Numerical Exploration via Least Squares Estimation on Three Dimensional MHD Yield Exhibiting Nanofluid Model with Porous Stretching Boundaries

The numerical study of a three-dimensional magneto-hydrodynamic (MHD) Casson nano-fluid with porous and stretchy boundaries is the focus of this paper. Radiation impacts are also supposed. A feasible similarity variable may convert a verbalized set of nonlinear “partial” differential equations (PDEs) into a system of nonlinear “ordinary” differential equations (ODEs). To investigate the solutions of the resulting dimensionless model, the least-square method is suggested and extended. Maple code is created for the expanded technique of determining model behaviour. Several simulations were run, and graphs were used to provide a thorough explanation of the important parameters on velocities, skin friction, local Nusselt number, and temperature. The comparison study attests that the suggested method is well-matched, trustworthy, and accurate for investigating the governing model’s answers. This method may be expanded to solve additional physical issues with complicated geometry.

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THREE-DIMENSIONAL STAGNATION-POINT FLOW OVER A PERMEABLE STRETCHING/SHRINKING SHEET WITH A SECOND ORDER SLIP FLOW

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.10.9.16 ◽

2021 ◽

Vol 10 (9) ◽

pp. 3273-3282

Author(s):

M.E.H. Hafidzuddin ◽

R. Nazar ◽

N.M. Arifin ◽

I. Pop

Keyword(s):

Differential Equations ◽

Stagnation Point ◽

Flow Model ◽

Nonlinear Partial Differential Equations ◽

Slip Flow ◽

Three Dimensional ◽

Flow Characteristics ◽

Second Order ◽

Stagnation Point Flow ◽

Shrinking Sheet

The problem of steady laminar three-dimensional stagnation-point flow on a permeable stretching/shrinking sheet with second order slip flow model is studied numerically. Similarity transformation has been used to reduce the governing system of nonlinear partial differential equations into the system of ordinary (similarity) differential equations. The transformed equations are then solved numerically using the \texttt{bvp4c} function in MATLAB. Multiple solutions are found for a certain range of the governing parameters. The effects of the governing parameters on the skin friction coefficients and the velocity profiles are presented and discussed. It is found that the second order slip flow model is necessary to predict the flow characteristics accurately.

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Heat transfer of three-dimensional micropolar fluid on a Riga plate

Canadian Journal of Physics ◽

10.1139/cjp-2018-0973 ◽

2020 ◽

Vol 98 (1) ◽

pp. 32-38 ◽

Cited By ~ 10

Author(s):

S. Nadeem ◽

M.Y. Malik ◽

Nadeem Abbas

Keyword(s):

Heat Transfer ◽

Heat Flux ◽

Differential Equations ◽

Surface Temperature ◽

Ordinary Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Three Dimensional ◽

Nonlinear Ordinary Differential Equations ◽

Exponential Order ◽

Riga Plate

In this article, we deal with prescribed exponential surface temperature and prescribed exponential heat flux due to micropolar fluids flow on a Riga plate. The flow is induced through an exponentially stretching surface within the time-dependent thermal conductivity. Analysis is performed inside the heat transfer. In our study, two cases are discussed here, namely prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux (PEHF). The governing systems of the nonlinear partial differential equations are converted into nonlinear ordinary differential equations using appropriate similarity transformations and boundary layer approach. The reduced systems of nonlinear ordinary differential equations are solved numerically with the help of bvp4c. The significant results are shown in tables and graphs. The variation due to modified Hartman number M is observed in θ (PEST) and [Formula: see text] (PEHF). θ and [Formula: see text] are also reduced for higher values of the radiation parameter Tr. Obtained results are compared with results from the literature.

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Numerical Study of the Influence of Nano-fluid Type on Thermal Improvement in a Three Dimensional Mini Channel

10.2174/9789814998185121010009 ◽

2021 ◽

pp. 87-100

Keyword(s):

Numerical Study ◽

Three Dimensional ◽

Fluid Type ◽

Nano Fluid ◽

Thermal Improvement

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Intelligent Identification and Locating System of Steel Coil Based on Laser Technology

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.496-500.1308 ◽

2014 ◽

Vol 496-500 ◽

pp. 1308-1312

Author(s):

Yu Chi Wang ◽

Si Yue Zhou ◽

Zheng Peng Yuan

Keyword(s):

3D Model ◽

Three Dimensional ◽

Least Square Method ◽

Least Square ◽

Circle Fitting ◽

Three Dimensional Model ◽

Laser Technology ◽

Steel Coil ◽

Main Emphasis ◽

Locating System

In this paper, a solution based on laser technology is proposed for steel coil handling. The main emphasis is placed on the problem of steel coil identification and locating. In this paper, we first use laser data to construct three dimensional model of the worksite. And then we slice up the 3D model repeatedly to get the section images and make them to fusion. In order to wipe off the disturb of line, a line detection method based on probabilistic hough transform is proposed. Finally an improved least square method used in circle fitting is discussed.

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Railroad track modeling based on the results of mobile laser scanning

Proceedings of Petersburg Transport University ◽

10.20295/1815-588x-2018-3-408-413 ◽

2018 ◽

pp. 408-413

Author(s):

Elena Lenchenkova

Keyword(s):

Mathematical Model ◽

Laser Scanning ◽

Dimensional Space ◽

Practical Importance ◽

Three Dimensional ◽

Least Square Method ◽

Least Square ◽

Railroad Track ◽

Railway Line ◽

Type Data

Objective: To develop a mathematical model of the railroad track based on the initial progressive-type data (laser scanning) in railroad design. Methods: Regression analysis (least-square method), as well as coordinate methods of calculating point position in space were applied. Results: The mathematical model, which could describe the position of the railroad track in three-dimensional space by means of mathematical relations, was obtained. Applicability of approximating models was established. The models make it possible to provide smoothing of laser survey data. Regularization and globalization algorithms of initial data were developed. Practical importance: The introduced model is universal when describing the position of the track at all stages of life cycle of the railway line. It is reasonable to apply the presented model in design engineering in order to balance survey errors, maintain the track in coordinates, as well as to calculate design and proﬁle parameters.

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Research of Binocular Positioning Mathematical Model Based on the Least Square Method

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.50-51.473 ◽

2011 ◽

Vol 50-51 ◽

pp. 473-477 ◽

Cited By ~ 2

Author(s):

Chun Feng Liu ◽

Xiao Li Meng ◽

Huan Cheng Zhang

Keyword(s):

Relative Position ◽

Three Dimensional ◽

Digital Camera ◽

Least Square Method ◽

Absolute Error ◽

Least Square ◽

Specific Data ◽

Centroid Algorithm ◽

Three Dimensional Coordinate ◽

The Relationship

By giving a centroid algorithm to extract pixel coordinates of each circle in the center of a circle under the coordinates, through the coordinate transformation the image coordinates can be obtained. Based on the data obtained from above to verify the model, from the specific data of the relative error, absolute error and error propagation theory to discuss the algorithm accuracy and stability. Finally using the least square method, according to the mean square error criteria for the establishment of a minimum of three-dimensional coordinate system fixed relative position of two cameras, binocular positioning mathematical models and by discussing the nature of matrix and the relationship between the relative position of the camera to calibrate the binocular digital camera.

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Least Square Inversed Analysis of Soil Parameter for Foundation with Two-Order Gradient Theoretic Method

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.243-249.2294 ◽

2011 ◽

Vol 243-249 ◽

pp. 2294-2299 ◽

Cited By ~ 1

Author(s):

Yao Feng Xie

Keyword(s):

Differential Equations ◽

Error Function ◽

Least Square Method ◽

Least Square ◽

Gradient Theory ◽

Mechanical Theory ◽

Soil Parameter ◽

True Value ◽

Initial Soil ◽

Calculation Results

Combined with two-order gradient theory, the least square inversed analysis of the soil parameter for the foundation is studied and put forward in detail. After the mechanical theory for the plate on the foundation is introduced, the controlling differential equations of the plate on the foundation which is subjected to vertical loads are deduced. Through utilizing Fourier transformative theory, the corresponding solutions to the plate on the foundation are gained. Linear algebra controlling equations for the plate are achieved which leads to solve the original differential equations more easily. The least square error function for the soil parameter on the plate is established and applied with the two-order gradient method. The inversed steps on the least square error function for the soil parameter are listed. The calculation results verify the conclusions that the soil parameter of the foundation can be efficiently inversed by applying the least square theory. When different initial soil parameter is set, the iterative computations can be convergent to the true value of the soil parameter. And this least square method can also be applied for the problem of inversed analysis of parameters for other foundation models.

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3D Localization Algorithm Based on Linear Regression and Least Squares in NLOS Environments

Computer and Information Science ◽

10.5539/cis.v11n4p1 ◽

2018 ◽

Vol 11 (4) ◽

pp. 1

Author(s):

Jiang Li ◽

Zhang Lei

Keyword(s):

Linear Regression ◽

Three Dimensional ◽

Least Square Method ◽

Mobile Terminal ◽

Base Station ◽

Least Square ◽

Time Of Arrival ◽

Localization Algorithm ◽

Positional Accuracy ◽

The Relationship

Based on the positive bias property of the time of arrival(TOA) measurement error caused by the non-line-of-sight(NLOS) propagation, a simple and effective three dimensional(3D) geometrical localization algorithm was proposed, the algorithm needs no prior knowledge of time delay distribution of TOA, and only linear regression was used to estimate the parameters of the relationship between the NLOS distance error and the true distance, thus, the approximate real distance between mobile terminal (MT) and base station (BS) was reduced, then, the 3D geometric localization of mobile terminal was carried out by the least square method. The experimental results shows the effectiveness of the algorithm, and the positional accuracy is far higher than the required accuracy by E-911 in NLOS environments.

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Stability analysis of heat transfer in nanomaterial flow of boundary layer towards a shrinking surface: Hybrid nanofluid versus nanofluid

10.3762/bxiv.2021.88.v1 ◽

2021 ◽

Author(s):

Aqeel ur Rehman ◽

Zaheer Abbas

Keyword(s):

Heat Transfer ◽

Stability Analysis ◽

Differential Equations ◽

Stable Solution ◽

Mhd Flow ◽

Least Square Method ◽

Dual Solutions ◽

Least Square ◽

Shrinking Sheet ◽

Hybrid Nanofluid

Many boundary value problems (BVPs) have dual solutions in some cases containing one stable solution (upper branch) while other unstable (lower branch). In this paper, MHD flow and heat transfer past a shrinking sheet is studied for three distinct fluids: kerosene hybrid nanofluid, kerosene nanofluid, and kerosene nanofluid. The partial differential equations (PDEs) are turned into ordinary differential equations (ODEs) using an appropriate transformation and then dual solutions are obtained analytically by employing the Least Square method (LSM). Moreover, stability analysis is implemented on the time-dependent case by calculating the least eigenvalues using Matlab routine bvp4c. It is noticed that negative eigenvalue is related to unstable solution i.e., it provides initial progress of disturbance and positive eigenvalue is related to stable solution i.e., the disturbance in solution decline initially. The impacts of various parameters, skin friction coefficient, and local Nusselt number for dual solutions are presented graphically. It is also noted that the results obtained for hybrid nanofluids are better than ordinary nanofluids.

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