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Article
Publication date: 21 February 2020

Tanmay Basak

This paper aims to investigate the thermal performance involving larger heating rate, targeted heating, heating with least non-uniformity of the spatial distribution of…

151

Abstract

Purpose

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).

Design/methodology/approach

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.

Findings

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 (Ac) and a few maxima of average power occur for fixed values of Ac 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).

Practical implications

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.

Originality/value

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 10
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 13 June 2019

Debayan Das, Leo Lukose and Tanmay Basak

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…

Abstract

Purpose

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.

Design/methodology/approach

Galerkin finite element method is used to solve the governing equations for a wide range of modified Darcy number, Dam = 10−5–10−2 with various fluid saturated porous media, Prm = 0.015 and 7.2 at a modified Rayleigh number, Ram = 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.

Findings

The strategic positioning of the double heaters (types 1-3) and the convective heatline vortices depict significant overall temperature elevation at both Dam = 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 Dam = 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 (Prm).

Practical implications

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.

Originality/value

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 14 November 2019

Leo Lukose and Tanmay Basak

The purpose of this paper is to study thermal (natural) convection in nine different containers involving the same area (area= 1 sq. unit) and identical heat input at the…

Abstract

Purpose

The purpose of this paper is to study thermal (natural) convection in nine different containers involving the same area (area= 1 sq. unit) and identical heat input at the bottom wall (isothermal/sinusoidal heating). Containers are categorized into three classes based on geometric configurations [Class 1 (square, tilted square and parallelogram), Class 2 (trapezoidal type 1, trapezoidal type 2 and triangle) and Class 3 (convex, concave and triangle with curved hypotenuse)].

Design/methodology/approach

The governing equations are solved by using the Galerkin finite element method for various processing fluids (Pr = 0.025 and 155) and Rayleigh numbers (103 ≤ Ra ≤ 105) involving nine different containers. Finite element-based heat flow visualization via heatlines has been adopted to study heat distribution at various sections. Average Nusselt number at the bottom wall ( Nub¯) and spatially average temperature (θ^) have also been calculated based on finite element basis functions.

Findings

Based on enhanced heating criteria (higher Nub¯ and higher θ^), the containers are preferred as follows, Class 1: square and parallelogram, Class 2: trapezoidal type 1 and trapezoidal type 2 and Class 3: convex (higher θ^) and concave (higher Nub¯).

Practical implications

The comparison of heat flow distributions and isotherms in nine containers gives a clear perspective for choosing appropriate containers at various process parameters (Pr and Ra). The results for current work may be useful to obtain enhancement of the thermal processing rate in various process industries.

Originality/value

Heatlines provide a complete understanding of heat flow path and heat distribution within nine containers. Various cold zones and thermal mixing zones have been highlighted and these zones are found to be altered with various shapes of containers. The importance of containers with curved walls for enhanced thermal processing rate is clearly established.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 October 2005

R. Sharma and O.P. Sha

To focus on grid generation which is an essential part of any analytical tool for effective discretization.

Abstract

Purpose

To focus on grid generation which is an essential part of any analytical tool for effective discretization.

Design/methodology/approach

This paper explores the application of the possibility of unstructured triangular grid generation that deals with derivationally continuous, smooth, and fair triangular elements using piecewise polynomial parametric surfaces which interpolate prescribed R3 scattered data using spaces of parametric splines defined on R2 triangulations in the case of surfaces in engineering sciences. The method is based upon minimizing a physics‐based certain natural energy expression over the parametric surface. The geometry is defined as a set of stitched triangles prior to the grid generation. As for derivational continuities between the two triangular patches C0 and C1 continuity or both, as per the requirements, has been imposed. With the addition of a penalty term, C2 (approximate) continuity can also be achieved. Since, in this work physics‐based approach has been used, the grid is analyzed using intersection curves with three‐dimensional planes, and intrinsic geometric properties (i.e. directional derivatives), for derivational continuity and smoothness.

Findings

The triangular grid generation that deals with derivationally continuous, smooth, and fair triangular elements has been implemented in this paper for surfaces in engineering sciences.

Practical implications

This paper deals with the important problem of grid generation which is an essential part of any analytical tool for effective discretization. And, the examples to demonstrate the theoretical model of this paper have been chosen from different branches of engineering sciences. Hence, the results of this paper are of practical importance for grid generation in engineering sciences.

Originality/value

The paper is theoretical with worked examples chosen from engineering sciences.

Details

Engineering Computations, vol. 22 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 7 July 2020

Ahamed Saleel C., Asif Afzal, Irfan Anjum Badruddin, T.M. Yunus Khan, Sarfaraz Kamangar, Mostafa Abdelmohimen, Manzoore Elahi M. Soudagar and H. Fayaz

The characteristics of fluid motions in micro-channel are strong fluid-wall surface interactions, high surface to volume ratio, extremely low Reynolds number laminar flow…

Abstract

Purpose

The characteristics of fluid motions in micro-channel are strong fluid-wall surface interactions, high surface to volume ratio, extremely low Reynolds number laminar flow, surface roughness and wall surface or zeta potential. Due to zeta potential, an electrical double layer (EDL) is formed in the vicinity of the wall surface, namely, the stern layer (layer of immobile ions) and diffuse layer (layer of mobile ions). Hence, its competent designs demand more efficient micro-scale mixing mechanisms. This paper aims to therefore carry out numerical investigations of electro osmotic flow and mixing in a constricted microchannel by modifying the existing immersed boundary method.

Design/methodology/approach

The numerical solution of electro-osmotic flow is obtained by linking Navier–Stokes equation with Poisson and Nernst–Planck equation for electric field and transportation of ion, respectively. Fluids with different concentrations enter the microchannel and its mixing along its way is simulated by solving the governing equation specified for the concentration field. Both the electro-osmotic effects and channel constriction constitute a hybrid mixing technique, a combination of passive and active methods. In microchannels, the chief factors affecting the mixing efficiency were studied efficiently from results obtained numerically.

Findings

The results indicate that the mixing efficiency is influenced with a change in zeta potential (ζ), number of triangular obstacles, EDL thickness (λ). Mixing efficiency decreases with an increment in external electric field strength (Ex), Peclet number (Pe) and Reynolds number (Re). Mixing efficiency is increased from 28.2 to 50.2% with an increase in the number of triangular obstacles from 1 to 5. As the value of Re and Pe is decreased, the overall percentage increase in the mixing efficiency is 56.4% for the case of a mixing micro-channel constricted with five triangular obstacles. It is also vivid that as the EDL overlaps in the micro-channel, the mixing efficiency is 52.7% for the given zeta potential, Re and Pe values. The findings of this study may be useful in biomedical, biotechnological, drug delivery applications, cooling of microchips and deoxyribonucleic acid hybridization.

Originality/value

The process of mixing in microchannels is widely studied due to its application in various microfluidic devices like micro electromechanical systems and lab-on-a-chip devices. Hence, its competent designs demand more efficient micro-scale mixing mechanisms. The present study carries out numerical investigations by modifying the existing immersed boundary method, on pressure-driven electro osmotic flow and mixing in a constricted microchannel using the varied number of triangular obstacles by using a modified immersed boundary method. In microchannels, the theory of EDL combined with pressure-driven flow elucidates the electro-osmotic flow.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 4 December 2018

Younes Menni, Ahmed Azzi and A. Chamkha

This paper aims to report the results of numerical analysis of turbulent fluid flow and forced-convection heat transfer in solar air channels with baffle-type attachments…

Abstract

Purpose

This paper aims to report the results of numerical analysis of turbulent fluid flow and forced-convection heat transfer in solar air channels with baffle-type attachments of various shapes. The effect of reconfiguring baffle geometry on the local and average heat transfer coefficients and pressure drop measurements in the whole domain investigated at constant surface temperature condition along the top and bottom channels’ walls is studied by comparing 15 forms of the baffle, which are simple (flat rectangular), triangular, trapezoidal, cascaded rectangular-triangular, diamond, arc, corrugated, +, S, V, double V (or W), Z, T, G and epsilon (or e)-shaped, with the Reynolds number changing from 12,000 to 32,000.

Design/methodology/approach

The baffled channel flow model is controlled by the Reynolds-averaged Navier–Stokes equations, besides the k-epsilon (or k-e) turbulence model and the energy equation. The finite volume method, by means of commercial computational fluid dynamics software FLUENT is used in this research work.

Findings

Over the range investigated, the Z-shaped baffle gives a higher thermal enhancement factor than with simple, triangular, trapezoidal, cascaded rectangular-triangular, diamond, arc, corrugated, +, S, V, W, T, G and e-shaped baffles by about 3.569-20.809; 3.696-20.127; 3.916-20.498; 1.834-12.154; 1.758-12.107; 7.272-23.333; 6.509-22.965; 8.917-26.463; 8.257-23.759; 5.513-18.960; 8.331-27.016; 7.520-26.592; 6.452-24.324; and 0.637-17.139 per cent, respectively. Thus, the baffle of Z-geometry is considered as the best modern model of obstacles to significantly improve the dynamic and thermal performance of the turbulent airflow within the solar channel.

Originality/value

This analysis reports an interesting strategy to enhance thermal transfer in solar air channels by use of attachments with various shapes

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 23 November 2020

Leo Lukose and Tanmay Basak

This paper aims to investigate the role of shapes of containers (nine different containers) on entropy generation minimization involving identical cross-sectional area…

Abstract

Purpose

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).

Design/methodology/approach

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 (Sψ and Sθ). Average Nusselt number ( Nub¯) and average dimensionless spatial temperature ( θ^) are also evaluated via the finite element basis sets.

Findings

Based on larger Nub¯, larger θ^ and optimal Stotal 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 Stotal) and concave (larger Nub¯). Containers with curved walls lead to enhance the thermal performance or efficiency of convection processes.

Practical implications

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.

Originality/value

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 Sψ (Sψ,max), Sθ (Sθ,max) and magnitude of Stotal 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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 2 November 2015

Si-feng Liu, Yingjie Yang, Zhi-geng Fang and Naiming Xie

The purpose of this paper is to present two novel grey cluster evaluation models to solve the difficulty in extending the bounds of each clustering index of grey cluster…

Abstract

Purpose

The purpose of this paper is to present two novel grey cluster evaluation models to solve the difficulty in extending the bounds of each clustering index of grey cluster evaluation models.

Design/methodology/approach

In this paper, the triangular whitenization weight function corresponding to class 1 is changed to a whitenization weight function of its lower measures, and the triangular whitenization weight function corresponding to class s is changed to a whitenization weight function of its upper measures. The difficulty in extending the bound of each clustering indicator is solved with this improvement.

Findings

The findings of this paper are the novel grey cluster evaluation models based on mixed centre-point triangular whitenization weight functions and the novel grey cluster evaluation models based on mixed end-point triangular whitenization weight functions.

Practical implications

A practical evaluation and decision problem for some projects in a university has been studied using the new triangular whitenization weight function.

Originality/value

Particularly, compared with grey variable weight clustering model and grey fixed weight clustering model, the grey cluster evaluation model using whitenization weight function is more suitable to be used to solve the problem of poor information clustering evaluation. The grey cluster evaluation model using endpoint triangular whitenization weight functions is suitable for the situation that all grey boundary is clear, but the most likely points belonging to each grey class are unknown; the grey cluster evaluation model using centre-point triangular whitenization weight functions is suitable for those problems where it is easier to judge the most likely points belonging to each grey class, but the grey boundary is not clear.

Details

Grey Systems: Theory and Application, vol. 5 no. 3
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 1 January 2007

J. Sun and S. Ekwaro‐Osire

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…

Abstract

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.

Details

Multidiscipline Modeling in Materials and Structures, vol. 3 no. 1
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 23 December 2015

Jinfeng Yu, Xiequan Liu and Xinhua Ni

Composite ceramic has the excellent properties at normal and high temperatures, especially when the structure of the composite eutectic is triangular symmetrical…

Abstract

Composite ceramic has the excellent properties at normal and high temperatures, especially when the structure of the composite eutectic is triangular symmetrical. Obviously, mechanical behavior and fracture properties of composite ceramic closely relates to the micro-structure of symmetrical triangular eutectic. In order to reveal the mechanical properties of eutectic composite ceramic, it is necessary to determine the intrinsic strength of triangular composite eutectic. Since the fiber and matrix of triangular symmetrical composite eutectic sharing a same covalent bond, the theoretical cohesion strength of symmetrical triangular eutectic was obtained by the combination-separation displacement of intrinsic bond. Basing on micro-structure plastic deformation before fracture of composite eutectic matrix, the dislocation pile-up model of eutectic composite ceramics was established. And then intrinsic bond fracture shear stress of triangular symmetrical composite eutectic was given by using the theory of dislocation pile-up. According to the macroscopic structure properties of triangular symmetrical composite eutectic and the distribution of stress field of composite eutectic, intrinsic strength of eutectic was obtained. The results shows that intrinsic strength of triangular symmetrical composite eutectic possessed clear size-dependence and the stress decreases with the increases of the diameter of fiber inclusions.

Details

World Journal of Engineering, vol. 12 no. 6
Type: Research Article
ISSN: 1708-5284

Keywords

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