High-conductivity Inserts Research Articles

Photovoltaic System Efficiency Enhancement with Thermal Management: Phase Changing Materials (PCM) with High Conductivity Inserts

- The electrical conversion efficiency of photovoltaic cells from solar radiation heavily depends on the cell temperature. Here we propose a novel thermal management strategy to keep the cell temperature in the same order to attain maximum efficiency. The comparative study presented is based on four solar module configurations: a conventional photovoltaic module (PVT module), a conventional module with PCM layer underneath (PVT/PCM-I), a configuration where fins embedded into PCM (PVT/PCM-II), and configuration where the bottom of the PCM layer in PVT/PCM-II was cooled via convection (PVT/PCM-III). The developed 3D numerical model is solved via ANSYS software involving the solar ray tracing radiation model for incident solar radiations and a transient melting-solidification thermo-fluid model to cater for PCM phase transition. Results from the numerical model were validated via a comparison of experimentally studied results presented in the literature. After 120 minutes, results show that the conversion efficiency of PV cells becomes 16.84%, 18.65%, 18.83%, and 18.98% after 120 minutes for PVT module, PVT/PCM-I, PVT/PCM-II, and PVT/PCM-III with an inlet velocity of 3m/s, respectively. For the respective configurations, the specific electrical power per unit area produced reaches 75.30W/m2, 83.39W/m2, 84.19W/m2, and 89.42W/m2 for solar radiation of 540W/m2 and 26°C ambient temperature. Results reveal that a 5 mm increase in the fin height for PVT/PCM-II results in a 0.22% increase in efficiency while a 0.5m/s increase in the inlet velocity of the cooling air for PVT/PCM-III results in about 0.06% increase in efficiency.

Design and Optimization of a Composite Heat Spreader to Improve the Thermal Management of a Three-Dimensional Integrated Circuit

Abstract This study establishes a numerical investigation of the optimal distribution of a limited amount of high thermal conductivity material to enhance the heat removal from 3D integrated circuits, IC. The structure of the heat spreader is designed as a composite of high thermal conductivity (Boron Arsenide) and moderate thermal conductivity (copper) materials. The volume ratio of high-conductivity inserts to the total volume of the spreader is set at a fixed pertinent ratio. Two different boundary conditions of constant and variable temperature are considered for the heat sink. To examine the impact of adding high-conductivity inserts on the cooling performance of the heat spreader, various patterns of the single and double ring inserts are studied. A parametric study is performed to find the optimal location of the rings. Moreover, the optimal distribution of the high-conductivity material between the inner and outer rings is found. The results show that for the optimal conditions, the maximum temperature of the 3D IC is reduced up to 10%; while at the same time, the size of the heat sink and heat spreader can be diminished by as much as 200%.

Evolutionary design of composite structures for thermal conductance and strength

This is a study of the evolving design of a composite material with inserts that are free to be configured and distributed through the base material. Several classes of shapes of inserts are considered competitively: parallel plates, staggered plates, forks, chains and diamonds. The architecture evolves in two directions (with two objectives), high thermal conductance and mechanical strength (stiffness). Relative to the base material, the inserts have higher thermal conductivity and lower modulus of elasticity. As a consequence, better architectures emerge from the tradeoff between thermal conductance and strength, for example, chain and diamond shaped inserts. The two-objective performance further improves when the inserts are distributed nonuniformly through the base material, such that the high conductivity inserts are not placed in the regions with the highest stresses.

Thermal and mechanical design of tangential hybrid microchannel and high-conductivity inserts for cooling of disk-shaped electronic components

The efficiency of electronic equipment is the cornerstone of technology development. Thermal conditions significantly affect the performance of electronic components. Moreover, mechanical strength, size, and mass are the parameters that impose some limitations. Thus, they should be considered in the high tech industry. Therefore, it is needed to examine both mechanical and thermal behaviors simultaneously. Microchannel and inserted high-conductivity materials are two usual cooling approaches. To improve cooling efficiency and mechanical strength, a new method named Hybrid is introduced here. This method is a combination of microchannel and high-conductivity methods. In this study, the consumed energy, the conductivity ratio of the material with high conductivity, peak temperature, and maximum Von Mises stress have been investigated and analyzed. For the hybrid method, the peak temperature and stress were minimized regarding the volume of high-conductivity change in the tangential direction of the duct. The results showed that the tangential hybrid method could decrease the peak temperature and peak Von Mises stress, up to 40% and 34% in comparison to the microchannel and high-conductivity inserts method.

Optimal mechanical and thermal architecture of high-conductivity inserts for cooling an electronic piece

Highly conductive inserts improve heat removal from electronic components remarkably; however, using these inserts is associated with a side effect: the mechanical strength deterioration of the piece. In this research, based on the constructal theory, the architecture of these inserts is optimized in such a way that the lowest maximum temperature and highest mechanical strength of the disc-shaped piece are achieved. Here, three patterns for the configuration of inserts embedded in the disc are studied, namely radial, dendritic with one level of pairing and dendritic with two levels of pairing. The total amount of high-conductivity inserts material is fixed, while the geometrical parameters of the inserts like length, the bifurcating locations and the angles of bifurcations are considered as degrees of freedom. It was observed that when 16 inserts were invoked, maximum temperature and stress were minimized. Results showed that changing the structure from radial to dendritic with one bifurcation causes a decrease in the maximum temperature and stress of about 17% and 3.2%, respectively. Also, it was seen that increasing the complexity of the structure by increasing the number of bifurcations from one to two leads to 5.6% reduction and 1% increment in minimal maximum temperature and optimal maximum stress, respectively.

Snowflake shaped high-conductivity inserts for heat transfer enhancement

Here, we show numerically how thermal resistance in a two-dimensional domain with a point heat source can be reduced with embedded high-conductivity snowflake shaped pathways. The external shape of the domain is square, and its boundaries are heat sink. The geometry of the inserted pathways which corresponds to the minimum Tmax was uncovered with the consideration of Constructal Theory, i.e. the constructal design. In the first assembly, number of mother (big) fins was uncovered as the area fraction increases. The results of the first assembly indicate that the increase in number of mother fins does not increase heat transfer after a limit number for the fins. After uncovering the mother pathway geometry corresponding to the minimum Tmax, the daughter (small) fins inserted at the tip of them, i.e. second assembly. In the second assembly, the fin ratios, small fin location and angle were discovered when the area fraction is fixed. In addition, in the third assembly, larger daughter fins were attached to mother fins. The results of the second and third assemblies document what should be the geometric length scales and the number of daughter fins in order to minimize Tmax. The constructal design uncovered is similar to the shape of snowflakes. Therefore, the results also uncover snowflakes correspond to the designs with minimum thermal conductivity, i.e., not mimicking the nature but understanding it with physics.

Optimum interfaces that maximize the heat transfer rate between two conforming conductive media

We consider conjugate heat transfer between two conductive and conforming media, with isothermal boundary conditions on the exposed surfaces, and continuity of the temperature and the heat flux along their interface. We address the inverse problem of finding the shape of the interface such that the heat transfer rate is maximized. We formulate three isoperimetric, shape optimization problems associated with three different applications: i) the optimal shape of corrugations (surface “roughness”), ii) the optimal shape of high conductivity inserts (inverted fins) and iii) the optimal shape of high conductivity fins. As expected, the optimal geometries have the shape of an extension of the high conductivity material into the low conductivity material. For the case of corrugations and inserts, the optimum shapes are triangular for small perimeters; for large perimeters and thick slabs they are elliptical and tend to cover the whole width/period of the domain. Optimum fins are characterized by long, shallow valleys and deep, narrow protrusions of the high conductivity material. For the parameters considered in this study, the width of the protrusion is approximately one quarter of the period.

Constructal structures with and without high-conductivity inserts for self-cooling

Constructal structures with and without high-conductivity inserts for self-cooling

Constructal structures with and without high-conductivity inserts for self-cooling

Constructal structures with and without high-conductivity inserts for self-cooling

Constructal Vascular Structures With High-Conductivity Inserts for Self-Cooling

In this paper, we show how a heat-generating domain can be cooled with embedded cooling channels and high-conductivity inserts. The volume of cooling channels and high-conductivity inserts is fixed, so is the volume of the heat-generating domain. The maximum temperature in the domain decreases with high-conductivity inserts even though the coolant volume decreases. The locations and the shapes of high-conductivity inserts corresponding to the smallest peak temperatures for different number of inserts are documented, x = 0.6L and D/B = 0.11 with two rectangular inserts. We also document how the length scales of the inserts should be changed as the volume fraction of the coolant volume over the high-conductivity material volume varies. The high-conductivity inserts should be placed nonequidistantly in order to provide the smallest peak temperature in the heat-generating domain. In addition, increasing the number of the inserts after a limit increases the peak temperature, i.e., this limit is eight number of inserts for the given conditions and assumptions. This paper shows that the overall thermal conductance of a heat-generating domain can be increased by embedding high-conductivity material in the solid domain (inverted fins) when the domain is cooled with forced convection, and the summation of high-conductivity material volume and coolant volume is fixed.

The natural emergence of asymmetric tree-shaped pathways for cooling of a non-uniformly heated domain

Here, we show that the peak temperature on a non-uniformly heated domain can be decreased by embedding a high-conductivity insert in it. The trunk of the high-conductivity insert is in contact with a heat sink. The heat is generated non-uniformly throughout the domain or concentrated in a square spot of length scale 0.1 L0, where L0 is the length scale of the non-uniformly heated domain. Peak and average temperatures are affected by the volume fraction of the high-conductivity material and by the shape of the high-conductivity pathways. This paper uncovers how varying the shape of the symmetric and asymmetric high-conductivity trees affects the overall thermal conductance of the heat generating domain. The tree-shaped high-conductivity inserts tend to grow toward where the heat generation is concentrated in order to minimize the peak temperature, i.e., in order to minimize the resistances to the heat flow. This behaviour of high-conductivity trees is alike with the root growth of the plants and trees. They also tend to grow towards sunlight, and their roots tend to grow towards water and nutrients. This paper uncovers the similarity between biological trees and high-conductivity trees, which is that trees should grow asymmetrically when the boundary conditions are non-uniform. We show here even though all the trees have the same objectives (minimum flow resistance), their shape should not be the same because of the variation in boundary conditions. To sum up, this paper shows that there is a high-conductivity tree design corresponding to minimum peak temperature with fixed constraints and conditions. This result is in accord with the constructal law which states that there should be an optimal design for a given set of conditions and constraints, and this design should be morphed in order to ensure minimum flow resistances as conditions and constraints change.

Optimum isothermal surfaces that maximize heat transfer

In this paper we formulate three inverse design, isoperimetric, shape optimization problems leading to optimum geometries that maximize the heat transfer rate. We examine both semi-infinite and finite, two-dimensional domains. The former is bounded from below by an isothermal periodic boundary while a constant heat flux is assumed at the far field; the latter is bounded by a periodic boundary at the bottom and a flat isothermal surface at the top. The objective is to find the optimum shape of the periodic boundary such that the heat transfer rate is maximized. We consider three different applications: (i) the optimal shape of corrugations (surface “roughness”), (ii) the optimal shape of high conductivity inserts (inverted fins) and (iii) the optimal shape of high conductivity fins. As expected, the optimum geometries have the shape of a depression, however the details of the geometries are quite interesting. In particular, the shape optimization problem associated with the inverse design of a high-conductivity extended surface/fin has led to some interesting results, with practical implications.

Disc cooled with high-conductivity inserts that extend inward from the perimeter

This paper considers the fundamental problem of how to shape rectangular high-conductivity inserts (fins) that are mounted on the rim of and protrude into a disc-shaped body that generates heat. The objective is to minimize the global thermal resistance by optimizing geometrically the distribution of a fixed amount of high-conductivity material through the material of lower conductivity. In addition to the fin geometry, three other design parameters are considered: the ratio between the high conductivity and low conductivity k ̃ , the relative amount of high conductivity material φ, and the number of sectors of the disc-shaped body, N. It is shown analytically and numerically that the thermal resistance can be minimized with respect to the fin aspect ratio, λ. The optimized geometry and performance are reported graphically as functions of k ̃ , φ and N. Good agreement is found between the analytical solution and the numerical results.

Constructal Placement of High-Conductivity Inserts in a Slab: Optimal Design of “Roughness”

This paper addresses the fundamental problem of how to facilitate the flow of heat across a conducting slab heated from one side. Available for distribution through the system is a small amount of high-conductivity material. The constructal method consists of optimizing geometrically the distribution of the high-conductivity material through the material of lower conductivity. Two-dimensional distributions (plate inserts) and three-dimensional distributions (pin inserts) are optimized based on the numerical simulation of heat conduction in a large number of possible configurations. Results are presented for the external and internal features of the optimized architectures: spacings between inserts, penetration distances, tapered inserts and constant-thickness inserts. The use of optimized pin inserts leads consistently to lower global thermal resistances than the use of plate inserts. The side of the slab that is connected to the high-conductivity intrusions is in effect a “rough” surface. This paper shows that the architecture of a rough surface can be optimized for minimum global contact resistance. Roughness can be designed.

Enhancing heat transfer in parallel-plate channels by using porous inserts

In the present work, transient forced convection in the developing region of parallel-plate ducts is numerically investigated. A high-thermal conductivity porous substrate is attached to the inner wall of one plate in order to enhance the heat transfer characteristics of the flow under consideration. The Darcy–Brinkman–Forchheimer model is used to model the flow inside the porous domain. The present study reports the effect of several operating parameters on the flow hydrodynamics and thermal characteristics. Mainly, the current study demonstrates the effects of porous layer thickness, Darcy number, thermal conductivity ratio, and microscopic inertial coefficient on the thermal performance of the present flow. It is found that the highest Nusselt Number is achieved at fully porous duct. Results show that for Darcy number less than 10 −4, the effect of microscopic inertial coefficient can be eliminated while for large microscopic inertial coefficient, higher than 10 3, the effect of Darcy number is observed to be insignificant. Heat transfer can be enhanced by: (1) using high thermal conductivity inserts, (2) decreasing Darcy number, and (3) increasing microscopic inertial coefficient. Also, the study shows that in the developing region, Darcy number and microscopic inertial coefficient have higher effect on the thermal and hydrodynamic behavior of the flow than that in the fully developed region.

The use of high thermal conductivity inserts to improve the cooling of cooked foods

The cooling of many cooked foods is limited by the rate at which heat can flow from the centre to the surface of the product. Investigations have studied the benefit of using high heat transfer devices including heat pipes, thermosyphons and solid metal rods to increase the cooling rate of hot foods. Cylinders of heated mashed potato, with or without high conductivity inserts, were cooled from 70°C to 10°C and 3°C in a blast chill room operating at 0°C. The inserts reduced the cooling time between 6% and 29% with heat pipes producing the greatest effect. The results show that heat pipes, thermosyphons and other heat transfer devices are a viable way for improving the cooling rate and uniformity of cooling of foods. The inserts have the potential to produce significant time saving and improvements in food quality and safety.

Three-dimensional tree constructs of “constant” thermal resistance

This article extends to three-dimensional heat flow the constructal method of minimizing geometrically the thermal resistance between a heat-generating volume and one point. Optimized is the geometry of each volume element, and the shape and distribution of high-conductivity inserts. The new feature is the maximization of the amount of heat-generating material that operates at temperatures close to the hot-spot level (Tmax). Volume elements and subsequent constructs acquire optimal shapes where all the external surfaces are isothermal at Tmax. The same, constant thermal resistance separates each surface point (Tmax) and the common heat-sink point (Tmin). The optimized architecture is pine-cone-like, with high-conductivity nerves and low-conductivity filling (and heat-generating) material. The similarities between the constant-resistance structures and the three-dimensional tree networks found in nature are discussed. The analogy between evolutionary flow systems and evolutionary mechanical support systems is reasoned based on the same (constructal) principle of pursuing objective (purpose) subject to global and local constraints.

Conduction trees with spacings at the tips

This paper documents two methods of improving the performance of volume-to-point tree networks for two-dimensional heat conduction. These improvements are offered relative to the design produced by the constructal method, in which optimized volume elements (building blocks) are presented and grouped into larger constructs, which are also optimized. The first improvement is that each construct is optimized with respect to all its degrees of freedom: unlike in the constructal method, the optimized features of the smaller building blocks are not preserved during the optimization of the construct. The second improvement opportunity is that spacings are allowed between the facing tips of neighboring high-conductivity inserts. All such spacings are optimized. Another new direction pursued in this paper is the optimization of tree networks that must fill a volume with prescribed external shape (e.g., square, or disk). The designs optimized numerically in this paper lower the volume-to-point resistance beyond the levels achieved based on the constructal method, and bring the shape of the conduction tree closer to the shapes seen in nature.

Constructal trees of circular fins for conductive and convective heat transfer

This paper extends to three dimensions and to convective heat transfer the constructal method of minimizing the thermal resistance between a volume and one point. In the first part of the paper, the heat flow mechanism is conduction, and the heat generating volume is occupied by low conductivity material ( k 0) and high conductivity inserts ( k p). At the elemental-volume level the inserts are shaped as constant-thickness disks. In the first assembly the disks are mounted on a common stem of k p material. The internal and external geometric aspect ratios of the elemental volume and the first assembly are optimized numerically subject to volume constraints. In the second part of the paper the interstitial spaces once occupied by k 0 material are bathed by forced convection. The k p inserts function as ‘fin material’, and the first assembly becomes a fin bush with cylindrical symmetry. The geometry of the first assembly is optimized subject to total volume and solid volume constraints. The optimal number of circular fins, the optimal external shape of the assembly, the optimal ratio of the central stem diameter divided by the circular fin thickness, and the maximized global conductance of the assembly are reported as functions of the external flow (pressure drop number) and volume fraction of fin material. It is also shown that the optimization sequence can be shortened (albeit with approximate results) by adopting at the first-assembly level the internal geometric aspect ratios that were optimized independently at the elemental-volume level.

Constructal tree networks for the time-dependent discharge of a finite-size volume to one point

This paper shows that the time needed to discharge a volume to a concentrated sink can be minimized by making appropriate changes in the geometry of the flow path. The time-dependent flow of heat between a volume and one point is chosen for illustration, however, the same geometric optimization method (the constructal principle) holds for other transport processes (fluid flow, mass transfer, conduction of electricity). There are two classes of geometric degrees of freedom in designing the flow path: the external shape of the volume, and the distribution (amount, location, orientation) of high-conductivity inserts that facilitate the volumetric collection of the discharge. The optimization of flow path geometry is executed in a sequence of steps that starts with the smallest volume elements and proceeds toward larger and more complex volume sizes (first constructs, second constructs, etc.). Every geometric feature is the result of minimizing the time of discharge, or the resistance in volume-to-point flow. The innermost details of the structure have only a minor effect on the minimized time of discharge. The high-conductivity inserts come together into a tree-network pattern which is the result of a completely deterministic principle. The interstices are equally important in this optimal design, as they are occupied by the low-conductivity material in which the energy charge was stored initially. The paper concludes with a discussion of the relevance on this deterministic principle—the constructal law—to predicting structure in natural flow, and to understanding why the geometry of nature is not fractal.