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1 – 10 of 12This paper aims to investigate the thermal performance involving larger heating rate, targeted heating, heating with least non-uniformity of the spatial distribution of…
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.
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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…
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 (
Findings
Based on larger
Practical implications
Comparison of entropy generation, intensity of thermal mixing (
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.
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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…
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 (
Findings
Based on enhanced heating criteria (higher
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.
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Damodara Priyanka, Pratibha Biswal and Tanmay Basak
This study aims to elucidate the role of curved walls in the presence of identical mass of porous bed with identical heating at a wall for two heating objectives: enhancement of…
Abstract
Purpose
This study aims to elucidate the role of curved walls in the presence of identical mass of porous bed with identical heating at a wall for two heating objectives: enhancement of heat transfer to fluid saturated porous beds and reduction of entropy production for thermal and flow irreversibilities.
Design/methodology/approach
Two heating configurations have been proposed: Case 1: isothermal heating at bottom straight wall with cold side curved walls and Case 2: isothermal heating at left straight wall with cold horizontal curved walls. Galerkin finite element method is used to obtain the streamfunctions and heatfunctions associated with local entropy generation terms.
Findings
The flow and thermal maps show significant variation from Case 1 to Case 2 arrangements. Case 1 configuration may be the optimal strategy as it offers larger heat transfer rates at larger values of Darcy number, Dam. However, Case 2 may be the optimal strategy as it provides moderate heat transfer rates involving savings on entropy production at larger values of Dam. On the other hand, at lower values of Dam (Dam ≤ 10−3), Case 1 or 2 exhibits almost similar heat transfer rates, while Case 1 is preferred for savings of entropy production.
Originality/value
The concave wall is found to be effective to enhance heat transfer rates to promote convection, while convex wall exhibits reduction of entropy production rate. Comparison between Case 1 and Case 2 heating strategies enlightens efficient heating strategies involving concave or convex walls for various values of Dam.
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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.
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Madhuchhanda Bhattacharya and Tanmay Basak
A few earlier studies presented infeasible heatline trajectories for natural convection within annular domains involving an inner circular cylinder and outer square/circular…
Abstract
Purpose
A few earlier studies presented infeasible heatline trajectories for natural convection within annular domains involving an inner circular cylinder and outer square/circular enclosure. The purpose of this paper is to revisit and illustrate the correct heatline trajectories for various test cases.
Design/methodology/approach
Galerkin finite element based methodology and space adaptive grid have been used to simulate natural convective flows within the annular domains. The prediction of heatlines involves derivatives at the nodes, which are evaluated based on finite element basis functions and contributions from neighboring elements.
Findings
The heatlines in the earlier work indicate infeasible heat flow paths such as heat flow from one portion to the other of isothermal hot walls and heat flow across the adiabatic walls. Current results illustrate physically consistent heat flow paths involving perpendicularly emerging heatlines from hot to cold walls for conductive transport, long heat flow paths around the closed-loop heatline cells for convective transport and parallel layout of heatlines to the adiabatic walls. Results also demonstrate complex heatlines involving multiple flow vortices and complex flow structures.
Originality/value
Current work translates heatfunctions from energy flux vectors, which are determined by using basis sets. This work demonstrates the expected heatline trajectories for various scenarios involving conductive and convective heat transport within enclosures with an inner hot object as a first attempt, and the results are precursors for the understanding of energy flow estimates.
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The purpose of this paper is to address various works on mixed convection and proposes 10 unified models (Models 1–10) based on various thermal and kinematic conditions of the…
Abstract
Purpose
The purpose of this paper is to address various works on mixed convection and proposes 10 unified models (Models 1–10) based on various thermal and kinematic conditions of the boundary walls, thermal conditions and/ or kinematics of objects embedded in the cavities and kinematics of external flow field through the ventilation ports. Experimental works on mixed convection have also been addressed.
Design/methodology/approach
This review is based on 10 unified models on mixed convection within cavities. Models 1–5 involve mixed convection based on the movement of single or double walls subjected to various temperature boundary conditions. Model 6 elucidates mixed convection due to the movement of single or double walls of cavities containing discrete heaters at the stationary wall(s). Model 7A focuses mixed convection based on the movement of wall(s) for cavities containing stationary solid obstacles (hot or cold or adiabatic) whereas Model 7B elucidates mixed convection based on the rotation of solid cylinders (hot or conductive or adiabatic) within the cavities enclosed by stationary or moving wall(s). Model 8 is based on mixed convection due to the flow of air through ventilation ports of cavities (with or without adiabatic baffles) subjected to hot and adiabatic walls. Models 9 and 10 elucidate mixed convection due to flow of air through ventilation ports of cavities involving discrete heaters and/or solid obstacles (conductive or hot) at various locations within cavities.
Findings
Mixed convection plays an important role for various processes based on convection pattern and heat transfer rate. An important dimensionless number, Richardson number (Ri) identifies various convection regimes (forced, mixed and natural convection). Generalized models also depict the role of “aiding” and “opposing” flow and combination of both on mixed convection processes. Aiding flow (interaction of buoyancy and inertial forces in the same direction) may result in the augmentation of the heat transfer rate whereas opposing flow (interaction of buoyancy and inertial forces in the opposite directions) may result in decrease of the heat transfer rate. Works involving fluid media, porous media and nanofluids (with magnetohydrodynamics) have been highlighted. Various numerical and experimental works on mixed convection have been elucidated. Flow and thermal maps associated with the heat transfer rate for a few representative cases of unified models [Models 1–10] have been elucidated involving specific dimensionless numbers.
Originality/value
This review paper will provide guidelines for optimal design/operation involving mixed convection processing applications.
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Pratibha Biswal and Tanmay Basak
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…
Abstract
Purpose
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.
Design/methodology/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 (
Findings
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
Practical implications
The results may be useful for the material processing applications.
Originality/value
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.
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Pratibha Biswal and Tanmay Basak
This paper is aimed to study natural convection in enclosures with curved (concave and convex) side walls for porous media via the heatline-based heat flow visualization approach.
Abstract
Purpose
This paper is aimed to study natural convection in enclosures with curved (concave and convex) side walls for porous media via the heatline-based heat flow visualization approach.
Design/methodology/approach
The numerical scheme involving the Galerkin finite element method is used to solve the governing equations for several Prandtl numbers (Prm) and Darcy numbers (Dam) at Rayleigh number, Ram = 106, involving various wall curvatures. Finite element method is advantageous for curved domain, as the biquadratic basis functions can be used for adaptive automated mesh generation.
Findings
Smooth end-to-end heatlines are seen at the low Dam involving all the cases. At the high Dam, the intense heatline cells are seen for the Cases 1-2 (concave) and Cases 1-3 (convex). Overall, the Case 1 (concave) offers the largest average Nusselt number (
Practical implications
Thermal management for flow systems involving curved surfaces which are encountered in various practical applications may be complicated. The results of the current work may be useful for the material processing, thermal storage and solar heating applications
Originality/value
The heatline approach accompanied by energy flux vectors is used for the first time for the efficient heat flow visualization during natural convection involving porous media in the curved walled enclosures involving various wall curvatures.
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Behrouz Mozafari, Ali Akbar Abbasian Arani, Ghanbar Ali Sheikhzadeh and Mahmoud Salimi
The purpose of this paper is to study the effects of using different Brownian models on natural and mixed convection fluid flow and heat transfer inside the square enclosure…
Abstract
Purpose
The purpose of this paper is to study the effects of using different Brownian models on natural and mixed convection fluid flow and heat transfer inside the square enclosure filled with the AlOOH–water nanofluid.
Design/methodology/approach
Due to fulfill of this demand, five different models for the effective thermal conductivity and viscosity of the nanofluid are considered. The following results are presented for the Ra=107 to 1010 and Ri=0.01 to 100, whereas the volume fraction of the nanoparticles is varied from φ = 0.01 to 0.04.
Findings
According to the obtained results, increasing of Rayleigh number and reduction of Richardson number leads to the higher values of the average Nusselt number and entropy generation. Also, it is realized that, variation trend of the average Nusselt number and entropy generation in all cases is increasing by growing the volume fraction. It is found that the obtained average Nusselt numbers and entropy generations with Koo and Kleinstreuer are the highest among all the studied cases, and it is followed by Patel, Vajjha and Das, Corcione and Maxwell–Brinkman models, respectively.
Originality/value
Based on the results of present investigation, the Nusselt number difference predicted between the Maxwell–Brinkman model (as constant-property model) and Koo and Kleinstreuer model is about 7.84 per cent at 0.01 per cent volume fraction and 5.47 per cent at 0.04 per cent volume fraction for the Rayleigh number equal to 107. The entropy generation difference predicted between the two above studied model is about 8.05 per cent at 0.01 per cent volume fraction and 5.86 per cent at 0.04 per cent volume fraction for the Rayleigh number equal to 107. It is observed that using constant-property model has a significant difference in the obtained results with the results of other variable-property models.
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