Modelling using dimensional analysis and optimization with grey-taguchi based fuzzy approach in s-eddg of skd-11 steel

The SKD-11 steel was machined by the hybrid surface-electro discharge diamond grinding (S-EDDG) machining process with an aim to determine the optimum setting of process parameters for multi-output optimization and thereafter developed the mathematical-models of material-removal-rate (MRR), and surface-roughness (Ra) through the Dimensional Analysis method. In this research work, Grey-Taguchi based Fuzzy method is utilized for multi-output optimization of process parameters. The various process-variables selected in this research work are current, voltage, wheel speed, pulse-on-time, duty-cycle, and nozzle flushing aid. Total 18 experiments have been conducted on S-EDDG set-up according to Taguchi’s L18 orthogonal array. The response table and Analysis of Variance investigation are used to determine the optimum setting of process control-parameters and further help to determine the impact of these control-factors on the multi-output performance index (MPI). In this research work, the Dimensional Analysis method is utilized for the development of mathematical models of MRR, and Ra. The experimental results and predicted estimation of values from the developed models were compared and showed satisfactory matching between them. The optimum combination of process variables suggested by the hybrid optimization method was validated through confirmation experiment whose result depicts that aimed MPI is significantly improved by 0.435. The suggested optimum setting of process variables helps the production engineer to set-up the economical-cum-efficient process.

A Novel Approach of Unit Conversion in the Lattice Boltzmann Method

The lattice Boltzmann method (LBM) is an alternative method to the conventional computational fluid dynamic (CFD) methods. It gained popularity due to its simplicity in coding and dealing with a complex fluid flow such as the multiphase flow. The method is based on the kinetic theory, which is mesoscopic scale. Hence, applying the LBM method for macroscopic problems requires a proper conversion from the physical scale (conventional units) to the mesoscopic scale (lattice units) and vice versa. The Buckingham π theorem and the principle of corresponding states are the popular methods used for data reductions and unit conversion processes in the LBM. Nevertheless, those methods have some issues, such as difficulty in converting specific quantities, such as thermo-physical properties. The current work uses a novel dimensional analysis method systematically for mapping properties’ units between scales. Moreover, the approach has the flexibility in selecting parameters to ensure the stability of the method of solution. Several benchmark examples are used to evaluate the feasibility and accuracy of the proposed approach. In conclusion, the proposed approach showed the flexibility of the mapping between meso-scale to macro-scales and vice versa on solid bases rather than ad-hoc methods.

ANALYSIS OF MATHEMATICS PROBLEMS IN THE 2013 CURRICULUM AND CAMBRIDGE CURRICULUM MATHEMATICS TEXTBOOKS

Several factors influence the success of learning; one of them is the quality of textbooks. Textbooks have a pivotal role in learning, namely, representing the teacher's explanation in front of the class. Curricula have continuously changed because they are far from the expectations. In Indonesia, many schools have implemented an international curriculum to improve school quality. One of the curricula used is the Cambridge curriculum. This study analyzed the types of problems in the Cambridge and 2013 curriculum mathematics textbooks, especially on quadratic equations. This research utilized a six-dimensional analysis method which consists of mathematical activities, complexity level, answer form, contextual features, response types, and mathematical features. Furthermore, the data collection technique was carried out by analyzing and describing the types of questions in the 2013 curriculum and the Cambridge curriculum mathematics textbooks. The analysis focused on the quadratic equation topic in the 2013 curriculum and the Cambridge curriculum mathematics textbooks. The results shows that there is no difference between the types of problems in the 2013 curriculum and the Cambridge curriculum mathematics textbooks for quadratic equation topics. The framework of this study could be a reference for further research and used by mathematics textbook writers to create more diverse types of questions.

Mathematical Formulae That Validate The Germ Terrain Duality Theory; The Comparative Size of The Immanent Cellular Dust [Microzymas]

Drug dosages, whether calculated via the ratio (rainbow), proportion, formulae or dimensional analysis method are determined by various factors. These factors include the weight of the patient and the route of administration. Both weight and route of drug administration are terrainrelated parameters.

Mathematical Formulae That Validate the Germ Terrain Duality Theory; The Comparative Size of the Immanent Cellular Dust [Microzymas]

Drug dosages, whether calculated via the ratio (rainbow), proportion, formulae or dimensional analysis method are determined by various factors. These factors include the weight of the patient and the route of administration. Both weight and route of drug administration are terrain related parameters.

Question analysis of mathematics textbook for 2013 curriculum and IB curriculum on quadratic equations

The goal of this study is to compare the types of questions between the 2013 Curriculum Mathematics textbooks and the IB Curriculum on quadratic equations. The approach used in this research is a six-dimensional analysis method consisting of: mathematical activity, the difficulty level of the questions, the types of answers expected, the contextual situation, the types of responses, and the stages of the mathematical questions. The data collection technique is conducted by evaluating and explaining the types of questions. The types of questions were obtained from the 2013 Curriculum Mathematics textbook and the IB Curriculum based on a six-dimensional analysis, namely: mathematical activity, question complexity, type of answer, contextual situation, type of response, and mathematical questions. Based on the type, the results of this study show that the questions in the 2013 curriculum mathematics textbooks are more varied than the questions in the IB curriculum mathematics textbooks on the subject of quadratic equations. However, based on the number, there are more questions in the IB curriculum mathematics textbook than the questions in the 2013 curriculum mathematics textbook.

Modeling of the Minimum Fluidization Velocity and the Incipient Fluidization Pressure Drop in a Conical Fluidized Bed with Negative Pressure

The modeling of the minimum fluidization velocity (U0mf) and the incipient fluidization pressure drop (ΔPmf) is a valuable research topic in the fluidization field. In this paper, first, a series of experiments are carried out by changing the particle size and material mass to explore their effects on U0mf and ΔPmf. Then, an Ergun equation modifying method and the dimensional analysis method are used to obtain the modeling correlations of U0mf and ΔPmf by fitting the experimental data, and the advantages and disadvantages of the two methods are discussed. The experimental results show that U0mf increases significantly with increasing particle size but has little relationship with the material mass; ΔPmf increases significantly with increasing material mass but has little relationship with the particle size. Experiments with small particles show a significant increase at large superficial gas velocity; we propose a conjecture that the particles’ collision with the fluidization chamber’s top surface causes this phenomenon. The fitting accuracy of the modified Ergun equation is lower than that of the dimensionless model. When using the Ergun equation modifying method, it is deduced that the gas drag force is approximately 0.8995 times the material total weight at the incipient fluidized state.