Multiple Quadratic Regression Research Articles

Modeling the hydromagnetic transient three-dimensional stagnation point flow of a couple stress Casson fluid over a bi-directional stretching sheet

A numerical study is performed to examine the magnetohydrodynamic effects on the transient three-dimensional stagnation point flow of a Casson fluid along a bi-directional stretching sheet. The physical model of the flow includes a sheet which is stretched in both the tangential directions and is thus called “bi-directional stretching”. The heat transfer mechanism includes the influences of space- and time-dependent non-uniform heat generation/absorption, as well as dissipation due to viscosity. The mathematical modeling of the problem involves the constitution of a set of coupled nonlinear boundary layer equations, together with suitable boundary conditions. The mathematical model thus developed is then subjected to suitable similarity transformations to arrive at a set of ordinary differential equations, which were then treated with the successive linearization method (SLM) to obtain approximate solutions for the velocity and temperature fields. A parametric study is carried out, and the results are discussed and presented graphically to analyze the behavior of the primary and secondary velocity distributions, as well as fluid temperature, along with significant physical quantities such as skin friction and Nusselt number for various values of the nondimensional parameters. Multiple quadratic regression analysis is also carried out to investigate the significance of parameters and to estimate the skin-friction and heat transfer coefficients.

Welding investigation of Hastelloy C-276 and parametric optimization using integrated MRA-TLBO algorithm during A-TIG process

A-TIG welding is a modified form of GTAW process that has become popular due to its ability to create high-quality welded joints with minimal cracks and distortion. This technique is commonly used to join various metals, including stainless steel, aluminum, titanium, and nickel alloys like Hastelloy C-276, which is used in fabrication of complex components across marine, nuclear, aerospace, and chemical industries. In this investigation, A-TIG welding of Hastelloy C-276 was studied using three parameters - welding current, welding speed, and gas flow rate - at three distinct levels. The impact of these parameters were analyzed on two responses, namely penetration depth and width of weld. Macrostructural investigation, sensitivity analysis, and parametric studies revealed that welding current (I) had the most influence, followed by speed of welding (S) and flow rate of gas(G). Full quadratic multiple regression analysis-based models were developed for both responses, which were found to be suitable with a higher coefficient of determination and an average percentage error of 2.165% and 2.624%, respectively. Additionally, a teaching learning based optimization algorithm was integrated with these models to identify the most effective A-TIG parameter combination for higher penetration depth and lower weld width. The MRA-TLBO integrated approach resulted in an optimal parametric combination of I (170A), S (180 mm min−1), and G (11.37 l min−1) that resulted in a penetration depth and weld width of 4.503 mm and 4.684 mm, respectively. Validation at this optimal setting showed an improvement of 3.365% and 1.284% for weld width and penetration depth, respectively, suggesting the robustness of the developed methodology.

Pico scale undershot waterwheel for ultra-low-head: Analytical, experimental and CFD method

In the 19th and early 20th century, the utilization and development of the undershot waterwheel (USWW) was massif. USWW represents a global warming and crisis electricity solution issue for the world. However, the best condition and design of USWW are still incomplete; previous research is based on assumptions. Hence, this work aims to theoretically estimate the power loss (head loss, leakage loss, and friction loss) occurring in USWW to predict the relation between the blade number and optimum operation. The investigation employs analytical and CFD methods, then validated with experimental data. Then, based on root mean square error (RMSE) analysis, the average RMSE of analytical results to experimental data was 9.02%, and of CFD data was 9.07%. Then, depict the blade number and optimum operation relation to USWW performance expressing using multiple quadratic polynomial regression. The empirical law identifies the 16-blades, and the working operation of 0.5 is USWW maximum performance in ultra-low-head.

Multiple solutions in magnetohydrodynamic stagnation flow of hybrid nanofluid past a sheet with mathematical chemical reactions model and stability analysis

The homogeneous heterogeneous reactions (H–H reactions) in the magnetohydrodynamic (MHD) boundary layer stagnated flow of an Al2O3–Cu–water base hybrid nanofluid past a stretching shrinking sheet are studied. A newly developed two-phase hybrid nanofluid model based on Buongiorno's model is used to understand the nanofluids behaviors. Multiple solutions are observed for specific ranges of various parameters, whose stabilities are checked and discussed, which seem to have been neglected in previously published articles about studies of MHD-stagnation flow and mathematical chemical reactions models using hybrid nanofluid. The heterogeneous reaction considered in this case is isothermal and first order, whereas the homogeneous chemical reaction is isothermal cubic autocatalytic. The solutions so captured are examined using various graphs to demonstrate the impact of different physical parameters, and their physical insights are also given. The results show that hybrid nanofluids, which have distinct functions in the processes of homogeneous and heterogeneous reactions, play a key role in the homogeneous–heterogeneous reactions' transport mechanism. The quadratic multiple regression analysis evaluations of the local Nusselt number demonstrate that the thermophoretic impact predominates over Brownian motion for both magnetic and non-magnetic effects.

Aero-Engine Blade Cryogenic Cooling Milling Deformation Simulation and Process Parameter Optimization.

For the machining of aero-engine blades, factors such as machining residual stress, milling force, and heat deformation can result in poor blade profile accuracy. To address this issue, simulations of blade milling were completed using DEFORM11.0 and ABAQUS2020 software to analyze blade deformation under heat-force fields. Process parameters such as spindle speed, feed per tooth, depth of cut, and jet temperature are used to design both a single-factor control and BBD test scheme to study the influence of jet temperature and multiple changes in process parameters on blade deformation. The multiple quadratic regression method was applied to establish a mathematical model correlating blade deformation with process parameters, and a preferred set of process parameters was obtained through the particle swarm algorithm. Results from the single-factor test indicated that blade deformation rates were reduced by more than 31.36% in low-temperature milling (-190 °C to -10 °C) compared with dry milling (10 °C to 20 °C). However, the margin of the blade profile exceeded the permissible range (±50 µm); therefore, the particle swarm optimization algorithm was used to optimize machining process parameters, resulting in a maximum deformation of 0.0396 mm when the blade temperature was -160 °C~-180 °C, meeting the allowable blade profile deformation error.

Regression analysis and features of negative activation energy for MHD nanofluid flow model: A comparative study

This article elucidates the impact of activation energy on magnetohydrodynamic (MHD) stagnation point nanofluid flow over a slippery surface in a porous regime with thermophoretic and Brownian diffusions. Negative activation energy is scarce in practice, but the impact of negative activation energy could not be neglected as it is noticed in chemical processes. The rate of some Arrhenius-compliant reactions is retarded by increasing the temperature and is therefore associated with negative activation energies, such as exothermic binding of urea or water. In some processes, the temperature dependence of the pressure-induced unfolding and the urea-induced unfolding of proteins at ambient pressure give negative activation energies. The present mathematical model is solved with successive linearization method (a spectral technique). A comparison of results is made for negative and positive values of activation energy. Apart from it, the quadratic multiple regression model is discussed briefly and explained with bar diagrams. It is observed that with rise in unsteadiness parameter from 0 to 1 (taking positive activation energy), skin friction and Sherwood number are increased by 9.36% and 19% respectively, and Nusselt number is decreased by 26%. However, for negative activation energy, 9.36% and 112% enhancement is observed in skin friction and Sherwood number, respectively.

Quadratic multiple regression and spectral relaxation approach for inclined magnetized Carreau nanofluid

Quadratic multiple regression and spectral relaxation approach for inclined magnetized Carreau nanofluid

Research on optimal multivariate thermal error modeling based on finite-element analysis

To improve the nonlinear fitting ability of multiple linear regression model in thermal error prediction of machine tools, an optimized thermal error modeling method based on test and simulation is proposed in this paper. Firstly, the finite-element analysis is used to complete the thermal-structure coupling analysis of the CNC machine tool. Based on the simulation results of temperature and deformation field of the machine tool, temperature-sensitive points (TSPs) are selected with fuzzy cluster analysis and correlation analysis. According to the simulation results, TSPs of the machine tool are fitted by quadratic polynomial from temperature to deformation. Finally, taking the deformation value of TSPs as the intermediate variable, the multiple linear regression model is established, and the optimized quadratic multiple regression thermal error model is obtained. The results show that the prediction curve of the optimized thermal error model based on on test and simulation is closer to the test curve, and the fitting index is better than that obtained from the traditional model. This method can effectively improve the nonlinear fitting ability of the thermal error model of CNC machine tools. Based on the thermal error model established in this paper, the compensation value of thermal error can be obtained by inputting the real-time measured temperature data of TSPs, which can effectively improve the machining accuracy of CNC machine tools.

Optimization-Design and Atomization-Performance Study of Aerial Dual-Atomization Centrifugal Atomizer

The aerial atomizer is the most essential component of the plant protection UAV (unmanned aerial vehicle). However, the structural optimization of existing aerial atomizers lacks comprehensive consideration of spray parameters and structural parameters, and there is a shortage of available atomizer spray models, resulting in the unstable effect of UAV application. In our previous work, an aerial dual-atomization centrifugal atomizer was developed. In order to obtain an aerial atomizer with good atomization effect and its atomization model, structural optimization at different rotation speeds and flow rates of the atomizer, and its atomization performance, are studied in this paper. Firstly, with the droplet volume median diameter (VMD) and spectral width (SRW) as the evaluation index, through the single-factor, Plackett–Burman and Box–Behnken tests, the influence of rotation speed, flow rate, tooth number and tooth shape were studied. The regression models of the droplet VMD and SRW were established using multiple quadratic regression fitting of the test data. Secondly, in order to achieve the lowest droplet VMD and SRW, the response surface method and post-hoc multiple comparison method were used to obtain the optimized structure of the atomizer’s rotation ring at different rotation speeds (600–7000 r/min) and flow rates (500–1000 mL/min). Lastly, with the effective swath width (ESW) of the optimized atomizer as the evaluation index, through the Box–Behnken test, the influence of rotation speed, flow rate and spray height were studied. The multiple quadratic regression model of ESW was established with the test data. The test results indicated that rotation speed, flow rate and tooth number had a significant effect on droplet VMD and SRW; tooth shape had no significant effect on the droplet VMD and SRW, however, the square tooth shape had the best atomization effect; and rotation speed, flow rate and spray height had a significant effect on ESW. The optimized structural parameters were tooth shape: square, and tooth number: 20. The determination coefficient R2 of the regression model of VMD, SRW and ESW were 0.9976, 0.9770 and 0.9974, respectively, which indicates that the model was accurate, and can evaluate and predict the spray effect. This paper provides an optimized dual-atomization centrifugal atomizer, and its regression models of VMD, SRW and ESW for UAV applications can provide a reference for efficient UAV spraying.

Thermal analysis and entropy generation of Darcy-Forchheimer ternary nanofluid flow: A comparative study

Ternary nanofluid is a novel class of working fluids with excellent heat transfer properties. A combination of three solid nanoparticles consisting of SWCNTs, TiO2, and MoS2 is investigated for Darcy-Forchheimer water-based ternary nanofluids. The related mathematical models are established by considering linear, quadratic and nonlinear thermal radiations. Numerical results and entropy generation analysis reveal the considerable influence of nonlinear thermal radiation on temperature and the reduced Nusselt number of ternary nanofluids. With the help of multiple quadratic regression, the impact of relevant parameters on the reduced Nusselt number is studied in depth. The results show that the temperature and Nusselt number are always the highest in the nonlinear thermal radiation model compared with the linear and quadratic ones, and they are most sensitive to the changes of Rd and δ. The thermal radiation properties of ternary nanofluids may potentially lead to more efficient solar energy conversion. This comparative study illustrates the advantages of ternary nanofluids in improving solar radiation utilization efficiency with nonlinear thermal radiation.

Multiple Quadratic Polynomial Regression Models and Quality Maps for Tensile Mechanical Properties and Quality Indices of Cast Aluminum Alloys according to Artificial Aging Heat Treatment Condition

To evaluate the quality of cast aluminum alloys quantitatively and intuitively, quality index and quality map have been used. Quality index and quality map are to quantitatively evaluate the quality of cast aluminum alloys according to yield strength (YS), ultimate tensile strength (UTS), elongation to fracture (Ef), and strain energy density (W). There are some quality indices such as Q, QR, QC, and Q0. The quality maps are generated to intuitively evaluate the quality level based on the quality indices. These quality indices and quality maps show the quality levels according to the pairs of tensile mechanical properties such as UTS and Ef, or YS and Ef, or YS and W. By using these quality maps, it is impossible to directly evaluate the quality levels according to the artificial aging heat treatment condition. We develop multiple quadratic polynomial regression models and quality maps for tensile mechanical properties and quality indices of the cast aluminum alloys according to artificial aging heat treatment condition. The performances of the regression models are evaluated using the mean absolute errors, mean relative errors, and coefficients of determination. The regression models and quality maps could be widely used to evaluate the quality of the cast aluminum alloys according to the aging heat treatment conditions and determine the rational aging heat treatment condition.

Using quadratic multiple linear regression models to investigate the effect of inoculant type and T6 heat treatment on microstructural, mechanical and corrosion properties of Al-Cu alloy produced by casting

In this study, the effect of different inoculant types such as AlSr10, Al3Ti1B and Al5Ti1B and T6 heat treatment on the microstructure, mechanical properties, and corrosion behavior of Al-5 %Cu alloy were thoroughly investigated. Al-5 % Cu without inoculant, Al-5 %Cu-AlSr10, Al-5 %Cu- Al3Ti1B and Al-5 %Cu- Al5Ti1B alloys were produced by casting, and they were subjected to T6 heat treatment. Microstructures of the alloys were characterized by optical microscopy, SEM with EDX module and XRD. To determine the mechanical properties of the alloys, hardness, tensile and Charpy-V impact tests were applied. Pin on disc and immerse corrosion tests were also carried out to observe grain size effect resulted from different inoculant types on wear and corrosion properties. Sr added Al alloy shows finer grain size than the Al-5 % Cu without inoculant. However, AlSr10 inoculant does not exhibit such good results as compared to Al3Ti1B and Al5Ti1B in terms of grain refinement. When the Al3Ti1B and Al5Ti1B inoculants were compared, 5Ti added one showed finest grains in the structure. In this regard, hardness, tensile strength, and wear resistance were increased systematically with decreasing grain size. Ductility in tensile test and toughness in Charpy-V impact tests of AlSr10 and Al3Ti1B added Al-5 %Cu alloys shows lower value than Al-5 %Cu alloy without inoculant. Corrosion damage increased with decreasing grain size. Further, the statistical performance of these models was tested and the closest model to the measurements was determined. It is expected that the applied quadratic models will be the best option for predicting yield strength, and weight loss in wear and corrosion properties.

Entropy Generation and Regression Analysis of Magnetohydrodynamic Stagnation Point Flow of a Casson Fluid with Radiative and Dissipative Heat Transfer and Hall Effects

The phenomenon of heat transfer is prevalent in industries and has an extensive range of applications. However, mostly the discussion of heat transfer problems is limited to the study of the first law of thermodynamics, which deals with energy conservation. It is just restricted to the quantity of energy, not to its quality; i.e., there is no difference between the work (high-grade energy) and the heat (low-grade energy). A measurement of the degree of randomness of energy in a system is known as entropy. It is unavailable for doing useful work because work takes place only from ordered molecular motion. Even though many boundary layer models exist in the literature to investigate the flow and heat transfer of various fluids along a stretching surface, they have not yet been used at their maximum ability. The main motive of the current research is to discuss entropy generation or its minimization during heat transfer. This work presents an entropy generation analysis for the transient three-dimensional stagnation point flow of a hydromagnetic Casson fluid flowing over a stretching surface in the existence of Hall current, viscous dissipation, and nonlinear radiation. The physical configuration of the present work is described in terms of partial differential equations (PDEs) of nonlinear nature. Furthermore, these PDEs are converted into ordinary differential equations by using some relevant similarity transformations. An efficient numerical method named as the spectral quasilinearization method (SQLM) is used to solve this model. The expression of the Bejan number and volumetric entropy generation rate is also computed. A parametric analysis, including the essential physical parameters, is performed to examine the influences of distinct flow parameters on the velocity profile, temperature profile, Bejan number, entropy generation number, and the coefficients of skin friction and the Nusselt number. In order to further insight into the emerging physical quantities of engineering interest, multiple quadratic regression models are used to estimate the coefficients of skin friction and heat transfer.

Experimentation and optimization of deep hole drilling parameters for SS316L

ABSTRACT There has been a rapidly increasing demand for mechanical deep hole drilling processes to create small diameter holes in automobile fuel injector bodies, landing gear in aerospace vehicles, surgical instruments, etc. In line with these manufacturing requirements, extensive experimental analysis based on L16 orthogonal array has been carried out in this work to investigate the characteristics of deep holes made on stainless steel AISI316 L using the Abrasive Waterjet Machining. The significance of input machining process parameters including Water Pressure, Stand-off Distance, and Abrasive Mass Flow Rate, and their influence on Kerf Angle, and Surface Roughness have been investigated. Further, the multi-parametric Analysis of Variance has been performed to investigate the statistical significance of machining parameters. The quadratic multiple linear regression models have been designed for the Kerf Angle and Surface Roughness by correlating with machining parameters. The Multi-Verse Optimizer (MVO) algorithm has been introduced in this work to define the optimal combination of machining parameters for simultaneous minimization of kerf angle and surface roughness and the result has been compared with Genetic and Ant-Lion Optimization algorithms. The comparison shows that the MVO algorithm outperformed others. Furthermore, a confirmation test has been performed to check the output of MVO algorithm.

Numerical simulation of heat and mass transfers radiative–convective fluid flow on a stretching porous surface with temperature‐dependent thermophysical properties

AbstractThis paper is focused on the analysis of heat and mass transfer radiative–convective fluid flow using quadratic multiple regression and numerical approach. The physical phenomenon is analyzed by utilizing partial differential equations (PDEs). Thermophysical properties, such as viscosity, thermal conductivity, and mass diffusivity, are varied and temperature‐dependent. This study is unique because of its applications in magnetohydrodynamic power accelerators, drilling operators, and bioengineering. The governing PDEs are transformed into coupled nonlinear ordinary differential equations (ODEs). The transformed ODEs are solved numerically using the spectral homotopy analysis method. Also, a quadratic multiple regression analysis is performed on quantities of engineering interest to show the significance of the flow parameters. It is observed that the heat and mass transfer process is affected by nonlinear buoyancy impact. The Lorentz force produced by the imposed magnetic field decline the thickness of the hydrodynamic boundary layer. Findings revealed that the nonlinear convective parameter and variable thermophysical properties are greatly affected by the rate of heat and mass transfer. Previously published work was used to validate the present one, which conformed with it. The slope of linear regression through data points is adopted to show the rate of change in skin friction, Nusselt, and Sherwood numbers during the flow phenomenon.

Quadratic multiple regression model and spectral relaxation approach for carreau nanofluid inclined magnetized dipole along stagnation point geometry

Researchers across the world have tried to explore the impact of non-Newtonian liquid flowing via an extendable surface with the inclusion of various effects due to its industrial and engineering applications like polymer production, paper production, filament extrusion from a dye, etc. This study investigates the behavior of stagnation point flow of Carreau liquid attached with inclined magnetic effect and spectral relaxation approach is utilized here for the numerical outcome. In this study, a few other vital features are attached like the quadratic multiple regression model for Nusselt number evaluation, passive control of nanoparticles, viscus heating thermophoresis, Brownian motion, and mixed convection, etc. Velocity disbursement visibility is analyzed by placing an inclined magnetic field. Physical model generates collection of partial differential equations (PDEs) and these PDEs are moved into ordinary differential equations by a similarity transformations scheme. Further for numerical process, spectral relaxation method is used. Growth in K causes a reduction in velocity because this parameter K creates the impedance to flowing resulting in confines the movement of liquid in restricted the plate. Direct relation is found between Ec and the energy file. In the case of S > 1, physically it is a representation of Joule and viscous dissipations. This article is novel in its sense that the influence of oblique magnetic force and second order velocity slippage on Carreau nano liquid and its numerical computation with help of the spectral relaxation method has never been done before. Furthermore, the quadratic multiple regression model has been employed to find the heat transition rate in the status of the Nusselt number.

Modelling convective transport of hybrid nanofluid in a lid driven square cavity with consideration of Brownian diffusion and thermophoresis

Previously, the homogenous models were predominant in hybrid nanofluid's studies. However, there is a serious deficiency in these models, that is, the heat transfer coefficients obtained by these models are inconsistent with the experimental results. To overcome this issue, we develop a novel hybrid nanofluid model based on the major slip mechanisms of nanofluids caused by Brownian diffusion and thermophoresis. The problem of flow and heat transfer of a hybrid nanofluid in a lid driven square cavity filled with porous medium is studied as an example to show the correctness and validity of this new model. Numerical results are given by means of the novel Coiflet wavelet homotopy analysis method in the terms of the Brownian motion and thermophoresis. The physical behaviors of hybrid nanofluids flow are discussed in terms of various quantities such as the stream-function, the isotherms, and the Nusselt and Sherwood numbers. The average Nusselt number evaluated with the help of the quadratic multiple regression analysis justifies that the thermophoretic effect is more dominant than the Brownian motion on Nusselt numbers at both walls.

Entropy generation analysis on convective radiative stagnation point flow of a Casson nanofluid in a non-Darcy porous medium with induced magnetic field and activation energy: the multiple quadratic regression model

The present article analyzes the entropy generation on the nonlinear thermally radiating magnetohydrodynamic Casson nanofluid flow closer to the stagnation point inside a non-Darcy porous medium with viscous dissipation, magnetic dissipation, mixed convection, and heat generation. The induced magnetic field's impact and the implications of the chemical reaction and the activation energy are also included in the study. A mathematical model based on the substantive problem is developed, consisting of nonlinear partial differential equations and compatible boundary conditions. The mathematical model is converted to a set of nonlinear ordinary differential equations with appropriate boundary conditions using a suitable similarity transformation, which is then solved using the spectral quasi-linearization method. A complete examination is executed for achieving in-depth information of different varying flow parameters' consequences on the flow field and the significant physical quantities using several graphs and tables. Using the regression models on the reduced Nusselt number NuxRex−1/2 and the reduced Sherwood number ShxRex−1/2, the maximum relative errors are shown as 0.15%–0.30% and 0.016024%–0.016225%, respectively. The present results signify that the larger velocity ratio parameter boosts the velocity along the x-axis and the transverse velocity for M = 3, but the transverse velocity for M = 1, temperature, and induced magnetic field follow a reverse pattern.

The Effects of Price Dispersion on Sales in the Automobile Industry: A Dynamic Panel Analysis

Price dispersion is an important indicator of pricing strategy and market efficiency. However, the relationship between price dispersion and sales has not been explored, especially for durable goods such as automobiles. In this study, we use a unique data set from Autohome comprising the actual transaction prices of buyers to assess the extent of price dispersion in the new automobile market. Based on an empirical analysis of over 222,592 price observations for 59 vehicle models collected over a period of 48 months, we find that the percentage difference ( PD) and coefficient of variation ( CV) of new automobile transaction prices are 43.4% and 9.9%, respectively. In addition, the empirical results show that the price dispersions lower for non-sedan type, Chinese car brands, and produced by state-owned companies. We further investigate whether the increase in the price dispersion of a new automobile has a positive impact on automobile sales using a multiple quadratic regression model. The findings show that price dispersion has positively impact of sales. More interestingly, negative quadratic effects are observed, indicating a concave-down-increasing relationship between price dispersion and sales. This implies that an extreme price dispersion is less helpful than a moderate price dispersion. These findings advance knowledge of consumer buying behavior and seller pricing strategies, with important theoretical contributions and practical implications for automobile companies.

Multi-objective optimization of disc brake structure based on heat transfer performance

As an important basis for its structural optimization design, the heat transfer performance has a key influence on the reliability of automobile brake. Based on the finite element method, the transient heat transfer of automobile disc brake is analyzed under the condition of dynamic convection heat transfer coefficient. According to the simulation results, the CCD (Central Composite Design) sampling scheme is used to transform the optimization variable and target variable into multiple design points in the decision space. The optimization variable includes the total thickness, the height of the ventilation slot, the angle between the sides of the ribs, the number of ribs while the target variable includes the mass and temperature peak. According to the multiple quadratic regression model, the response surface function is constructed, and the approximate model of optimization analysis is obtained. The error analysis shows that the response surface function is equipped with good fitting accuracy. In order to facilitate the extremum search, the optimization of the quality is transformed into the constraint condition, and the multi-objective optimization problem of the brake disc is transformed into the single objective optimization problem. Through the sequential quadratic programming method, the Pareto optimal solution set of the optimal mathematical model is found. The results show that the temperature peak value is reduced by 7.8 % under the condition where the quality of the ventilation plate is basically unchanged. By weighting the Pareto optimal solution sets of different quality intervals, a good result evaluation of ventilation panel optimization is achieved.