Amount Of High Conductivity Material Research Articles

Topology Optimization for Diffusive Heat Transfer in a Domain with Internal Heat Generation using Optimality Criteria

The standard volume to point heat conduction problem is used to determine the optimal topology that maximises the heat transfer. Unlike the constructed theory, the present investigation considers heat dissipation potential function as the objective function, whose gradient field is taken as the criterion for allocation of the limited amount of high conductivity material over the domain. The considered domain is rectangular in geometry, where all its sides are insulated except a centrally located patch on one of the sides, which is maintained at a constant temperature. FEM is used to compute the temperature and it is supplied to the topology optimization algorithm to determine the distribution of material with varied thermal conductivity over the domain. Grid independency is performed for five different grid sizes varying from 10x10 to 90x90. The variation of computation time and objective function with mesh refinement is reported.

Constructal entransy dissipation rate minimization of a disc

Disc cooling problem is optimized by taking entransy dissipation rate minimization as optimization objective. The non-dimensional mean temperature difference of the disc cooling model with radial high conducting fins inserted is deduced. The effects of the fin geometry, the fin aspect ratio, the ratio between the high conductivity and low conductivity, the relative amount of high conductivity material and the number of high conducting fins on the entransy dissipation rate of disc cooling are analyzed. The optimization results show that the high conducting fin should be extended to the centre of circle as the heat transfer effect of the high conducting fins is improved, and there exists an optimal fin aspect ratio corresponding to minimum entransy dissipation rate for different high conducting effects of the fin, and the number of high conducting fins has a slight effect on the entransy dissipation rate. Comparison with those for maximum temperature difference minimization shows that the constructs based on entransy dissipation rate minimization are different from those based on maximum temperature difference minimization, but the optimal constructal shape changing potentials of the number of fins and the relative amount of high conductivity material are similar.

Homogenization of temperature field and temperature gradient field

The homogenization of temperature field and temperature gradient field are very important for many devices, systems and equipments, such as satellites and electronic devices. This paper discusses the distribution optimization of the limited high conductivity material with the simulated annealing algorithm to homogenize the temperature field in a two-dimensional heat conduction problem. At the same time, the temperature gradient field is homogenized with the bionic optimization method. The results show that the two optimization targets are consistent to some extent, while the bionic optimization method could save much computing time. In addition, there are threshold values for the amount of high conductivity material and the ratio of the high conductivity to the low conductivity beyond which further increasing these values brings very little improvement on the homogenization of temperature field and temperature gradient field.

Constructal optimisation of heat generating volumes

Cooling of electronics by conduction with high thermal conductivity paths located in heat generating, low conductivity volumes are investigated using constructal theory. A new mathematical solution for the fundamental problem of how to collect and channel to one point the heat generated volumetrically in a low conductivity volume of a given size is developed using the Lagrange Multiplier Method. Additionally, at the fundamental step, the optimisation procedure is exact. No approximation has been made about the geometrical characteristics of the fundamental element. In solutions of the fundamental elements, the amount of high conductivity material (high conductivity paths) through the volume is fixed.

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.

Electrical anisotropy and conductivity distribution functions of fractal random networks and of the crust: the scale effect of connectivity

SUMMARY All explanations of the high-conductivity layers (HCL) found by magnetotellurics in the middle or lower crust incorporate a mixture of a low-conductivity rock matrix and a highly conductive phase, for example graphite or saline fluids. In most cases the bulk conductivity of the mixture does not depend on the conductivity of the rock matrix but rather (1) on the amount of high-conductivity material and, in particular, (2) on its geometry. The latter is quantitatively described by the parameter ‘electrical connectivity'. Decomposition of the observed bulk conductivity of the mixture into these two parameters results in an ill-posed problem. Even if anisotropy occurs in the HCL, three output parameters (highly conductive phase fraction, connectivity with respect to the X direction, connectivity with respect to the Y direction) have to be estimated from the two bulk conductivities of the anisotropic HCL. The additional information required for solving this problem is provided if instead of single-site data the conductivities from many field sites are evaluated: a sample distribution of the conductivity can then be obtained. Ensembles of random networks are used to create theoretical distribution functions which match the empirical distribution functions to some extent. The use of random resistor networks is discussed in the context of other established techniques for the treatment of two-phase systems, such as percolation theory and the renormalization group approach. Models of embedded networks explain the discrepancy between ‘small’ anisotropy (2-3) on the laboratory scale and large anisotropy (10-100) found in electromagnetic field surveys encompassing volumes of several cubic kilometres. Strong anisotropy can indicate low electrical connectivity, and a possible explanation is that a network stays close to the percolation threshold.

Constructal-theory network of conducting paths for cooling a heat generating volume

This paper develops a solution to the fundamental problem of how to collect and ‘channel’ to one point the heat generated volumetrically in a low conductivity volume of given size. The amount of high conductivity material that is available for building channels (high conductivity paths) through the volume is fixed. The total heat generation rate is also fixed. The solution is obtained as a sequence of optimization and organization steps. The sequence has a definite time direction, it begins with the smallest building block (elemental system) and proceeds toward larger building blocks (assemblies). Optimized in each assembly are the shape of the assembly and the width of the newest high conductivity path. It is shown that the paths form a tree-like network, in which every single geometric detail is determined theoretically. Furthermore, the tree network cannot be determined theoretically when the time direction is reversed, from large elements toward smaller elements. It is also shown that the present theory has far reaching implications in physics, biology and mathematics.