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It is known that the iterative roots of continuous functions are not necessarily unique, if it exist. In this note, by introducing the set of points of coincidence, we study the iterative roots of order preserving homeomorphisms. In particular, we prove a characterization of identical iterative roots of an order preserving homeomorphism using the points of coincidence of functions.

The purpose of this paper is to discuss published research in rotorcraft which has taken place in India during the last ten years. The helicopter research is divided into the following parts: health monitoring, smart rotor, design optimization, control, helicopter rotor dynamics, active control of structural response (ACSR) and helicopter design and development. Aspects of health monitoring and smart rotor are discussed in detail. Further work needed and areas for international collaboration are pointed out.

The archival journal papers on helicopter engineering published from India are obtained from databases and are studied and discussed. The contribution of the basic research to the state‐of‐the‐art in helicopter engineering science is brought out.

It is found that strong research capabilities have developed in rotor system health and usage monitoring, rotor blade design optimization, ACSR, composite rotor blades and smart rotor development. Furthermore, rotorcraft modeling and analysis aspects are highly developed with considerable manpower available and being generated in these areas.

Two helicopter projects leading to the “advanced light helicopter” and “light combat helicopter” have been completed by Hindustan Aeronautics Ltd These helicopter programs have benefited from the basic research and also provide platforms for further basic research and deeper industry academic collaborations. The development of well‐trained helicopter engineers is also attractive for international helicopter design and manufacturing companies. The basic research done needs to be further developed for practical and commercial applications.

This is the first comprehensive research on rotorcraft research in India, an important emerging market, manufacturing and sourcing destination for the industry.

Nanofluid exhibits higher density, higher viscosity, higher thermal conductivity and reduced specific heat capacity along with improved heat transfer characteristics. It is comparatively better than conventional fluids in terms of thermo-physical properties. This paper aims to investigate experimentally the overall performance of the shell and tube heat exchanger operated under two different configurations – without baffles (STHX_1) and with baffles (STHX_2) using 0.01 Vol.% and 0.02 Vol.% of CuO-W nanofluid.

Two different configurations, one without baffles (STHX_1) and other with single segmental baffles (STHX_2), are chosen with all other dimensional details of shell and tube remaining same. Water is used as base fluid. CuO nanoparticle is chosen, as its thermal conductivity is higher compared to other metal oxides. A comparative study on the thermal performance of these shell and tube heat exchangers are performed by considering different Vol.% concentrations of CuO-W nanofluid and the outcome are compared with the base fluid (i.e., water). The influence of varying the mass flow rate of the tube side fluid by keeping shell side fluid mass flow rate as constant and vice versa on the thermal performance of shell and tube heat exchanger are studied.

The modified shell and tube heat exchanger with baffles (STHX_2) give an improved performance. The heat transfer coefficient improved by about 11.28 and 7.54 per cent for 0.02 and 0.01 Vol.% of CuO-W nanofluid compared to water. Overall heat transfer coefficient for STHX_2 enhanced between 118.26% to 123.06% in comparison with base fluid for 0.02 Vol.% of CuO-W nanofluid whereas, it improved between 79.20% to 87.51% for 0.01 Vol.% of CuO-W nanofluid. Similarly, the actual heat transfer enhanced between 71.79% to 77.77% and between 48.71% to 55.55% for 0.02 and 0.01 Vol.% of CuO-W nanofluid, respectively. Moreover, mass flow rates of the working fluids significantly influence the performance of the shell and tube heat exchanger.

Two cases are considered here. first, by varying the shell side fluid mass flow rate and keeping the tube side fluid mass flow rate as constant. Later, tube side fluid mass flow rates are varied and shell side fluid mass flow rate is kept constant. It is found that in Case 2, for both 0.01 and 0.02 Vol.% of CuO-W nanofluid, highest performance is obtained for 150 kg/h of shell side and tube side fluid flows involving STHX_2. Finally, the modified shell and tube heat exchanger with baffle arrangement gives the best performance by using 0.02 Vol.% of CuO-W nanofluid.

The effect of magnetic field dependent (MFD) viscosity on the onset of convection in a ferromagnetic fluid layer heated from below saturating rotating porous medium in the presence of vertical magnetic field is investigated theoretically by using Darcy model. The resulting eigen value problem is solved using the regular perturbation technique. Both stationary and oscillatory instabilities have been obtained. It is found that increase in MFD viscosity and increase in magnetic Rayleigh number is to delay the onset of ferroconvection, while the nonlinearity of fluid magnetization has no influence on the stability of the system.

The thermal perturbation method is employed for analytical solution. A theory of linear stability analysis and normal mode technique have been carried out to analyze the onset of convection for a fluid layer contained between two impermeable boundaries for which an exact solution is obtained.

The conditions for the system to stabilize both by stationary and oscillatory modes are studied. Even for the oscillatory system of particular frequency dictated by physical conditions, the critical Rayleigh numbers for oscillatory mode of the system were found to be greater than for the stationary mode. The system gets destabilized for various physical parameters only through stationary mode. Hence, the analysis is restricted to the stationary mode. To the Coriolis force, the Taylor number T_a is calculated to discuss the results. It is found that the system stabilizes through stationary mode for values of and for oscillatory instability is favored for Ta > 104. Therefore the Taylor number T_a leads to stability of the system. For larger rotation, magnetization leads to destabilization of the system. The MFD viscosity is found to stabilize the system.

This research paper is new and original.

Nowadays, the applications of metal matrix composites are tremendously increasing in engineering fields. Consequently, the demand for precise machining of composites has also grown enormously. The purpose of this paper is to reduce production cost and simultaneously improve desired product quality through optimal parameter setting using WASPAS and MOORA.

Metal matrix composites were fabricated using stir casting process, with aluminum 6063 as matrix and titanium carbide as reinforcement. Fabricated composite samples were machined on medium duty lathe using cemented carbide tool. All the experiments were carried out based on Box–Behnken design. Comparison of multi objective optimization based on ratio analysis and weighted aggregated sum product assessment in optimizing four parameters, namely, “cutting speed,” “feed rate,” “depth of cut” and “reinforcement weight percent of composite samples”; evaluating their influence on material removal rate, cutting force and surface roughness were carried out.

The output achieved by both MOORA and WASPAS are in similar MCDM) techniques in the selection of machining parameters.

The results obtained in the present paper will be helpful for decision makers in manufacturing industries, who work in metal cutting area, to select the suitable levels for the parameters by implementing the MCDM techniques.

The novelty of this paper is making an attempt to select better MCDM technique based on the comparison of results obtained for the individual technique.

This study aims to analyse the changes in mechanical and wear performance of aluminium alloy when yttrium oxide particles are incorporated. The microstructures are studied to analyse the change in the grain structures. Worn surfaces are observed via scanning electron microscope to study the wear mechanism in detail.

Stir casting is used to incorporate varying composition of yttrium particles, having an average particle size of 25 micrometer, in aluminium alloy 6063 matrix. Wear testing is carried out by DUCOM manufactured high temperature rotatory tribometer, and an indentation test is used for analysing the microhardness of the fabricated samples.

Microhardness of the material is increased with the increasing content of particulate addition. With the increasing content of reinforcement, more refined grains are produced. The load is transferred from the matrix to more rigid yttrium oxide particles. These factors contributed to escalated microhardness of the reinforced samples. Particulate addition enhanced the wear performance of the material; this might be attributed to increased microhardness and formation of an oxide layer.

Aluminium composites are finding wide applications in various industries, and there is always a requirement of material with enhanced tribological properties. Yttrium oxide particles exhibit improved mechanical properties, and their interaction with the aluminium matrix has not been studied much in the past. So, in this work, yttrium oxide incorporated aluminium matrix is studied.

This research aims to examine the impact of friction stir processing (FSP) treatment on an aluminum alloy, especially the AD31T alloy derived from the Al-Fe-Mg-Si system. The aim is to assess the influence of different processing techniques on the microstructure and physical and mechanical characteristics of the material, with a specific focus on structural and bulk imperfections inside the stir zone (SZ).

The study demonstrates that augmenting the linear velocity of the tool within the 25–100 mm/min range results in significant enhancements. The enhancements include a decrease in the heat-affected zone (HAZ), a reduction in the extent of volume defects inside the SZ and a more uniform deformation. The microstructural analysis results are corroborated by data acquired from microhardness and electrical conductivity studies, confirming the beneficial influence of modifying the tool’s linear velocity on the material parameters.

This study provides significant observations on the changes in microstructure and the generation of flaws throughout the process of FSP of AD31T alloy. These results have practical implications for improving the characteristics of the alloy and optimizing the production conditions.

All samples exhibit a distinct reduction in electrical conductivity within the initial third of the sample, aligning with the transitional region between the base metal (BM) and the HAZ. This underscores the importance of understanding the transitional zones during FSP.

The purpose of this paper is to develop a mathematical model for optimizing the metal removal rate (MRR) through Response Surface Methodology (RSM). The developed model helps us to analyze the influence of individual input machining parameters (cutting speed, feed rate, weight percentage) on the responses in machining of Al-TiB₂ composite.

RSM is used to optimize the MRR by developing a mathematical model. Three factors, three-level box Behnken design matrix in RSM is employed to carry out the experimental investigation. The “Design Expert 8.0” software is used for regression and graphical analysis of the data are collected. The optimum values of the selected variables are obtained by solving the regression equation and by analyzing the response surface contour plots. Analysis of variance (ANOVA) is applied to check the validity of the model and for finding the significant parameters.

The response surface model developed, helps to calculate the MRR at different input cutting parameters with the chosen range with more than 95 per cent confidence intervals.

The effect of machining parameters on MRR during machining of Al-TiB₂ composites using RSM has not been previously analyzed.

This paper presents the application of grey modeling for thermal spray processing parameter analysis in less data environment.

Based on processing knowledge, key processing parameters of thermal spray process are analyzed and preselected. Then, linear and non-linear grey modeling models are integrated to mine the relationships between different processing parameters.

Model A reveals the linear correlation between the HVOF process parameters and the characterization of particle in-flight with average relative errors of 9.230 percent and 5.483 percent for velocity and temperature.

The prediction accuracies of coatings properties vary, which means that there exists more complex non-linear relationship between the identified input parameters and coating results, or more unexpected factors (e.g. factors from material side) should be further investigated.

According to the modeling case in this paper, method has potential to deal with other diverse modeling problems in different industrial applications where challenge to collecting large quantity of data sets exists.

It is the first time to apply grey modeling for thermal spray processing where complicated relationships among processing parameters exist. The modeling results show reasonable results to experiment and existing processing knowledge.

The purpose of this study is to determine the enablers of the quality of work life (QWL) of employees working in the Garment industries.

The study was carried out in a fivefold step. In the first step, the enablers of QWL were identified through an exhaustive literature survey, in the second step identified vital few components through Pareto analysis. Then the third step was followed by exploratory factor analysis (EFA) to further, to identify the precise components and validate the same using confirmatory factor analysis in fourth step. The final step included interpretive structural modeling and Cross-Impact Matrix Multiplication Applied to Classification analysis to model the validated components and determine the interrelationships and linkages.

Predominant QWL enablers of employees working in the garment industries are training and development, satisfaction in job, compensation and rewards, relation and co-operation, grievance handling, work environment, job nature, job security and facilities.

In this study, the interpretive structural model is designed based on the opinion of the experts who are working in the garment industry considering the responses from employees in garment sectors. The framework can be extended further to the other sectors.

In future, the researchers in QWL may develop a model to quantify the level of employees’ QWL who are working in different sectors. Enablers of QWL are essential, and based on this further statistical analysis can be carried out. This study will provide limelight to the researchers in choosing the valid and reliable set of enablers for the empirical studies. Organizations can get benefit by implementing the outcome of this research for the enhancement of the QWL of employees.

The study was carried out in 133 garment industries where 851 workers constituted the final valid responses that were considered for analysis. The outcomes from the study help administrators, policy and decision-takers in taking decisions to enhance QWL.