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Natural convection
Published in S. Mostafa Ghiaasiaan, Convective Heat and Mass Transfer, 2018
The main objectives of nondimensionalization are to reduce the number of parameters in the mathematical problem, derive relevant dimensionless numbers, perform order-of-magnitude comparisons among various terms, and figure out some important functional dependencies.
Multiple Objective Decision-Making Methods in Supplier Selection
Published in Sachin K. Mangla, Sunil Luthra, Suresh Kumar Jakhar, Anil Kumar, Nripendra P. Rana, Sustainable Procurement in Supply Chain Operations, 2019
Global Criterion Method is located in the classification of MODM methods where preference information is not used, and it reaches the solution without requiring any information from the decision maker. The preliminary studies on Global Criterion Method were initiated by Yu (1973) and Zeleny (1973). The most important feature of this method is that it is a scaler function that transforms more than one objective function mathematically into one single objective function (Marler and Arora 2004). The vector that minimizes at most one collective criterion, which is composed of multiple criteria based on a specific rule, is the optimal vector. In other words, it transforms k number of objective functions into one single objective problem (Tabucannon 1988). Each objective function in the global function is stated as a ratio. Nondimensionalization is important as objective functions have different dimensions (units). The best solution for the problem varies on the selected p-value. While these deviations are weighted proportionally to the largest deviation with the greatest weight based on p = 2 proposed by Salukvadze (1974), the same significance is given to all deviations based on p = 1 proposed by Boychuk and Ovchinnikov (1973). In case of p > 2, the weight of deviations will be greater. As the normalization is carried out based on the positive ideal solutions of objectives, the global objective value will be within the range of [0;1]. Global Criteria Method is provided mathematically below. () Min∑i=1i(fi(x*)−fi(x)fi(x*))pSubjecttoAx≤bx≥0.
Artificial neural network-based multiple-input multiple-output metamodel for prediction of design parameters for a high-speed rail viaduct
Published in Structure and Infrastructure Engineering, 2023
Susmita Panda, Arnab Banerjee, Ajinkya Baxy, Bappaditya Manna, Sondipon Adhikari
This article proposes a semi-analytical methodological framework for efficient prediction of bridge responses, including displacement, shear force, and bending moment, using analytical modelling. Further, to bypass the extensive computation, an ANN-based MIMO metamodel is developed in this article. Based on the developed mathematical formulation for moving load over the bridge, non-dimensional input and output parameters are derived to produce data for the training of neural networks. The concept of non-dimensionalization optimises the entire computation process and increases efficiency. The robustness of the proposed metamodel is verified with the actual analytical model. Moreover, the prediction ability of the present framework is investigated by developing a user interface to allow researchers and engineers to design simply-supported bridges with various ranges of parameters. A user-friendly platform for comparing the resulting response with the codal provision has also been made within the interface.
Time and length scales in governing equations and boundary conditions for on-chip electrophoretic sample separation
Published in Numerical Heat Transfer, Part A: Applications, 2019
Pegah Pezeshkpour, Gerry Schneider, Carolyn Ren
The geometric boundaries as well as the equations and boundary conditions for the electric potential, fluid flow, and concentration fields are presented in detail. The advantage of the nondimensionalization approach is to identify all governing parameters for the problem without making preliminary or arbitrary choices.
Nonsimilar forced convection simulations of water-copper nanofluid flow through a porous medium in the presence of thermal radiations, heat generation and viscous dissipation
Published in Waves in Random and Complex Media, 2022
Wenhao Cheng, Musawara Safeer, Umer Farooq, Shahzad Munir, Jifeng Cui, Chakravarthula S K Raju
In this article, Khanafer nanoliquid model by incorporating the impacts of thermal radiations, heat generation and viscous dissipation on MHD flow instigated by a non-linear stretching sheet is studied. The given nonsimilar system is approximated through LNS approximations. Using LNS approximations, the dimensionless system is analytically approximated through ODEs. The main advantage of nondimensionalization is the particular dilution in the number of parameters. The given problem entails 9 parameters but after the nondimensionalization, they are reduced to only 6 parameters. The effects of governing parameter such as n, M, K, ϕ, Ec, R, Q, Pr and ξ on velocity and temperature distributions are explred. In Table 1, it is depicted that the thermophysical characteristics of and (Cu). Table 2 presents the authenticity of the present results in limiting case by comparing it with Hady et al. [52] and Ahmed et al. [48]. Table 3 shows that the range of dimensionless parameters for stable or convergent solutions. The obtained range of dimensionless parameters is as follows, , , , , , , , and . The comparison of local similar and nonsimilar simulations for and Nu are shown in Tables 4 and 5. The percentage difference of important transport quantities between local similar and non-similar solutions illustrates the effectualness of nonsimilar modeling.