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This paper aims to investigate the thermal performance involving larger heating rate, targeted heating, heating with least non-uniformity of the spatial distribution of temperature and larger penetration of heating within samples vs shapes of samples (circle, square and triangular).

Galerkin finite element method (GFEM) with adaptive meshing in a composite domain (free space and sample) is used in an in-house computer code. The finite element meshing is done in a composite domain involving triangle embedded within a semicircular hypothetical domain. The comparison of heating pattern is done for various shapes of samples involving identical cross-sectional area. Test cases reveal that triangular samples can induce larger penetration of heat and multiple heating fronts. A representative material (beef) with high dielectric loss corresponding to larger microwave power or heat absorption in contrast to low lossy samples is considered for the current study. The average power absorption within lossy samples has been computed using the spatial distribution and finite element basis sets. Four regimes have been selected based on various local maxima of the average power for detailed investigation. These regimes are selected based on thin, thick and intermediate limits of the sample size corresponding to the constant area of cross section, Ac involving circle or square or triangle.

The thin sample limit (Regime 1) corresponds to samples with spatially invariant power absorption, whereas power absorption attenuates from exposed to unexposed faces for thick samples (Regime 4). In Regimes 2 and 3, the average power absorption non-monotonically varies with sample size or area of cross section (A_c) and a few maxima of average power occur for fixed values of A_c involving various shapes. The spatial characteristics of power and temperature have been critically analyzed for all cross sections at each regime for lossy samples. Triangular samples are found to exhibit occurrence of multiple heating fronts for large samples (Regimes 3 and 4).

Length scales of samples of various shapes (circle, square and triangle) can be represented via Regimes 1-4. Regime 1 exhibits the identical heating rate for lateral and radial irradiations for any shapes of lossy samples. Regime 2 depicts that a larger heating rate with larger temperature non-uniformity can occur for square and triangular-Type 1 lossy sample during lateral irradiation. Regime 3 depicts that the penetration of heat at the core is larger for triangular samples compared to circle or square samples for lateral or radial irradiation. Regime 4 depicts that the penetration of heat is still larger for triangular samples compared to circular or square samples. Regimes 3 and 4 depict the occurrence of multiple heating fronts in triangular samples. In general, current analysis recommends the triangular samples which is also associated with larger values of temperature variation within samples.

GFEM with generalized mesh generation for all geometries has been implemented. The dielectric samples of any shape are surrounded by the circular shaped air medium. The unified mesh generation within the sample connected with circular air medium has been demonstrated. The algorithm also demonstrates the implementation of various complex boundary conditions in residuals. The numerical results compare the heating patterns for all geometries involving identical areas. The thermal characteristics are shown with a few generalized trends on enhanced heating or targeted heating. The circle or square or triangle (Type 1 or Type 2) can be selected based on specific heating objectives for length scales within various regimes.

The purpose of this paper, computational fluid dynamics (CFD) work, is to promote turbulent thermal convection in a heated circular tube using a passive scheme of a slotted twisted sheet.

The inventive design uses square-cut and conjugate triangular perforations to diversify the twisted tape for better thermal convection. The current novel passive scheme methodology is accomplished by carving the same square cuts and slitting various sizes of equilateral triangle perforations (side length varies between 8 and 16 mm). The re-normalisation group turbulence model and the semi-implicit method for pressure-linked equation method examine the turbulent thermal convection aspects of all simulations at different Reynolds numbers (6,000, 10,000 and 14,000).

The analyses of simulations exhibit that the placement of a twisted tape with triangle perforations and equidistant square cuts can effectually promote thermal convection in a circular tube. A larger-sized triangle perforation can increase the thermal convection enhancement and thermal performance factor, but an enlarged perforation may decrease the thermal convection enhancement and thermal performance factor. As a result, compared with the smooth circular tube, the circular tube with the slotted twisted sheet slit by a 10 mm equilateral triangle brings about the maximum improvement ratio of the mean Nusselt number of about 2.8 at Re = 6,000. Under weighing the friction through the circular tube, the tube with the slotted twisted sheet slit by a 10 mm equilateral triangle gains the best thermal performance factor of about 1.36 at Re = 6,000.

The working fluid is water and its physical features are assumed to be constant. In addition, the fluid is considered a steady flow in this CFD work.

These CFD predictions will benefit the development of heat exchanger tubes equipped with a slotted twisted sheet to acquire preferable thermal convection enhancement.

Higher thermal performance achieved by placing a slotted twisted tape in a heated tube will benefit society in lower energy consumption, machinery maintenance costs and impact on the environment.

This study combined triangle perforations and square cuts on the twisted sheet. This combination can induce the fluid flow across the sheet to disturb the swirling flow and then promote the fluid mixing to increase thermal convection. Therefore, this modified tape can be a profitable passive device for designing a heat exchanger.

This paper aims to investigate the role of shapes of containers (nine different containers) on entropy generation minimization involving identical cross-sectional area (1 sq. unit) in the presence of identical heating (isothermal). The nine containers are categorized into three classes based on their geometric similarities (Class 1: square, tilted square and parallelogram; Class 2: trapezoidal type 1, trapezoidal type 2 and triangular; Class 3: convex, concave and curved triangular).

Galerkin finite element method is used to solve the governing equations for a representative fluid (engine oil: Pr = 155) at Ra = 10³–10⁵. In addition, finite element method is used to solve the streamfunction equation and evaluate the entropy generation terms (S_ψ and S_θ). Average Nusselt number ( Nub¯) and average dimensionless spatial temperature ( θ^) are also evaluated via the finite element basis sets.

Based on larger Nub¯, larger θ^ and optimal S_total values, containers from each class are preferred as follows: Class 1: parallelogrammic and square, Class 2: trapezoidal type 1 and Class 3: convex (larger θ^, optimum S_total) and concave (larger Nub¯). Containers with curved walls lead to enhance the thermal performance or efficiency of convection processes.

Comparison of entropy generation, intensity of thermal mixing ( θ^) and average heat transfer rate give a clear picture for choosing the appropriate containers for processing of fluids at various ranges of Ra. The results based on this study may be useful to select a container (belonging to a specific class or containers with curved or plane walls), which can give optimal thermal performance from the given heat input, thereby leading to energy savings.

This study depicts that entropy generation associated with the convection process can be reduced via altering the shapes of containers to improve the thermal performance or efficiency for processing of identical mass with identical heat input. The comparative study of nine containers elucidates that the values of local maxima of S_ψ (S_ψ,max), S_θ (S_θ,max) and magnitude of S_total vary with change in shapes of the containers (Classes 1–3) at fixed Pr and Ra. Such a comparative study based on entropy generation minimization on optimal heating during convection of fluid is yet to appear in the literature. The outcome of this study depicts that containers with curved walls are instrumental to optimize entropy generation with reasonable thermal processing rates.

The purpose of the study is to provide a dataset about geometrical constructions of early Ottoman tombs for conservation studies. Thus, a proposal for the restitution phase of the damaged tombs aims to develop.

The study is composed of four phases. First, the representative plan and section drawings of early Ottoman Tombs were redrawn; second, a geometrical analysis was made, a proposal table was prepared for the restitution of the damaged tombs; and last, this table was applied to tomb examples and restitution drawings are verified with the original situation of the tombs.

Early Ottoman tombs may be interpreted through geometric shapes, including the square, circle, triangle, octagon, arsin grid and quadrature systems. The arsin grid system provides information about the position of the domes and the height of the drums and windows. Quadrature establishes the highest point of domes and entrances. The proposal table, developed from the obtained results, facilitated the identification of the original elements, including the dome, drum, window and portal. This information is crucial for conducting further studies on restitution.

The abundance and dispersed nature of tomb structures compared to other architectural designs pose challenges in their scholarly examination. The early Ottoman tombs, which experienced an increase in numbers following the Conquest of Istanbul, serve as the initial expressions and embodiments of novel architectural endeavors. Thus, the determination of design ideas of the early Ottoman tombs sheds light on Ottoman architectural practice, which has remained largely unknown and guided the conservation studies of the tombs that have lost their integrity and originality.

The boundary element method has been used to obtain the electrical capacitances of the unit equilateral triangle, square, regular tetrahedron and cube. For each of these objects, a series of values of the number N of segments has been used and then empirical formulae have been used to extrapolate N to infinity. The singularities of the charge densities at the edges and corners of these objects can be characterised by power laws, the relevant exponents of which have also been determined.

This paper aims to describe the method for solving vibration problem of electro‐magneto‐elastic plate of polygonal (triangle, square, pentagon and hexagon) cross‐sections using Fourier expansion collocation method (FECM).

A mathematical model is developed to study the wave propagation in an electro‐magneto‐elastic plate of polygonal cross‐sections using the theory of elasticity. The frequency equations are obtained from the arbitrary cross‐sectional boundary conditions, since the boundary is irregular in shape; it is difficult to satisfy the boundary conditions along the surface of the plate directly. Hence, the FECM is applied along the boundary to satisfy the boundary conditions. The roots of the frequency equations are obtained by using the secant method, applicable for complex roots.

From the literature survey, it is clear that the free vibration of electro‐magneto‐elastic plate of polygonal cross‐sections have not been analyzed by any of the researchers, also the previous investigations in the vibration problems of electro‐magneto‐elastic plates are based on the traditional circular cross‐sections only. So, in this paper, the wave propagation in electro‐magneto‐elastic plate of polygonal cross‐sections is studied using the FECM. The computed non‐dimensional frequencies are plotted in the form of dispersion curves and their characteristics are discussed.

The researchers have discussed the circular, rectangular, triangular and square cross‐sectional plates by the boundary conditions. In this problem, the author studied the vibrations of polygonal (triangle, square, pentagon and hexagon) cross‐sectional plates using the geometrical relation which is applicable to all the cross‐sections. The problem may be extended to any kinds of cross‐sections by using the proper geometrical relations.

This study seeks to focus on the annular flow between rectangular and equilateral‐triangular ducts under all possible arrangements. The aim of this work is to obtain accurate prediction of the friction factor of this flow using high‐order finite element method.

Steady and fully developed laminar flow of incompressible Newtonian fluid in an annulus of variable cross‐sectional geometry is investigated numerically. Accurate prediction of the friction factor of this flow was obtained using high‐order finite element method.

The results were in agreement with already published findings in the literature. It was found that a higher annular area ratio will lead to a monotonic increase in fRe value in the case of regular annuli, and will lead to an increase followed by a decrease in fRe value in the case of irregular annuli. Also, it was, found that irregular annuli have lower fRe value than regular annuli, and that the square‐in‐triangle case has the lowest fRe value, whereas the square‐in‐square case has the highest fRe value.

Accurate prediction of the friction factor of the laminar flow in irregular annuli was obtained. Also, the obtained results can be utilized to optimize the annular geometries under consideration. In addition, the obtained results can lead to the design of more efficient heat exchangers.

This paper aims to obtain the film thickness, friction torque and pumping rate and analyze the effects of roughness and surface micro-dimple texture (circular, square and equilateral triangle) on the performance of the oil seal.

On the basis of elastohydrodynamic lubrication and the pumping mechanism of rotating shaft seal, this paper establishes a numerical model of hybrid lubrication of oil seal in sealing area. The model is coupled with fluid mechanics, rough peak contact mechanics and deformation analysis.

The results show that surface texture significantly improves the lubrication properties of the oil seal. The oil seal with the square texture has the largest oil film thickness, while the equilateral triangle texture has a better effect on the pumping rate.

To get closer to the real working environment of the oil seal, based on the surface roughness, this paper studies the effect of the texture shapes applied to the oil seal lip surface on the performance of the oil seal. The critical roughness and rotational speed values with zero pumping rate are obtained, which provides a theoretical basis for the correct selection of oil seals.

This study aims to analyze the impact of fractional derivatives on heat transfer and entropy generation during transient free convection inside various complex porous enclosures, such as triangle, L-shape and square-containing wavy surfaces. These porous enclosures are saturated with Cu-water nanofluid and subjected to the influence of a uniform magnetic field.

In the present study, Darcy’s model is used for the momentum transport equation in the porous matrix. Additionally, the Caputo time fractional derivative is introduced in the energy equation to assess the heat transfer phenomenon. Furthermore, the total entropy generation has been computed by combining the entropy generation due to fluid friction (S_ff), heat transfer (S_ht) and magnetic field (S_mf). The complete mathematical model is further simulated using the penalty finite element method, and the Caputo time derivative term is approximated using the L1 scheme. The study is conducted for various ranges of the Rayleigh number (102≤Ra≤104), Hartmann number (0≤Ha≤20) and fractional order parameter (0<α<1) with respect to time.

It has been observed that the fractional order parameter α governs the characteristics of entropy generation and heat transfer within the selected range of parameters. The Bejan number associated with heat transfer (Be_ht), fluid friction (Be_ff) and magnetic field (Be_mf) further demonstrate the dominance of flow irreversibilities. It becomes evident that the initial evolution state of streamlines, isotherms and local entropy varies according to the choice of α. Additionally, increasing Ra values from 10² to 10⁴ shows that the heat transfer rate increases by 123.8% for a square wavy enclosure, 7.4% for a triangle enclosure and 69.6% for an L-shape enclosure. Moreover, an increase in the value of Ha leads to a reduction in heat transfer rates and entropy generation. In this case, Bemf→1 shows the dominance of the magnetic field irreversibility in the total entropy generation.

Recently, fractional-order models have been widely used to express numerous physical phenomena, such as anomalous diffusion and dispersion in complex viscoelastic porous media. These models offer a more accurate representation of physical reality that classical models fail to capture; this is why they find a broad range of applications in science and engineering.

The fractional derivative model is used to illustrate the flow pattern, heat transfer and entropy-generating characteristics under the influence of a magnetic field. Furthermore, to the best of the author’s knowledge, a fractional-derivative-based mathematical model for the entropy generation phenomenon in complex porous enclosures has not been previously developed or studied.

The purpose of this paper is to investigate the impact of ultrasonic vibration (UV) and tool pin profile on mechanical properties and microstructural behaviour of AA7075-T651 and AA6061-T6 joints was analysed.

The joints were fabricated using three different tool pin profiles such as cylindrical, square and triangle. For each tool pin profile, two different UV powers of 1.5 kW and 2 kW were used.

On both the advancing and retreating sides of the weld, the thermo-mechanically affected zone has the lowest microhardness. In all joints, the tensile fracture locations match to the minimum hardness values. Field emission scanning electron microscope fractography of tensile tested specimens reveals heterogeneous modes of brittle, shear and ductile fracture. Three-point bending analysis was performed to determine the ductility and soundness of the weld joint. The acoustic softening effect of UV, as well as the static and dynamic ratio of tool pin profile, plays an important role in determining the material flow and mechanical behaviour of the joint.

Dissimilar aluminium joining fascinates many applications like aircraft, aerospace, automobiles, ship building and electronics, where fusion welding is a very intricate process because of the deviation in its physical and chemical properties.

From this study investigation, it is found that the square pin profiled tool with 2 kW UV power produces metallurgical defect-free and mechanically sound weld with maximum tensile strength, hardness and bending load of 297 MPa, 151HV and 3.82 kN, respectively.