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The purpose of the paper is to study natural convection within porous square and triangular geometries (design 1: regular isosceles triangle, design 2: inverted isosceles triangle) subjected to discrete heating with various locations of double heaters along the vertical (square) or inclined (triangular) arms.

Galerkin finite element method is used to solve the governing equations for a wide range of modified Darcy number, Da_m = 10⁻⁵–10⁻² with various fluid saturated porous media, Pr_m = 0.015 and 7.2 at a modified Rayleigh number, Ra_m = 10⁶ involving the strategic placement of double heaters along the vertical or inclined arms (types 1-3). Adaptive mesh refinement is implemented based on the lengths of discrete heaters. Finite element based heat flow visualization via heatlines has been adopted to study heat distribution at various portions.

The strategic positioning of the double heaters (types 1-3) and the convective heatline vortices depict significant overall temperature elevation at both Da_m = 10⁻⁴ and 10⁻² compared to type 0 (single heater at each vertical or inclined arm). Types 2 and 3 are found to promote higher temperature uniformity and greater overall temperature elevation at Da_m = 10⁻². Overall, the triangular design 2 geometry is also found to be optimal in achieving greater temperature elevation for the porous media saturated with various fluids (Pr_m).

Multiple heaters (at each side [left or right] wall) result in enhanced temperature elevation compared to the single heater (at each side [left or right] wall). The results of the current work may be useful for the material processing, thermal storage and solar heating applications.

The heatline approach is used to visualize the heat flow involving double heaters along the side (left or right) arms (square and triangular geometries) during natural convection involving porous media. The heatlines depict the trajectories of heat flow that are essential for thermal management involving larger thermal elevation. The mixing cup or bulk average temperature values are obtained for all types of heating (types 0-3) involving all geometries, and overall temperature elevation is examined based on higher mixing cup temperature values.

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.

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 this study is to numerically and experimentally investigate the natural convection heat transfer in flat plates and plates with square, trapezoidal and triangular corrugations.

This work is an extension of the previous studies by Verderio et al. (2021a, 2021b, 2021c, 2021d, 2022a). An experimental apparatus was built to measure the plates’ temperatures during the natural convection cooling process. Several physical parameters were evaluated through the experimental methodology. Free and open-source computational tools were used to simulate the experimental conditions and to quantitatively and qualitatively evaluate the thermal plume characteristics over the plates.

The numerical results were experimentally validated with reasonable accuracy in the range of studied RaLP for the different plates. Empirical correlations of Nu¯LPexp=f(RaLP), h¯conv=f(RaLP) and Nu¯LPexp⋅(A/AP)=f(RaLP), with good accuracy and statistical representativeness, were obtained for the studied geometries. The convective thermal efficiency of corrugated plates (Δη), as a function of RaLP, was also experimentally studied quantitatively. In agreement with the findings of Oosthuizen and Garrett (2001), the experimental and numerical results proved that the increase in the heat exchange area of the corrugations has a greater influence on the convective exchange and the thermal efficiency than the disturbances caused in the flow (which reduce h¯conv). The plate with trapezoidal corrugations presented the highest convective thermal efficiency, followed by the plates with square and triangular corrugations. It was also proved that the thermal efficiency of corrugated plates increases with RaLP.

The results demonstrate that corrugated surfaces have greater thermal efficiency than flat plates in heating and/or cooling systems by natural convection. This way, corrugated plates can reduce the dependence on auxiliary forced convection systems, with application in technological areas and Industry 4.0.

The empirical correlations obtained for the corrected Nusselt number and thermal efficiency for the corrugated plate geometries studied are original and unpublished, as well as the experimental validation of the developed three-dimensional numerical code.

The purpose of this paper is to assess the efficiency, effectiveness and performance of logistics companies in Singapore and Malaysia which are the growing logistics hubs in Asia by using a triangular data envelopment analysis (DEA). It also identifies various factors that significantly affect the efficiency, effectiveness and performance of the Singaporean and Malaysian logistics companies and proposes ways to improve their competitiveness.

First, this study employs a triangular DEA to evaluate the efficiency and effectiveness of the companies. Second, Tobit regression is used to explore the factors that affect logistics performance. Third, the managerial decision-making matrix is addressed and suggestions made to help logistics managers improve performance.

The results reveal that small firms, on average have more potential than the large ones. The results also demonstrate that investment influences firm performance significantly.

This paper is the first attempt to apply a triangular DEA-based approach by decomposing performance into efficiency and effectiveness for logistics companies in Singapore and Malaysia.

Zero-failure reliability testing aims at demonstrating whether the product has achieved the desired reliability target with zero failure and high confidence level at a given time. Incorporating accelerated degradation testing in zero-failure reliability demonstration test (RDT) facilitates early failure in high reliability items developed within short period of time to be able to survive in fiercely competitive market. The paper aims to discuss these issues.

The triangular cyclic stress uses one test chamber thus saving experimental cost. The parameters in model are estimated using maximum likelihood methods. The optimum plan consists in finding out optimum number of cycles, optimum specimens, optimum stress change point(s) and optimum stress rates.

The optimum plan consists in finding out optimum number of cycles, optimum specimens, optimum stress change point(s) and optimum stress rates by minimizing asymptotic variance of estimate of quantile of the lifetime distribution at use condition subject to the constraint that total testing or experimental cost does not exceed a pre-specified budget. Confidence intervals of the design parameters have been obtained and sensitivity analysis carried out. The results of sensitivity analysis show that the plan is robust to small deviations from the true values of baseline parameters.

For some highly reliable products, even accelerated life testing yields little failure data of units in a feasible amount of time. In such cases accelerated degradation testing is carried out, wherein the failure termed as soft failure is defined in terms of performance characteristic of the product exceeding its critical (threshold) value.

The authors make assessment on RMB valuation and to contribute to the fierce debate on this important issue, which is perceived to have a great effect on the improvement or deterioration in trade balance. A triangular analysis approach is put forward and empirical assessment is made. The paper aims to discuss these issues.

A triangular analysis approach based on no arbitrage conditions for three currencies, and causality and influence analysis.

First, it has been found that the movements in the RMB dollar exchange rate do influence the dollar euro exchange rate and the former do have a causality effect on the latter, in both the long run and the short term. Second, it is implied that the RMB is overvalued vis-à-vis the US dollar, as the analysis suggests that an overvalued euro vis-à-vis the US dollar would imply a kind of overvaluation of the RMB vis-à-vis the US dollar, and by any conventional measures the euro has appeared to be overvalued vis-à-vis the US dollar, especially in the months before the last financial crisis.

First, the peg of the RMB to the US dollar that undervalues the RMB vis-à-vis the US dollar will not help promote China's overall trade balance or export even if undervaluation of currencies can ever help improve nations' terms of trade. Second, no stability in RMB exchange rates can be claimed by pegging the RMB to the US dollar, as the exchange rate of the RMB vis-à-vis currencies other than the US dollar would be as volatile as that between the US dollar and the euro and other convertible currencies.

A new triangular analysis approach in international finance research. First, there is an advantage to adopt this seemingly simple analytical framework: it is highly reliable; no triangular arbitrage conditions have to be met even under exchange controls, whilst PPP may not hold even with flexible exchange rate regimes. Second, it does away with the thinking confined to small open economies that has dominated academic research for so long and is totally inapplicable to the RMB case.

The purpose of this research paper is to identify determinants influencing hotel room design now and in the future to offer hotel owners, hotel investors, architects and other partners involved in hotel planning, a framework regarding hotel room design 2030. Based both on theoretical foundations and empirical findings, guidelines for an innovative future hotel room design are evolved and represented by a triangular model.

A detailed analysis of basic and topic-related hotel management literature as well as of promising best practices of leading international hotel companies is supplemented by the evaluation of 27 expert interviews with hoteliers of varying hotel conceptions in Germany, Austria and Spain.

The paper presents qualitative as well as quantitative results of the applied methodology and leads to the emergence of a triangular model for an innovative future hotel room design approach.

Safety and security aspects (both physical and virtual) as well as sustainability as a limiting factor have not been further discussed within the model construction so far.

The theoretical findings and the emergent framework may be customized to the determining factors and specific needs of individual hotels, hotel consortia or hotel chains to meet the needs of hotel room design 2030.

This research paper offers guidelines beyond design aspects by considering target group priorities, technological innovation and economical aspects.

The purpose of this paper is to perform a numerical study for heat transfer through natural convection in the presence of a constant magnetic field in an incompressible steady nanofluid flow inside an isosceles triangular cavity.

For this flow problem, the left wall of the cavity subjected to uniform/nonuniform heat was considered, while right and bottom walls of the cavity were kept cold. The obtained equations were solved by using the Galerkin weighted residual technique. Results are computed for a wide range of parameters including Rayleigh number (Ra) (10^3 < Ra < 10^7), Hartman number (Ha) (0 < Ha < 60), and heat-generation/-absorption coefficient (q) (−10 < q < 10), while, Prandtl number (Pr) was kept fixed at 6.2. These computed results are presented in terms of stream functions, isotherms, Nusselt numbers and average Nusselt numbers through figures.

It is observed that, in case of uniform heating of the side wall, the strength of stream lines’ circulations increases with an increase in Ra and decreases with an increase in Ha. Similarly, by increasing heat-absorption coefficient q, an increase in the circulation strength is noted and the circulation cell moves towards the left wall in the presence of a heat sink (q < 0) and moves to the cold right wall in the presence of a heat source (q > 0). In the case of nonuniformly heated left wall in the presence of a heat source (q > 0), a higher-temperature gradient is observed in the cavity and isotherms are clustered to the left wall in the lower portion and to right wall in the upper portion; these appear to be straight and parallel to the x-axis near the bottom wall. On the other hand, the heat transfer rate along all the walls of the cavity is observed to be higher for smaller values of q. Whereas, Nusselt number along the bottom wall (Nu-B) increases with an increase in the values of x, while, that along the left wall (Nu-L) first increases and then decreases. But Nusselt number along the right wall (Nu-R) is found to be qualitatively opposite to Nu-L with an increase in distance x. Whereas, average Nusselt number increases with an increase in Rayleigh number Ra and heat-generation/-absorption coefficient q.

The problem is formulated for an incompressible flow; viscous dissipation has been neglected, negligible induced magnetic field has been considered and local thermal equilibrium has been considered.

Results presented in this paper are original and new for the effects of a uniform magnetic field on the natural convection of Cu–water nanofluid in a triangular cavity. Hence, this study is important for researchers working in the area of heat transfer in cavity flows involving the nanofluid to become familiar with the flow behavior and properties.

The purpose of this study is to increase the jet mixing effectiveness of Mach 1.6 axisymmetric jet using semi-circular corrugated triangular tabs (Tabs A, B and C), in which the locations of the semi-circular corrugations are varied along the leaned sides of the triangular tabs.

The tabs are fixed at the exit of the nozzle facing each other 180° apart. To quantify the jet mixing effectiveness of the semi-circular corrugated tabs, Pitot pressure measurements were carried out for the cases of over-expansion, marginally over-expansion and under-expansion levels of Mach 1.6 jet, along the jet centerline and the jet spread, along and normal to the tab axis.

The results exhibit that the semi-circular corrugated Tab A augments the jet mixing when compared to Tabs B and C. This impact in jet mixing is strongly due to the small-scale vortices shed from the tabs and the mixed effect of the corrugation locations and expansion ratio. The maximum percentage reduction in core length is about 73.6 per cent for the jet with semi-circular corrugated Tab A at NPR 5, whereas it is 71.4 and 67.1 per cent for Tabs B and C, respectively.

The reduction in core length of the jet with minimum thrust loss is obtained by controlling the jet used with semi-circular corrugated triangular tabs of equal blockage ratio 5.12 per cent with respect to the nozzle exit diameter.

The locations of the semi-circular corrugations varied systematically at the equally leaned sides of the triangular tab ensure the novelty of this study.