. The results show that an increase in the Reynolds and Brinckmann numbers corresponds to an increase in entropy production. Furthermore, a high electric field accelerates fluid velocity, whereas the unsteadiness parameter and the presence of a magnetic field slow it down. This study is beneficial to other researchers as well as technical applications in thermal science because it discusses the factors that lead to the working hybrid nano-liquid thermal enhancement. Full article

Flat mini heat pipes (FMHPs) are often used in cooling systems for various power electronic components, as they rapidly dissipate high heat flux densities. The main objective of the present work is to experimentally investigate whether differences in the rate of vapor formation occur on an internal structure containing trapezoidal microchannels and porous sintered copper powder material. Several parameters, such as hydraulic diameter and fluid velocity through the material, as a function of the internal structure porosity, were determined by calculation for a steady state regime. Reynolds number was determined as a function of porosity, according to Darcy’s law, and the Nusselt number was calculated. Since the flow is Darcy-type through the porous medium inside the FMHP, the Darcy friction factor was calculated using five methods: Colebrook, Darcy–Weisbach, Swamee–Jain, Blasius, and Haaland. After experimental tests, it was found that when the porous and trapezoidal microchannel layers are wetted at the same time, the vaporization progresses at a faster rate in the porous material, and the duration of the process is shorter. This recommends the use of such an internal structure in FMHPs since the manufacturing technology is simpler, the materials are cheaper, and the heat flux transport capacity is higher. Full article

This paper presents a variable density topology optimization method to numerically investigate the optimal drag-reduction shape of objects in the two-dimensional and three-dimensional flows with steady incompressible external flow conditions, taking into account material volume constraints. By introducing the porous media model, the artificial Darcy friction is added to the Navier-Stokes equation to characterize the influence of materials on the fluid. Material density is applied to implement material interpolation. By transforming the boundary integral form of viscous dissipative expression of drag into the volume integral of artificial Darcy friction and convection term, we solve the problem of drag expression on the implicit interface corresponding to the structure. The continuous adjoint method is used to analyze gradient information for iteratively solving topology optimization problems. We obtain the relevant topology optimization structures of the minimum drag shapes, investigate the effect of the low Reynolds number on the drag force corresponding to two objective functions and discuss the mechanism of drag reduction by a hydrodynamic body shape. Full article

The influence of stress jump conditions on a steady, fully developed two-layer magnetohydrodynamic electro-osmotic nanofluid in the microchannel, is investigated numerically. A nanofluid is partially filled into the microchannel, while a porous medium, saturated with nanofluid, is immersed into the other half of the microchannel. The Brinkmann-extended Darcy equation is used to effectively explain the nanofluid flow in the porous region. In both regions, electric double layers are examined, whereas at the interface, Ochoa-Tapia and Whitaker’s stress jump condition is considered. The non-dimensional velocity, temperature, and volume fraction of the nanoparticle profiles are examined, by varying physical parameters. Additionally, the Darcy number, as well as the coefficient in the stress jump condition, are investigated for their profound effect on skin friction and Nusselt number. It is concluded that, taking into account the change in shear stress at the interface has a significant impact on fluid flow problems. Full article

This paper presents a numerical model of a four-pass supercritical steam superheater with a complex flow system. The specific heat of steam is a function of temperature and pressure, and the specific heat of flue gas is a function of temperature. Pressure and temperature changes along the length of the tubes were also determined. The modified Churchill equation was used to calculate the steam-side friction factor of Darcy–Weisbach. The flue gas temperature variations behind the individual superheater tube rows were calculated. The steam and wall temperature distributions were determined in each tube row along its length. Knowing the temperature of the tube walls and the steam along the flow direction enables the selection of the correct steel grade for the tubes. Thanks to this advantage of the proposed method, the investment can be reduced in superheater construction without the danger of overheating the tube material. The results of the superheater simulation were compared with the results of measurements on the actual object. The proposed numerical method can find application in steam superheaters’ design and performance calculations. It can also be used to monitor superheater operating parameters, which are difficult to measure due to the high flue gas temperature. Full article

The aim of this study is to examine the Darcy–Forchheimer flow = of $H_{2}O$-based $Al-A{l}_2{O}_3/$$Cu-A{l}_2{O}_3$ hybrid nanofluid past a heated stretchable plate including heat consumption/ generation and non-linear radiation impacts. The governing flow equations are formulated using the Naiver–Stokes equation. These flow equations are re-framed by using the befitted transformations. The MATLAB bvp4c scheme is utilized to compute the converted flow equations numerically. The graphs, tables, and charts display the vicissitudes in the hybrid nanofluid velocity, hybrid nanofluid temperature, skin friction coefficient, and local Nusselt number via relevant flow factors. It can be seen that the hybrid nanofluid velocity decreased as the magnetic field parameter was increased. The hybrid nanofluid temperature tended to rise as the heat absorption/generation, nanoparticle volume friction, and nonlinear radiation parameters were increased. The surface drag force decreased when the quantity of the magnetic parameter increased. The larger size of the radiation parameter led to enrichment of the heat transmission gradient. Full article