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Two simple and efficient contour plotting algorithms are presented. The first algorithm is a colour‐fill algorithm. The second algorithm is a colour‐fill algorithm as well as a contour line plotting algorithm. Using adaptive quadtree subdividing and linear interpolation, both algorithms are easy to implement. In addition, the contour plotting for a given mesh can be performed parallelly since plotting the contour of an element is totally independent of any other element.

A very fast interactive contour plotting package is presented. Any finite element mesh is automatically converted into a contour plotting mesh composed of 3‐noded triangular elements. The resulting contours are smooth and accurate provided the analysis mesh is sensible.

The TRIXEL algorithm and theory are presented for colour‐fill contouring. The algorithm is simple, efficient, easily implemented and it readily adapts to parallel processing. Examples are given and a Fortran 77 source listing is included.

This study was conducted to analyze the effects of machining parameters on the specific energy consumption in the computerized numerical control lathe turning operation of a hardened alloy steel roll at low cutting speeds. The aim was to minimize its consumption.

The design matrix was based on three variable factors at three levels. Response surface methodology was used for the analysis of experimental results. Optimization was carried out by using the desirability function and genetic algorithm. A multiple regression model was used for relationship build-up.

According to desirability function, genetic algorithm and multiple regression analysis, optimal machining parameters were cutting speed 40 m/min, feed 0.2 mm/rev and depth of cut 0.50 mm, which resulted in minimal specific energy consumption of 0.78, 0.772 and 0.78 kJ/mm³, respectively. Correlation analysis and multiple regression model found a quadratic relationship between specific energy consumption with power consumption and material removal rate.

In the past, many researchers have developed mathematical models for specific energy consumption, but these models were developed at high cutting speed, and a majority of the models were based on the material removal rate as the independent variable. This research work developed a mathematical model based on the machining parameters as an independent variable at low cutting speeds, for a new type of large-sized hardened alloy steel roll. A multiple regression model was developed to build a quadratic relationship of specific energy consumption with power consumption and material removal rate. This work has a practical application in hot rolling industry.

A parabolic trough solar collector is an advanced concentrated solar power technology that significantly captures radiant energy. Solar power will help different sectors reach their energy needs in areas where traditional fuels are in use. This study aims to examine the sensitivity analysis for optimizing the heat transfer and entropy generation in the Jeffrey magnetohydrodynamic hybrid nanofluid flow under the influence of motile gyrotactic microorganisms with solar radiation in the parabolic trough solar collectors. The influences of viscous dissipation and Ohmic heating are also considered in this investigation.

Governing partial differential equations are derived via boundary layer assumptions and nondimensionalized with the help of suitable similarity transformations. The resulting higher-order coupled ordinary differential equations are numerically investigated using the Runga-Kutta fourth-order numerical approach with the shooting technique in the computational MATLAB tool.

The numerical outcomes of influential parameters are presented graphically for velocity, temperature, entropy generation, Bejan number, drag coefficient and Nusselt number. It is observed that escalating the values of melting heat parameter and the Prandl number enhances the Nusselt number, while reverse effect is observed with an enhancement in the magnetic field parameter and bioconvection Lewis number. Increasing the magnetic field and bioconvection diffusion parameter improves the entropy and Bejan number.

Nanotechnology has captured the interest of researchers due to its engrossing performance and wide range of applications in heat transfer and solar energy storage. There are numerous advantages of hybrid nanofluids over traditional heat transfer fluids. In addition, the upswing suspension of the motile gyrotactic microorganisms improves the hybrid nanofluid stability, enhancing the performance of the solar collector. The use of solar energy reduces the industry’s dependency on fossil fuels.

IN this paper an attempt is made to describe rapid, precise, efficient methods for solving aeroplane geometry problems by analytic geometry.

The paper focuses on two topics, optimizing the proposed triangular tube for crashworthiness and solving a non‐linear programming problem by a “mapping” technique, which the condition of Lagrange Multiplier Theorem is violated within the feasible region. The purpose of studying optimized triangular tubes is to prepare them for redesigning vehicle bumpers. The dimension optimization of triangular tube is carried out for its thickness and lateral length, based on the accomplished shape optimization under an impact. The load uniformity is taken as the objective function, which is defined as the ratio of maximum peak force and means crushing force. Meanwhile the mean crushing force and absorbed energy are treated as constraints. Based on FEA analysis, the regression functions for load uniformity, mean crushing force, and absorbed energy are formulated by RSM. The result has shown that triangular tube possesses an optimization region, under which the better‐integrated property can be achieved to supply a more safety environment for vehicular occupants.

Finite element meshes can today be used to represent very complex structures because of high performance hardware and software. Although a very successful contributor to modern engineering analysis, such techniques are prone to certain classes of numerical analysis errors which have been long recognized and widely investigated. A more recently recognized source of error has, however, received the attention of analysts, being due to the shape distortion effects of popular types of element, such as isoparametric elements. A mesh scanning program, BERQUAL, part of the BERSAFE system, highlights such potential sources of error, but a more precise assessment is only possible from the final results since element performance depends on the stress gradients in each element. Hence additional error checking using certain stress error measures has been devised and implemented in the post‐processing program PLOTTER, part of the BERSAFE system, to enable rapid, interactive, screen diagnosis. The error measures and implementation details are described and illustrated with suitable examples of progressive shape distortion effects.

This study aims to investigate the influence of wall curvature in a semicircular thermal annular system on magneto-nanofluidic flow, heat transfer and entropy generation. The analysis is conducted under constant cooling surface and fluid volume constraints.

The mathematical equations describing the thermo-fluid flow in the semicircular system are solved using the finite element technique. Four different heating wall configurations are considered, varying the undulation numbers of the heated wall. Parametric variations of bottom wall undulation (f), buoyancy force characterized by the Rayleigh number (Ra), magnetic field strength represented by the Hartmann number (Ha) and inclination of the magnetic field (γ) on the overall thermal performance are studied extensively.

This study reveals that the fluid circulation strength is maximum in the case of a flat bottom wall. The analysis shows that the bottom wall contour and other control parameters significantly influence fluid flow, entropy production and heat transfer. The modified heated wall with a single undulation exhibits the highest entropy production and thermal convection, leading to a heat transfer enhancement of up to 21.85% compared to a flat bottom. The magnetic field intensity and orientation have a significant effect on heat transfer and irreversibility production.

Further research can explore a wider range of parameter values, alternative heating wall profiles and boundary conditions to expand the understanding of magneto-nanofluidic flow in semicircular thermal systems.

This study introduces a constraint-based analysis of magneto-nanofluidic thermal behavior in a complex semicircular thermal system, providing insights into the impact of wall curvature on heat transfer performance. The findings contribute to the design and optimization of thermal systems in various applications.

Deals with the non‐stationary pure convection equation in two dimensions. An attribute of the method is that the advective fluxes are approximated by taking the flow orientations into consideration. The interfacial numerical fluxes are interpolated by virtue of the rational areas which depend on the corner velocity vectors. This leads to a discrete system containing dissipative artifacts in regions normal to the local streamline. Conducts two‐dimensional fundamental studies for the flux discretization developed. These analyses give insight into the order‐of‐accuracy, and the scheme stability. According to the underlying positivity definition, this explicit scheme is, furthermore, classified as conditionally monotonic. This scheme has been applied successfully to solve smooth, sharply varied, and discontinuous transport problems.