Thermal/fluid characteristics of isotropic plain-weave screen laminates as heat exchange surfaces

A simple-to-fabricate woven mesh, consisting of bonded laminates of two-dimensional plain-weave conductive screens is described. Geometric equations show that these porous matrices can be fabricated to have a wide range of porosity and a highly anisotropic thermal conductivity vector. A mathematical model of the thermal performance of such a mesh, deployed as a heat exchange surface, is developed. Apparatus to measure both the pressure drop and heat transfer coefficient are described Measurements of pressure drop and overall heat transfer rate are reported and used with the performance model to develop correlation equations of mesh friction factor and Colburn j-factor as a function of coolant properties, mesh characteristics and flow rate through the mesh. A heat exchanger performance analysis delineates conditions where the screen-laminate technology offers superior performance. NOMENCLATURE A face area of mesh screen, WH Ac cross-section area of mesh screen, tW cf compression factor c fluid specific heat d wire diameter of mesh screen Dh hydraulic diameter of mesh screen / friction factor G fluid mass velocity h unit surface conductance H height of mesh screen j Colburnj-factor J modified Colburn j-factor k thermal conductivity ke effective thermal conductivity M mesh number n number of screen layers of the lamination P pressure Pr Prandtl number q heat transfer rate q" heat flux Re Reynolds number St Stanton number t thickness of mesh screen T temperature U effective conductance of mesh screen W width of mesh screen P heat transfer surface area to volume ratio AP pressure drop s porosity p fluid density H fluid viscosity Subscripts / fluid /, o inlet, outlet s solid x, yt z coordinates INTRODUCTION Kays and London [1984] have pointed out that a most effective way to increase the performance of a heat exchanger is to increase its surface area to volume ratio, P. Small-particle packed beds and foamed metals are expanded materials having large values of /? Unfortunately, due to the tortuosity effect in * Graduate Student, Department of Mechanical Engineering. Member A " Professor, Department of Mechanical Engineering,, Member AIAA Copyright © 2002 The American Institute of Aeronautics and Astronautics, Inc. All rights reserved American Institute of Aeronautics and Astronautics (c)2002 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. conjunction with the high porosity ( £ ) of these materials, their effective thermal conductivity, ke is relatively small so that much of the gain in performance obtained by having a large fi is lost by having a relatively small ke. Typical values of ke in spherical particle packed beds are 10% 15% of the particle thermal conductivity [Kaviany, 1995]. Commercially available metal foam such as aluminum foam has an effective thermal conductivity that ranges from only 2% to 6% of the base metal value [Ashby et al, 2000]. An anisotropic porous matrix having a large surface area to volume ratio and high effective thermal conductivity in a particular direction will result in a very effective heat exchange surface. Such a matrix can be fabricated by layering and bonding plain-weave screens to form a three-dimensional matrix. Xu and Wirtz [2002] have shown that plain-weave screen laminates can be configured to have a large surface area to volume ratio and high effective thermal conductivity in a particular direction, with effective thermal conductivities of anisotropic screen laminates approaching 78% of base material values. In addition, screen laminates are simple to manufacture and can be fabricated to have a wide range of porosity. They can be incorporated into the design of a flow-through module or cold plate heat exchanger, resulting in a compact, high-flux device with reasonable pressure drop characteristics. Tong and London [1957] reported measurements of friction factor and mesh heat transfer coefficient for inline plain weave laminates and staggered cross-rod matrices (no interweaving). They used a calorimetric method to measure the local heat transfer coefficient of one heated filament inside the array. Since other filaments upstream of the "measurement filament" were not heated, their correlations are expected to predict heat transfer coefficients that are higher than would be expected if all wire filaments of the array were heated. Miyabe et al. [1982] report heat transfer coefficient correlations for plain-weave screen laminates that are in close agreement with those of Tong and London. However, they do not describe their measurement techniques. Armour and Cannon [1968] report pressure drop correlations for plain-weave screens, but not laminations of screens. Xu and Wirtz [2002] develop a model for the in-plane effective thermal conductivity of screen-laminates, and Koh and Fortini [1974] report an empirical correlation for the cross-plane component Previous correlations for the wire-element heat transfer coefficient in screen laminates may predict overly high values, and there does not appear to be a pressure drop database for laminated systems. The objective of the present work is to document thermal/fluid characteristics of plain-weave screen laminates and to develop woven mesh heat exchanger technology with particular attention to single-fluid parallel plate heat exchangers. In this paper we present an analytical model for heat transfer in screen laminate systems. Laboratory experiments leading to mesh pressure drop and heat transfer correlations are described. A heat exchanger performance analysis is used to delineate operating regimes where the screen-laminate systems offer superior performance. THEORETICAL BACKGROUND Geometry of screen laminate