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The purpose of this paper is to focus on the advanced solution of the parametric non-linear model related to the Rayleigh-Benard laminar flow involved in the modeling of natural thermal convection. This flow is fully determined by the dimensionless Prandtl and Rayleigh numbers. Thus, if one could precompute (off-line) the model solution for any possible choice of these two parameters the analysis of many possible scenarios could be performed on-line and in real time.

In this paper both parameters are introduced as model extra-coordinates, and then the resulting multidimensional problem solved thanks to the space-parameters separated representation involved in the proper generalized decomposition (PGD) that allows circumventing the curse of dimensionality. Thus the parametric solution will be available fast and easily.

Such parametric solution could be viewed as a sort of abacus, but despite its inherent interest such calculation is at present unaffordable for nowadays computing availabilities because one must solve too many problems and of course store all the solutions related to each choice of both parameters.

Parametric solution of coupled models by using the PGD. Model reduction of complex coupled flow models. Analysis of Rayleigh-Bernard flows involving nanofluids.

The purpose of this paper is to solve non‐linear parametric thermal models defined in degenerated geometries, such as plate and shell geometries.

The work presented in this paper is based in a combination of the proper generalized decomposition (PGD) that proceeds to a separated representation of the involved fields and advanced non‐linear solvers. A particular emphasis is put on the asymptotic numerical method.

The authors demonstrate that this approach is valid for computing the solution of challenging thermal models and parametric models.

This is the first time that PGD is combined with advanced non‐linear solvers in the context of non‐linear transient parametric thermal models.

Vibration of large membranes has great utility in engineering application such as in important parts of drums, pumps, microphones, telephones and other devices. So, to obtain a numerical solution of this type of problems is necessary and important. In general, in existing approaches, involved parameters and variables are defined exactly. Whereas in actual practice, it may contain uncertainty owing to error in observations, maintenance-induced error, etc. So, the main purpose of this paper is to solve this important problem numerically under fuzzy and interval uncertainty to have an uncertain solution and to study its behaviour.

In this study, the authors have considered a new approach is known as double parametric form of fuzzy number to model uncertain parameters. Along with this a semianalytical approach, i.e. variational iteration method, has been used to obtain uncertain bounds of the solution.

The variational iteration method has been successfully implemented along with the double parametric form of fuzzy number to find the uncertain solution of the vibration equation of a large membrane. The advantage of this approach is that the solution can be written in a power series or a compact form. Also, this method converges rapidly to obtain an accurate solution. Various cases depending on the functional value involved in the initial conditions have been studied and the behaviour has been analysed. Applying the double parametric form reduces the computational cost without separating the fuzzy equation into coupled differential equations as done in traditional approaches.

The vibration equation of large membranes has been solved under fuzzy and interval uncertainty. Uncertainties have been considered in the initial conditions. New approaches, i.e. variational iteration method along with the double parametric form, have been applied to solve the vibration equation of large membranes.

Currently, the design, technological features of voices, and their analysis of various applications are being simulated with the requirement to communicate at a greater distance or more discreetly. The purpose of this study is to explore how voices and their analyses are used in modern literature to generate a variety of solutions, of which only a few successful models exist.

The mel-frequency cepstral coefficient (MFCC), average magnitude difference function, cepstrum analysis and other voice characteristics are effectively modeled and implemented using mathematical modeling with variable weights parametric for each algorithm, which can be used with or without noises. Improvising the design characteristics and their weights with different supervised algorithms that regulate the design model simulation.

Different data models have been influenced by the parametric range and solution analysis in different space parameters, such as frequency or time model, with features such as without, with and after noise reduction. The frequency response of the current design can be analyzed through the Windowing techniques.

A new model and its implementation scenario with pervasive computational algorithms’ (PCA) (such as the hybrid PCA with AdaBoost (HPCA), PCA with bag of features and improved PCA with bag of features) relating the different features such as MFCC, power spectrum, pitch, Window techniques, etc. are calculated using the HPCA. The features are accumulated on the matrix formulations and govern the design feature comparison and its feature classification for improved performance parameters, as mentioned in the results.

This paper aims to study a non-Newtonian micropolar fluid flow over a bidirectional flexible surface for multiple exact solutions of momentum boundary layer and thermal transport phenomenon subject to wall mass flux, second-order slip and thermal jump conditions.

The coupled equations are transformed into ordinary differential equations using similarity variables. Analytical and numerical techniques are used to solve the coupled equations for single, dual or multiple solutions.

The results show that the stretching flow, shrinking flow, the wall drag, thermal profile and temperature gradient manifest large changes when treated for special effects of the standard parameters. The role of critical numbers is definitive in locating the domains for the existence of exact solutions. The nondimensional parameters, such as mass transfer parameter, bidirectional moving parameter, plate deformation strength parameter, velocity slips, material parameter, thermal jump and Prandtl number, are considered, and their physical effects are presented graphically. The presence of governing parameters exhibits special effects on the flow, microrotation and temperature distributions, and various exact solutions are obtained for the special parametric cases.

The originality and value of this work lie in its exploration of non-Newtonian micropolar fluid flow over a bidirectional flexible surface, highlighting the multiple exact solutions for momentum boundary layers and thermal transport under various physical conditions. The study provides insights into the effects of key parameters on flow and thermal behavior, contributing to the understanding of complex fluid dynamics.

Presents a multiple‐objective mathematical programming model to co‐ordinate logistics decisions with those on the interface between the production and marketing departments. The model can help decide on an overall budget to request from senior management for logistics and these interfaces, and in systematically allocating the funds between transport, inventory and production. In so doing, this multi‐period model specifies the timing and quantity of raw‐material purchases, and the location and timing of production activities and distribution flows. The budget for expenditures on logistics and its interface activities is taken as an objective to minimise, instead of as a given dollar level to be satisfied. A second objective is to maximise the profit of logistics and its related interfaces. Trade‐offs between these two conflicting aims yields the decision maker′s “best compromise” solution.

This study aims to carry out the analysis of Rayleigh-Bénard convection within enclosures with curved isothermal walls, with the special implication on the heat flow visualization via the heatline approach.

The Galerkin finite element method has been used to obtain the numerical solutions in terms of the streamlines (ψ ), heatlines (Π), isotherms (θ), local and average Nusselt number ( Nut¯) for various Rayleigh numbers (10³ ≤ Ra ≥ 10⁵), Prandtl numbers (Pr = 0.015 and 7.2) and wall curvatures (concavity/convexity).

The presence of the larger fluid velocity within the curved cavities resulted in the larger heat transfer rates and thermal mixing compared to the square cavity. Case 3 (high concavity) exhibits the largest Nut¯ at the low Ra for all Pr. At the high Ra, Nut¯ is the largest for Case 3 (high concavity) at Pr = 0.015, whereas at Pr = 7.2, Nut¯ is the largest for Case 1 (high concavity and convexity).

The results may be useful for the material processing applications.

The study of Rayleigh-Bénard convection in cavities with the curved isothermal walls is not carried out till date. The heatline approach is used for the heat flow visualization during Rayleigh-Benard convection within the curved walled enclosures for the first time. Also, the existence of the enhanced fluid and heat circulation cells within the curved walled cavities during Rayleigh-Benard heating is illustrated for the first time.

This study aims to optimize the parametric combination of injected slub yarn to achieve least abrasive damage on fabrics produced from it.

Single base injected slub yarn structural parameters, vis-à-vis slub length, slub thickness and slub frequency, were varied during preparation of yarn samples under this research work. A total of 17 yarn samples were produced according to the Box and Bhenken design of the experiment. Subsequently knitted and woven (using injected slub yarns in the weft only) fabric samples were prepared from these yarns. Yarn and fabric samples were abraded with standard instruments to see the impact of yarn structural parameters on abrasive damage of fabric in terms of fabric mass loss and appearance deterioration. From the test results, empirical models relating to slub parameters and fabric abrasion behavior were developed through a backward elimination regression approach. Subsequently, a set of optimal parametric combinations was derived with multi-objective evolutionary algorithms by using MATLAB software. This was followed by ranking all optimal solutions through technique for order preference by similarity to idle solution (TOPSIS) score analysis.

The injected slub yarn’s structural parameters have a strong influence on the abrasive damage of knitted and woven fabric. It is seen that the best suitable parametric combination of slub parameters for achieving the least abrasive damage is not the same for knitted and woven fabric.

The spinner can explore this concept to find out the best suitable parametric combination during pattern making of injected slub yarn through MATLAB solution followed by TOPSIS score analysis based on their priority of criteria level to ensure better abrasion behavior of fabric produced.

Optimization of parametric combination of injected slub yarns will help to ensure production of fabric with most resistance to abrasion for specific applications. The studies showed that the optimal solution for woven and knitted fabrics is different. The result indicates that in the case of knitted fabric, comparatively lesser slub thickness is found to be suitable for getting better fabric abrasion resistance, whereas in the case of woven fabric, comparatively higher slub thickness is found suitable for the same.

Recently, fractional differential equations have been used to model various physical and engineering problems. One may need a reliable and efficient numerical technique for the solution of these types of differential equations, as sometimes it is not easy to get the analytical solution. However, in general, in the existing investigations, involved parameters and variables are defined exactly, whereas in actual practice it may contain uncertainty because of error in observations, maintenance induced error, etc. Therefore, the purpose of this paper is to find the dynamic response of fractionally damped beam approximately under fuzzy and interval uncertainty.

Here, a semi analytical approach, variational iteration method (VIM), has been considered for the solution. A newly developed form of fuzzy numbers known as double parametric form has been applied to model the uncertainty involved in the system parameters and variables.

VIM has been successfully implemented along with double parametric form of fuzzy number to find the uncertain dynamic responses of the fractionally damped beam. The advantage of this approach is that the solution can be written in power series or compact form. Also, this method converges rapidly to have the accurate solution. The uncertain responses subject to impulse and step loads have also been computed and the behaviours of the responses are analysed. Applying the double parametric form, it reduces the computational cost without separating the fuzzy equation into coupled differential equations as done in traditional approaches.

Uncertain dynamic responses of fuzzy fractionally damped beam using the newly developed double parametric form of fuzzy numbers subject to unit step and impulse loads have been obtained. Gaussian fuzzy numbers are used to model the uncertainties. In the methodology using the alpha cut form, corresponding beam equation is first converted to an interval-based fuzzy equation. Next, it has been transformed to crisp form by applying double parametric form of fuzzy numbers. Finally, VIM has been applied to solve the same for the general fuzzy responses. Various numerical examples have been taken in to consideration.