In this study, micropolar fluid flow in a channel subject to a chemical reaction is investigated analytically using least square method (LSM) and numerically. Some efforts are done to show ...reliability and performance of the present method compared with the numerical method (Runge–Kutta fourth-order) to solve this problem. The results reveal that the LSM can achieve suitable results in predicting the solution of these problems. Also, the effect of consequential parameters such as Reynolds number (Re), micro rotation and Peclet number on the stream function, velocity and temperature distribution is discussed. The results show that the stream function decreases with increase of Reynolds number and velocity boundary layer thickness decreases as Re increases. With increase of Peclet number (Pe) the oscillation of temperature fluid and concentration profile increases. Furthermore, the effect of the Reynolds and Peclet numbers on Nusselt and Sherwood numbers is completely investigated from the physical view point in the present study.
•The stream function decreases with increase of Reynolds number and velocity boundary layer thickness decreases as Re increases.•With increase of Peclet number (Pe) the oscillation of temperature fluid and concentration profile increases.•Also Increase in Reynolds number leads to increase in Nusselt number but the value of Nusselt number decrease with increase of Peclet number.
•LSM is an accurate technique for simulating heat transfer in circular porous fins.•Rectangular, convex, triangular and exponential variable sections are considered.•Radiation and convection from ...porous fin are considered.•Effects of material and geometry on heat transfer from fins are studied.
In this study, heat transfer and temperature distribution equations for circular convective–radiative porous fins are presented. It’s assumed that the thickness of circular fins varies with radius so four different shapes, rectangular, convex, triangular and exponential, are considered. The heat transfer through porous media is simulated using passage velocity from the Darcy’s model. After deriving equation for each geometry, Least Square Method (LSM) and fourth order Runge–Kutta method (NUM) are applied for predicting the temperature distribution in the porous fins. The selected porous fin’s materials are Al, SiC, Cu and Si3N4. Results reveal that LSM has very effective and accurate in comparison with the numerical results. As a main outcome, Si3N4-exponential section fin has the maximum amount of transferred heat among other fins.
•Flow model is presented for Cu-Al2O3/Water hybrid nanofluid and ethylene–glycol based Cu-nanoparticles.•Mathematical modeling is constructed for time-dependent thermal conductivity on rotating ...flow.•Least square Galerkin method (LSGM) is adopted to determine the solution of complex nature model.•Solutions are obtained for skin friction and Nusselt number for each kind of nanoparticles mixture.
This paper scrutinizes the significant effects of nonlinear thermal radiation and time-dependent thermal conductivity due to rotating flow of Cu-Al2O3-water hybrid nanofluid over a three-dimension stretching sheet. The influence of bouncy forces and magnetic field are also considered. The obtained set of partial differential equations (PDEs) converted to a simplified set of ordinary differential equations (ODEs) by introducing the feasible similarity transformation. Least square method (LSM) is adopted to examine the solution of developed model. The obtained solutions are compared with the well-known numerical technique: Runge-Kutta method of order fourth (RK-4). Significant influence of various physical parameters on the velocities and temperature are explained in detailed through graphical representations. Behavior of skin friction coefficient and local Nusselt number due the variation of numerous parameters also discussed in detail. The velocity profiles F′(η) and G′(η) for the case of Cu-Al2O3-water are dominant as compare to Cu-water and Al2O3-water while the fluid temperature is dropped for Cu-Al2O3-water case as compare to Cu-water and Al2O3-water. It is noticed that, variation in the Hartmann, porosity and suction/injection parameters cause to increase the friction at the surface. Opposite behavior of skin friction coefficient is observed by increasing the strength of rotational, Grashof number and slip parameter. Obtained results and comparative study witnesses that the least square technique is well-matched with existing results and it can be applied for complex nature models.
•We proposed three types of urbanization modes for impact analyses.•Economic growth is the major determinant of changes in cultivated land.•In future, urbanization of cities will exert more impacts ...on cultivated land.
This article aims to evaluate the impact of urbanization and different urbanization modes on cultivated land changes using an econometric model that incorporates socio-economic and policy factors in the eastern China, which experience the great urbanization in recent years. Based on land-use remote sensing data interpreted from Landsat Thematic Mapper/Enhanced Thematic Mapper digital images of Chinese Academy of Sciences and a unique set of socio-economic data, an econometric model is developed to empirically estimate the impacts on cultivated land changes. Although urbanization has an effect on the changes of cultivated land, its effect is marginal. Moreover, the expansion of built-up areas in different urbanization modes causes varying impacts on changes in cultivated land use in different regions. Assuming that other factors remain constant, compared with the expansion of villages or the development of small towns, in the periods of 1995–2000, the urbanization in the more developed eastern region alleviates the loss of cultivated land by 7%, while during 2000–2008 the rapid urbanization lead to the cultivated land loss increase by 29.2%. The policies designed to protect cultivated land by encouraging people move to small towns may actually accelerate the occupation of cultivated land.
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•Development and validation of chemometric assisted UV–Visible spectrophotometric methods for simultaneous estimation of antiretroviral drug.•The proposed methods are statistically ...compared with reported UPLC method.•These methods are simple, accurate, precise and less expensive, and can be applied for the routine quality control analysis of selected drugs and their combined tablet dosage form.
Darunavir ethanolate (DRV) and Cobicistat (CBS) is a combination of antiretroviral drugs used for the treatment of human immunodeficiency virus (HIV) infections. Two Chemo-metric assisted UV-spectrophotometric methods were developed for simultaneous estimation of DRV and CBS in tablet dosage form, namely; partial least square (PLS) and Classical least square method (CLS). The proposed methods were successfully applied for simultaneous determination of DRV and CBS in a laboratory mixture and their tablet formulation to achieve maximum sensitivity and lowest error. The applied methods were validated as per ICH guidelines and found to be linear in the concentration range of 5-30μg/mL for DRV and 5-30μg/mL for CBS. The developed methods were statistically comared with reported UPLC method where no significant difference was found relating to both accuracy and precision. Thus, the proposed methods can be effectively utilized for the routine quality control assessment of these drugs in commercial tablet dosage form.
•An overview of parameter estimation process of Proton Exchange Membrane of Fuel Cell (PEMFC).•Review of various conventional and recent methods and optimization techniques adopted for parameter ...estimation of PEMFC.•Values of parameters extracted by all these methods used by the researchers in the literature.•A comparison of all the optimization techniques used based on computational time, complexity, convergence speed, number of iterations, and computational performance.
Proton Exchange Membrane Fuel Cell (PEMFC) is one of the rising clean form of energy. Due to various advantages of PEMFCs, they have widespread applications. The structure of Fuel Cell systems is multivariate and non-linear. Thus it becomes necessary to model the system properly for simulation, design and analysis purpose. The mathematical model developed on the basis of empirical equations are used for designing purpose of PEMFC. The voltage obtained at the output of fuel cell depends on losses occurring in the system namely activation loss, concentration loss, and ohmic loss. These losses depend on certain parametric coefficients. Thus, these parametric coefficients are optimized to minimize the losses and to improve the output of PEMFC. Researchers have used various optimization methods to estimate and optimize parametric coefficients that affect the steady state and dynamic behaviour of different fuel cell models as these values are not provided in the manufacturer’s datasheet. This paper presents an inclusive review of various technique used for parameter estimation of PEMFC model such as Least Square method, Artificial Neural Networks, metaheuristic techniques and bio-inspired methods. A brief overview of the methods used, novelty introduced to the methods to solve the objective function and get exact V-I curve along with the validation technique has been presented. This article will be a state of the art for researchers in this field to come up with new techniques or modified version of the techniques for optimizing the coefficients by comparing them with the methods already used in literature. This review will help engineers and researchers to visualise more advancements that could be done in the field of fuel cell system to make it most promising and reliable clean energy system.
In this paper, a novel physics-informed neural networks (PINNs) called deep reduced-order least-square (ROLS) is proposed. The deep ROLS is a combination of reduced-order and least-square methods in ...the context of PINN methodology. The key idea of the deep ROLS is to convert a higher-order PDE to a system of lower-order PDEs by using primary and secondary variables, then the loss function constituted by integrals of corresponding squared residuals over the problem domain is minimized. Specifically, the squared residuals are established based on L2 norm of respective reduced-order PDE terms, and the Gauss–Legendre quadrature rule is applied to approximate their integrals. A multi-network structure is also designed, in which each sub-network serves as one field variable corresponding to each reduced-order PDE. Moreover, this work proposes a scheme to handle both essential and natural boundary conditions (BCs) directly. The deep ROLS demonstrates its better advantages in comparison to original PINN method in terms of solution accuracy, computational cost and data efficiency for several beam bending problems having continuous and discontinuous solutions.
•Proposes a novel framework of PINN for high-order PDEs.•The deep reduced order least square for non-differentiable problems.•Imposes all boundary conditions inside neural networks.•Approximate multi-variables simultaneously.
Analytical Hierarchical Process (AHP) along with fuzzy set theory has been used extensively in the Multi-Criteria Decision Making (MCDM) process in which fuzzy numbers are utilized to represent human ...judgments more realistically. Over the past couple of decades, numerous articles have been published proposing algorithms through which priority vector (or weight vector) can be calculated from fuzzy comparison matrices. The aim of this study is to conduct a comprehensive performance analysis of the most popular algorithms proposed in this domain in terms of accuracy of weights calculated from fuzzy comparison matrices. Such an analysis is much needed by the researchers and practitioners. However none is available. An experimental analysis is conducted and the performance of various algorithms are evaluated with varying three parameters i.e., the size of the comparison matrix, the level of fuzziness and the level of inconsistency. We found that modified Logarithmic Least Squares Method and Fuzzy Inverse of Column Sum Method (FICSM) generally outperformed other algorithms, while Fuzzy Extent Analysis (FEA) which is the most frequently used algorithm in the literature provides the least accurate results. Furthermore, it was observed that a modified version of FEA method significantly improved its performance.
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•Two-dimensional peristaltic nanofluid flow in an asymmetric channel is modeled.•Both upper and lower channel walls are considered in a wavy shape.•Least Square Method (LSM) is ...introduced as efficient analytical method for solution.•The effect of some parameters are discussed on results.
In this study, asymmetric peristaltic nanofluid flow in a two dimensional wavy channel is modeled and the heat transfer analysis is performed for it. Both upper and lower channel walls are considered in constant temperature and wavy shape. The governing equations were solved for five type’s nanofluids and least square method (LSM) analytical method using the Maple 15.0 mathematical software is applied as the efficient solution method for solving the governing equation. The effect of some parameters existed in the equations (Brinkman number, thermal and velocity slip parameters, Grashoff number and etc.), are discussed on the velocities and temperature functions. As an important outcome, reverse flow and maximum velocity were observed in channel throat and maximum temperature area occurred near the lower wall due to its higher temperature in boundary condition. Also, Brinkman number, thermal slip parameter and Grashoff number increments enhanced the temperatures values in channel.
