Friction Factor Values Research Articles

Pore-Scale multi-objective shape optimization of triply periodic minimal surface cellular architectures: Volumetric Nusselt number versus friction factor

Triply Periodic Minimal Surface (TPMS) cellular architectures, i.e., minimal surfaces that are periodic in three independent directions, have attracted interest in the engineering community for their potential in heat transfer applications with severe volume constraints due to their high surface-to-volume ratio, unique geometrical properties and smooth porous structure. Such performance can be conveniently controlled by tuning the TPMS unit type, relative density, and structural parameters. In this study, a multi-objective optimization process is carried out to investigate how pore-scale geometric characteristics affect the heat transfer performance of TPMS, and which combinations result in an optimal trade-off between heat dissipation capability and associated pressure drop in terms of the Nusselt number and friction factor. The analysis is performed using an in-house Genetic Algorithm routine that generates the structure, allowing for a wider and denser range of investigation, and incorporates a commercial finite element CFD software as a black box fitness function. Over 14,000 unique combinations between two heat transfer boundary conditions (constant wall heat flux, fixed wall temperature) and several flow inlet conditions are investigated. The optimization achieved an increase in performance of up to 245 % in terms of volumetric Nusselt number, which was accompanied, however, by a significant, although reasonable, increase in friction factor values. The results also show specific trends among the geometric characteristics studied, which are then contextualized through the use of CFD analysis. Finally, empirical correlations are derived to cluster the non-dominated solutions obtained, enabling the reader to choose the best cellular TPMS structure by selecting the desired level of trade-off between convection heat transfer and flow resistance.

Identifying effective parameters on capillary tube performance with HCFCs, HFCs blends, and hydrocarbon refrigerants: Numerical assessment

This work offers a comprehensive numerical evaluation of the performance of capillary tube utilizing different refrigerants, including HCFCs, HFCs blends (Zeotropic, Azeotropic), and hydrocarbon, such as such as R22, R404A, R407C, R410A, R507A, and R290 refrigerants to predict the critical length of the adiabatic capillary tube. Utilizing a comprehensive thermodynamic model is applied to simulate the behavior of different refrigerants. Moreover, the effective design parameters based on the internal diameter for the adiabatic capillary tube (ACT), inside surface tube roughness, degree of subcooled, metastable region, condenser diameter, design of evaporator pressure (at critical length), condenser operating pressure, and refrigeration capacity are considered. The numerical model is developed based on the governing equations for mass, momentum, and energy, while a specified empirical equations are employed to represent each of the friction factor for single-and-two phase flow and metastable region. The results showed that the longest length of the ACT of 10.5 m revealed with R410A at mass flow rate of 8 g/s compared with 0.25 m at mass flow rate of 16 g/s for R290. Also, the results showed that the minimum value of friction factor of 0.0189 for R410A compared with maximum value of 0.0208 for R407C. The developed model is validated with available experimental results and models under different operation conditions and is found expectable with a good agreement. Where the standard error for different refrigerant with range value between (2.774% to 3.677%). However, the model represents accurate prediction the flow behavior and the thermal performance of the ACT.

Assessing a transitional and turbulent overland flow resistance law for surfaces with different roughness

The control and management of soil erosion phenomena caused by rainfall and runoff is a significant issue in sloping landscapes, especially if they are scarcely or not vegetated. The study of the relationship between soil roughness and flow resistance is a fundamental step in improving the knowledge of erosion processes. In this study, the suitability of a theoretically deduced flow resistance law, based on a power-velocity profile, was assessed by transitional and turbulent overland flow data obtained in laboratory and available in the literature. These measurements were obtained in a sloping (slope in the range 1–40 %) rectangular flume, testing the effects of six different roughness conditions. At first, for each investigated roughness condition, the available measurements were used to calibrate and test the equation relating the Γ function of the velocity distribution, the flow Froude number, and the channel slope. For all the investigated conditions, this analysis allowed for demonstrating that the flow resistance law gives a reliable estimate of the Darcy–Weisbach friction factor, with errors ≤±5 % for 89.8–100 % of the examined cases with reference to the considered roughness condition. Then, using coefficients b (1.05) and c (0.562) of the Γ function available in the literature, the roughness effect was exclusively attributed to the a coefficient. In this case, the friction factor values calculated by the flow resistance law, with b = 1.05 and c = 0.562 and the a values corresponding to the different roughness conditions, are characterized by errors ≤±5% for 70.4–100 % of the cases. Finally, the power relationships between the calibrated a, b, and c coefficients of the Γ function, and Manning’s n values, corresponding to the roughness of the investigated surfaces, pointed out that the a coefficient is the most affected by the roughness conditions, as the exponent of Manning’s assumes the highest value. The significance of this research is due to the fact that a relevant issue in modeling overland flow is to define the resistance coefficient for variable roughness, especially the vegetated ones.

Reducing Torque and Drag in Extended-Reach Wells Using Thermoplastic Polymers for Protective Sliding Rings

Extended-reach drilling represents an advanced way of drilling and accessing reservoirs that were previously economically not feasible to drain, impossible to reach or in an environmentally sensitive area. One of the main issues that appears while drilling such wells is caused by the high values of friction factor which cause high values of torque and drag. One of the suggested solutions is to use a protective sliding ring made from materials such as POM, Teflon and PA6 in combination with lubricants added to a polymer mud system. First, measurements were conducted on a lubricity tester to choose the best material and, after finishing, a mechanical wear test was conducted on a specially designed device to measure mechanical wear. Results showed that Teflon showed lower values of friction factor in comparison to steel and the mechanical wear was minimal. The lowest value of friction force was recorded for blocks made from Teflon in tested mud systems. It is also noticeable that, in polymer mud with weighting additives and lubricant, the value of the friction force is higher than in polymer mud with lubricant only.

Machine learning analysis of thermophysical and thermohydraulic properties in ethylene glycol- and glycerol-based SiO2 nanofluids

The study investigates the heat transfer and friction factor properties of ethylene glycol and glycerol-based silicon dioxide nanofluids flowing in a circular tube under continuous heat flux circumstances. This study tackles the important requirement for effective thermal management in areas such as electronics cooling, the automobile industry, and renewable energy systems. Previous research has encountered difficulties in enhancing thermal performance while handling the increased friction factor associated with nanofluids. This study conducted experiments in the Reynolds number range of 1300 to 21,000 with particle volume concentrations of up to 1.0%. Nanofluids exhibited superior heat transfer coefficients and friction factor values than the base liquid values. The highest enhancement in heat transfer was 5.4% and 8.3% for glycerol and ethylene glycol -based silicon dioxide Nanofluid with a relative friction factor penalty of ∼30% and 75%, respectively. To model and predict the complicated, nonlinear experimental data, five machine learning approaches were used: linear regression, random forest, extreme gradient boosting, adaptive boosting, and decision tree. Among them, the decision tree-based model performed well with few errors, while the random forest and extreme gradient boosting models were also highly accurate. The findings indicate that these advanced machine learning models can accurately anticipate the thermal performance of nanofluids, providing a dependable tool for improving their use in a variety of thermal systems. This study's findings help to design more effective cooling solutions and improve the sustainability of energy systems.

Condensation heat transfer performance of R290 in a plate heat exchanger for electric vehicle heat pumps

In the continuous improvement of electric vehicles driving range, a heat pump system with low-global warming potential (GWP) refrigerant is a promising solution. In the present work, the condensation heat transfer coefficient (HTC) and frictional pressure drop (FPD) were experimentally evaluated in an offset strip fins embedded plate heat exchanger (PHE), using an eco-friendly, low-GWP refrigerant R290 as the working fluid. A Modified Wilson Plot Method was used to predict the heat transfer of the coolant side (water/ethylene glycol; 50/50 %). The main focus of the present study revolves around the R290-to-coolant condensation experiment, wherein we analyzed the influence of mass flux (G = 20–50 kg m−2 s−1), heat flux (q = 3–12 kW m−2), and saturation temperature (Tsat = 40–55 °C) on HTC and FPD within the PHE while variable mean vapor quality (xm). According to the results, all experimental conditions were fall in the forced-convection condensation regime. The results state that HTC increases with a rise in q, G, and xm, but decreases with a surge in Tsat. Conversely, FPD increases with a rise in G and xm, and decreases with a escalation in Tsat, while q has no significant impact. Correlations were developed to predict the Nusselt number and friction factor values of R290 with mean absolute errors of 10.6 % and 11.2 %, respectively. These correlations are compared to previous research findings, signifying their efficacy in predicting the heat transfer characteristics of R290 within PHEs.

Experimental investigation on heat transfer and friction factor characteristics for novel hybrid roughness used in solar air heater

ABSTRACT The influence of heat transfer and frictional characteristics of air that is turbulent and transitting rectangular channel textured by novel hybrid roughness (multi-V shaped ribs combined with hemispherical protrusion in V-fashion) has been studied experimentally. A uniform solar intensity of 1000 W/m2 is incident over the opposite side of the roughened plate. The relative roughness pitch, angle of attack, Reynolds number, hydraulic diameter, relative protrusion pitch, and relative gap width majorly influence the thermal and frictional characteristics of solar air heater. In this research paper, the effect of Reynolds number from 4281 to 18,250, relative protrusion pitch from 0.375 to 0.625 and relative gap width from 2 to 4 on heat transfer and friction factor on hybrid roughness geometry have been studied. The highest value of Nusselt number is 4.15 obtained at a relative protrusion pitch of 0.5, relative gap width of 2 compared to smooth duct and Reynolds number value of 18,250. By increasing the Reynolds number, the value of friction factor keeps on decreasing and highest value of friction factor of about 3.8 is obtained at a relative protrusion pitch of 0.375, Reynolds number value of 4,281 and relative gap width of 4 as compared to smooth duct. The results of the experiment shows that hybrid roughness performs thermally better than their solitary roughness geometries. Further, Nusselt number and friction factor correlations were also developed and show a very good match with the experimental results.

Models based analysis of radiative induced MHD hybrid nanofluid flow over an exponentially stretching sheet

The study focuses on the flow of hybrid nanofluid, induced by magnetic and radiation effects, across an exponentially stretched sheet. The research examines the impact of temperature-dependent properties of the hybrid nanofluid on the sheet. Water is used as the base fluid, and SWCNT and MWCNT are employed as nanoparticles. The study includes a discussion of the Yamada–Ota, Xue and Tiwari–Das models of hybrid nanofluids. The governing system of flow is presented mathematically, and boundary layer approximations are used to reduce differential equations. The differential equations are transformed into dimensionless ordinary differential equations (ODEs) by using transformations. The dimensionless system of equations is then solved numerically. The results of the flow model are offered in tabular and graphical forms. We observed that Tiwari–Das model of hybrid nanofluid achieved more heat transfer and friction factor values when compared to other models of Xue and Yamada–Ota models of hybrid nanofluid. Temperature curves are noted to be enhanced by enlargement in the nano-concentration factor. If the nano-concentration increased in the fluid which boosted the thermal conductivity of the liquid, then as a result, the temperature of fluid enhanced at surface.

Improving flow efficiency in micro and mini-channels with offset strip fins: A stacking ensemble technique for Accurate friction factor prediction in steady periodically developed flow

A novel machine-learning model for micro and mini-channel friction factor prediction is presented in this article. In recent years, periodic array offset strip fins in micro and mini channels have gained attention due to their compactness and aid in heat transfer in chemical processing and electronic cooling devices. The research uses fin length-to-height ratios below one, and Reynolds numbers between one and six hundred contain 2765 geometrically dimensioned. The friction factor, the most significant barrier to heat transfer channel use, must be accurately estimated to design efficient systems. The Krylov subspace method is implemented using the finite element method using the FEniCS software. Additionally, three machine learning algorithms, Catboost, XGboost, and Random Forest regressors, are implemented to predict the friction factor for periodic steady flow through channels with offset strip fin arrays, and the corresponding prediction performance is analysed. A stacking ensemble model is proposed to enhance the precision of friction factor forecasts. The results demonstrate that the proposed method outperforms empirical correlations in predicting friction factor values for specific performance evaluation metrics with an absolute error of 0.403%, indicating that the model accurately represents the complexity of the data.

Heat Transfer Enhancement of Impinging Jet-Corrugated Solar Air Heaters

Abstract Solar air heater (SAH) is one of many applications of solar energy, but it has low thermal performance. To cater to this issue, a novel corrugated jet-impinging channel has been proposed for the absorbing plate of SAHs. The Nusselt number, pressure loss pumping power, and friction factor were computed by experimental and numerical studies for three different arrangements of jets, i.e., 1 × 1 square, 2 × 2, and 3 × 3 jet array with three target plates, i.e., smooth, trapezoidal, and sinusoidal corrugated plates over the Reynolds number range of 1740–2700 and jet-to-target plate spacing of 5.1–14.6. It was observed that jet-to-target plate distance and multiple jets impinging can affect the heat transfer enhancement significantly. An optimization study has been performed using the statistical Taguchi method. The optimum value of Nusselt number was found for the trapezoidal corrugated target plate, with 3 × 3 multiple jet impingement, jet-to-target plate distance of 5.1, and Reynolds number value of 2700, while the optimum value of friction factor was found for 3 × 3 jet impingement. Computational fluid dynamics (CFD) and experimental data are found to be in good agreement. An increase of 11 times was observed in the thermal performance factor as compared to the base case. Trapezoidal corrugation seems to be the effective profile for SAHs.

Experimental Analysis of Additively Manufactured Latticework Coupons

Abstract The capabilities and the precision of additive manufacturing processes have been tremendously increased in the last years, and this trend is not expected to be close to an end. Researchers, in the gas turbine industry, are focusing on the technology implementation on cooling systems. The aim of the present work is to investigate the performances of eight different geometries in order to exploit the cooling potential of some challenging latticework schemes with respect to traditional ones such as smooth channel, dimples, and pin fins. Test coupons consisting of those cooling structures embedded inside a rectangular cooling channel with dimensions of 56 mm width, 5 mm height, and 68 mm length were fabricated by means of direct metal laser melting technique. Since an aim of the present work is to evaluate the shape deformation associated with this additive process, the results of the CT scan imaging technique are presented. The performances are characterized both in terms of averaged heat transfer and friction factor values inside the test coupons by means of steady-state technique with a constant wall temperature boundary condition. The investigated flow Reynolds numbers range from 18, 000 to 40, 000. These values allow the authors to provide a deeper understanding of the latticework structures performances at Reynolds numbers beyond the range typically investigated in the literature. An efficiency index is employed to compare the performances of each geometry. Although the obtained results reveal that none of the tested geometries outperforms the other ones, the latticework arrangements show a heat transfer enhancement with respect to a porosity decrease. In addition, the good capability in terms of heat transfer of the lattice structures measured in the present work suggests the use of such technologies for twofold optimization process based on mechanical resistance and heat transfer characteristics.

Thermal performance analysis of triangular solar air heater duct having broken V-shaped ribs

In the present investigation, a numerical study has been done to analyse the effect of attachment of broken V-shaped ribs on the heating surface of the triangular-shaped solar air heater duct. The roughness and flow parameters include relative roughness pitch (between 8 and 14), angle of attack (between 30 and 75 degrees) and Reynolds number (between 4000 and 20,000). The effect on heat transfer and flow characteristics has been observed due to variation in parameters. Considerable enhancement in convective heat transfer is observed along with frictional effect and indicated by Nusselt number and friction factor values. All the variations resulted in an increase in the performance of a solar air heater, which was indicated by the value of the thermohydraulic performance parameter being more than 1. Abbreviations: CFD, Computational fluid dynamics; SAH, Solar air heater; THPP, Thermohydraulic performance parameter

Performance study on turbulent heat transfer using rectangular air duct integrated with continuous and intermittent ribs turbulators

To continue the scientific path specialized in enhancing the thermal performance of thermal systems, several tests are carried out to improve the overall performance of a rectangular duct as air flows through it. This study reports experimentally and numerically the heat transfer enhancement and overall performance of a rectangular air duct with various arrangement of continuous and intermittent ribs turbulators. The ribs are inserting in several array arrangements at a 90o relative to the direction of flow. Three ribs lengths s= 30, 60 and 150 mm employed with the several arrangements that?s tested in the current study, with the pitch ratios (p/e)= 5.0 and height ratios (e/H) = 0.330. These cases include: continuous ribs case (CR), intermittent-continuous-intermittent ribs case (ICIR) and intermittent-ribs (IR). Reynolds number (Re) is ranging from 10,000 to 35,000. The experimental work was performed by designed and fabricated test rig while the numerical work was performed in commercially ANSYS Fluent 17.2. the outcomes show that (IR) case offers the best overall performance for all tested velocities, its 1.54 for experimental study and 1.57 for numerical study at Re=10000. Also, the highest friction factor values are found in (IR) case, it is found to be 0.082 in Re=10000.

Comparisons on the thermal and entropic performance of helical tubes with varying cross-sections with constant wall temperature

This study investigates the thermal-hydraulic behavior of helical tubes with different cross-section types. The flow was considered to be in a turbulent flow regime, and the wall temperature of the tube was considered to be constant. Circle, horizontal oval, vertical oval, square, horizontal rectangle, vertical rectangle, equilateral triangle, and hexagons were eight cross-section types assessed in this study. Findings demonstrated that across the evaluated range of mass flow rates, cases with triangular cross-sections had the highest friction factor values. Also, it was observed that these cases have the largest and the most intense vorticity among all other cases. It was revealed that cases with sharp regions include vortices that increase the loss of kinetic energy. In circular cross-section and triangular cross-section examples, the Nu number was most varied. There is a 58% difference between maximum Nu values for circular and triangular cross-sections. The case with a circular cross-section and a mass flow rate of 2 kg/s exhibited the highest PEC factor value of approximately 1.001. Finally, it was determined that a circle cross-section is the best according to the first law of thermodynamics, but a triangular cross-section performed 52% better when compared to other cross-section forms according to the second law of thermodynamics.

Effect of particle size on second law of thermodynamics analysis of Al2O3 nanofluid: Application of XGBoost and gradient boosting regression for prognostic analysis

In this study, the current research delves into the influence of nanoparticle size on turbulent forced convective heat transfer, entropy generation, and friction factor. The investigation focused on three different sizes (30 nm, 50 nm, and 80 nm) of Al2O3 nanoparticles (NPs) suspended in a water-based nanofluid (NF) with a 1 vol% concentration flow in a circular tube. The nanoparticles (NPs) were characterized using various characterization techniques. The stability and pH of the NF were determined, and its viscosity (VST) and thermal conductivity (TC) were measured at a temperature of 60 °C. Heat transfer experiments were conducted with varying particle sizes and Reynolds number (Re), maintaining a fluid inlet temperature of 60 °C. The results indicated that the NF containing 30 nm particles exhibited higher VST and TC compared to the other samples and the base fluid. The maximum enhancement in Nu for Al2O3 (30 nm) and Al2O3 (80 nm) NFs is 60.7 and 18.5 % greater than that of base fluid, respectively. The maximum and minimum total entropy generation (Sgen,T) value of 0.499 and 0.286 observed for base fluid and Al2O3 NF (30 nm), respectively at low Re. The highest friction factor enhancement for Al2O3 NF (30 nm) exceeded by 9.4 % compared to the base fluid, and the maximum thermal performance factor observed for Al2O3 NF (30 nm) was 1.57. Finally, regression analysis was employed to establish correlations for estimating Nu and friction factor values. Prognostic models were developed using two sophisticated machine learning algorithms, XGBoost and Gradient Boosting Regression (GBR). Both models demonstrated exceptional prediction abilities, achieving over 99 % accuracy rates based on the experimental data.

NUMERICAL AND EXPERIMENTAL INVESTIGATION OF TUBE BUNDLE HEAT EXCHANGER ARRANGEMENT EFFECT ON HEAT TRANSFER PERFORMANCE IN TURBULENT FLOWS

This study examines the friction factor, convective heat transfer, and area goodness factor of both inline and staggered tube bundles. The Finite Volume Method (FVM) is used for numerical simulations. Experimental and numerical approaches are utilized. Both 18.0 mm and 21.6 mm longitudinal distances are investigated. It is recommended to use ratio coefficients to reduce computation time. The proportion coefficients are used to obtain predictions for the three-dimensional cases based on the two-dimensional results or to transfer the 2D results to 3D. In addition, three turbulence models were utilized and compared within an Unsteady Reynolds Averaged Navier-Stokes (URANS) formulation. Experimental results validated numerical predictions. The thermal boundary conditions consist of a constant inlet temperature and a uniform heat flux on the support plate. Reynolds number is changed from 989 to 6352, while the Prandtl number remains at 0.70. Nusselt number and friction factor values have been observed to increase with increasing Reynolds number in all geometric configurations. The staggered configurations result in greater Nusselt number and friction factor values compared to inline configurations. The Nusselt number and pressure drop experience negative and positive effects, respectively, as the distance between rows decreases. SST turbulence models typically predict reasonable outcomes for all geometric configurations.

Enhancing solar air heater efficiency with 3D cylinder shaped roughness elements

Solar air heaters (SAHs) harness solar radiation to warm the air. This study investigates the efficacy of 3D cylindrical roughness features in enhancing heat transfer and reducing friction losses within SAHs. The configuration involves inline and staggered placement of 3D cylindrical roughness elements beneath the absorber surface. Through ASHRAE standard 93–77 testing, heat transfer and friction factors are examined across various cylinder roughness setups, with parameters such as relative roughness pitch (p/h) and gap (w/h) considered. The channel aspect ratio (W/B) is set at 5, and a relative roughness height (h/D) of 0.06 is maintained and flow Reynolds number (Re) is varied from 3000 to 8000. Regression analysis reveals a significant relationship between heat transfer and friction. Notably, at Re = 7910, p/h = 20, and w/h = 8 for staggered cylinder roughness, average friction factor (fav) increases by 171.3 %, and average nusselt number (Nuav) increases by 69.7 %. Similarly, the efficiency index (η) peaks at 0.8192 with inline roughness at Re = 2969, p/h = 20, and w/h = 8. The introduced 3D cylinder roughness elements disrupt the laminar sub-layer, amplifying convective heat transfer while curbing friction losses. This approach optimizes SAH performance within the studied parameter range, showcasing potential improvements for utilizing solar energy. Experimental results, along with expressions for average friction factor (fav) and average Nusselt number (Nuav), underscore the benefits of cylinder-shaped roughness geometries while maintaining h/D = 0.06. These findings introduce an innovative convective heat transfer method, enhancing SAH efficiency. Furthermore, the anticipated average friction factor (fav) and average Nusselt number (Nuav) values align within error limits of ±6.63 % and ±6.62 %, respectively, with improved regression coefficients indicating the stronger relationship and the influence of independent variables on dependent variables.

Comparison of Flow Boiling Characteristics between Minichannel and Macrochannel in Solar Still-Numerical Study

The thermal performance of a rectangular minichannel has been estimated for various heat fluxes (1 kW/m2 to 2 kW/m2) and fluid mass flux rates (20 g/s to 40 g/s). The mixture model is used to determine two-phase flow characteristics in the mini-macro channel. The focus of the present work is to establish prime factors for the enhancement of vapor fractions inside the minichannel (<3 mm) and macrochannel (>3 mm). The fluid flow characteristics are explained with help of temperature difference (the wall side and water film side), friction factor, Nusselt number, evaporative thin film thickness, heat transfer coefficient and vapor fraction. Validation of current simulation with earlier research article shows good agreement. The friction factor value for the minichannel and macrochannel are 0.0004 and 0.0011, respectively. It is found that heat transfer is significantly more in macrochannel pipes compared with minichannels. By using the dimensional analysis, empirical correlation is developed for vapor fraction with dependent parameters such as channel diameter, fluid mass flow rate and heat flux the first time. The predicted correlation of vapor fraction and film thickness help to understand the pronounced effect of channel diameter on heat transfer.

Evaluation of the effects of grass and shrub cover on overland flow resistance and its attributes under simulated rainfall

Vegetation plays a crucial role in controlling soil erosion and regulating overland flow connectivity. However, the effects of vegetation coverage on the overland flow resistance mechanisms remain unclear. This study aimed to examine the impact of grass and shrub cover on the resistance to overland flow concerning a random patch distribution pattern. This was achieved through a series of simulated rainfall experiments. Thirty slope surfaces with different vegetation coverages, consisting of complete combinations of five grass and six shrub coverages, were tested under five rainfall intensities (60–120 mm h−1) and three slope gradients (8.75%–26.79%). The results indicated that the Darcy–Weisbach friction factor (f) values on unvegetated slopes ranged from 0.455 to 1.385, whereas those on vegetated slopes ranged from 0.500 to 5.624. Vegetation coverage increased flow resistance on hillslopes, and the relationship between f and the Reynolds number (Re) was influenced by vegetation cover and the slope gradient; thus, it showed a positive correlation when vegetation form resistance was dominant. In contrast, a negative correlation was observed. According to the t-test results, the linear superposition method had limitations in calculating overland flow resistance and was only applicable when the grass coverage was 10%. Moreover, as the coverage increased, significant differences (p < 0.05) emerged between the total resistance and the linear summation of the individual resistance components. Additional vegetation resistance plays a significant role in impeding the water flow, contributing up to 50% of the total resistance. Finally, an equation for calculating additional vegetation resistance was developed using dimensional analysis and multiple nonlinear regression. The accuracy of the equation was validated by comparing it with experimental results (NSE = 0.918, RMSE = 0.144). These findings emphasize the effectiveness of constructing grass-shrub communities and increasing vegetation coverage as measures for soil and water conservation.

Stagnation-point flow of Williamson fluid along a stretched plate with convective thermal condition and activation energy

The implication of a stagnation-point flow together with the influence of activation energy in a Williamson fluid, which consists of tiny particles, over an expansive plate is analyzed numerically. Conditions of convective heat and mass motion with features of irregular movement and thermal-migration of particles influenced by viscous dissipation and convective heat surface condition are checked in the study. The conversion of the model equations from the initially formulated partial derivatives to ordinary ones is implemented by similarity transformations while an unconditionally stable Runge-Kutta-Fehlberg integration plus shooting technique are then used to complete the integration. Various interesting effects of the physical parameters are demonstrated graphically and explained appropriately in order to make accurate predictions. Moreover, the accuracy of the solution is verified by comparing the values of the skin friction factor with earlier reported ones in literature under limiting constraints. It is worth mentioning that the velocity profiles flatten down as the magnitude of the magnetic field factors expands but this causes a boost in the fluid’s temperature. The concentration field also appreciates with activation energy but depreciates with chemical reaction and Schmidt number.