AIAA JOURNAL Vol. 42, No. 5, May 2004 Design of Multifunctional Honeycomb Materials Carolyn Conner Seepersad, ∗ Benjamin M. Dempsey, ∗ Janet K. Allen, † Farrokh Mistree, ‡ and David L. McDowell § Georgia Institute of Technology, Atlanta, Georgia 30332-0405 Extruded metal honeycombs [linear cellular alloys (LCAs)] are designed for a multifunctional application that demands not only structural performance but also heat transfer capabilities. The manufacturing process for LCAs enables complex in-plane cell topologies that may be tailored to achieve desired functionality. As a result, certain mechanical and heat transfer properties of LCAs are superior to those of hexagonal honeycombs or stochastic metal foams. Both periodic and functionally graded LCAs are designed for a structural heat transfer device for an electronic cooling application. The design problem is formulated as a multiobjective decision. Approximate models of structural and heat transfer performance, such as finite difference heat transfer simulations, are employed to analyze designs efficiently. A portfolio of heat exchanger designs is generated with both periodic and functionally graded cell topologies. Tradeoffs are assessed between thermal and structural performance. Previous authors have focused primarily on analysis of the structural and thermal properties of cellular materials; here, a design perspective is adopted. Given a set of rigorous analytical models, the emphasis is on synthesis of cellular designs and identification of superior design regions. Nomenclature A = coefficient matrix A i (x) = achievement of a goal b = applied load vector c p = specific heat of the fluid c pav = specific heat evaluated at the mean of the inlet and exit temperature D = heat exchanger depth d h = internal width of a cell d + i = overachievement deviation variable d − i = underachievement deviation variable d v = internal height of a cell E s = elastic modulus of solid material ˜ E x = overall structural elastic stiffness in x direction ˜ E y = overall structural elastic stiffness in y direction G i = goal target value Gr = Grashof number H = heat exchanger height h i = height of cells in row i k f = fluid conductivity k s = solid cell wall conductivity L = total length of the linear cellular alloy (LCA) ˙ M = total mass flow rate ˙ m = mass flow rate per cell in an LCA with a uniform cross section ˙ m cell = mass flow rate in a cell N = total number of nodes N h = number of cells in horizontal direction Nu = Nusselt number N v = number of cells in vertical direction Presented as Paper 2002-5626 at the AIAA/ISSMO 9th Symposium on Multidisciplinary Analysis and Optimization, Atlanta, GA, 4–6 September 2002; received 10 August 2003; accepted for publication 15 November 2003. Copyright c  2004 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rose- wood Drive, Danvers, MA 01923; include the code 0001-1452/04 $10.00 in correspondence with the CCC. ∗ Graduate Research Assistant, G.W. Woodruff School of Mechanical En- gineering. Member AIAA. † Senior Research Scientist, G.W. Woodruff School of Mechanical Engi- neering. Senior Member AIAA. ‡ Professor, G.W. Woodruff School of Mechanical Engineering; far- rokh.mistree@me.gatech.edu. Associate Fellow AIAA. § Regents’ Professor and Carter N. Paden, Jr., Distinguished Chair in Met- als Processing, G.W. Woodruff School of Mechanical Engineering. n = total number of cells in an LCA cross section Q = total heat transfer rate Re = Reynolds number T exit = exit fluid temperature of a cell T in = inlet temperature of the fluid T s = specified constant wall temperature t h = horizontal cell wall thickness t v = vertical cell wall thickness W = heat exchanger width W i = weight for goal I w i = width of cells in column i x = unknown temperature vector Z = deviation or objective function l = nodal spacing in the z direction P = pressure drop x = nodal spacing in the x direction y = nodal spacing in the y direction ρ f = density of the fluid I. Introduction M ULTIFUNCTIONAL materials are integrated systems that serve multiple roles such as structural load bearing, ther- mal management, energy absorption, or other roles. These multi- functional material systems have compelling potential applications, including actively cooled supersonic aircraft or spacecraft skins, engine combustor liners, and lightweight structural elements with internal damping. Linear or two-dimensional cellular materials are particularly suitable for multifunctional applications that require not only structural performance but also lightweight thermal or energy absorption capabilities. Certain structural and thermal properties of extruded cellular honeycomb materials, so-called linear cellular al- loys (LCAs), are superior to those of metallic foams with equivalent densities. For example, LCAs exhibit greater in-plane stiffness and strength and out-of-plane specific energy absorption than stochastic metal foams. 1,2 LCAs are advantageous as heat exchangers due to larger surface area density and lower pressure drop, two factors that compensate for lower heat transfer coefficients for laminar forced convection than for turbulent forced convection in stochastic metal foams with comparable relative densities. 3 In addition, the manufacturing process for LCAs facilitates the fabrication of multifunctional cellular materials. Powder slurries are extruded through a die and then exposed to thermal and chemical treatments in a process developed by the Lightweight Structures Group at the Georgia Institute of Technology. 4 Extruded metal- lic cellular structures can be produced with nearly arbitrary two- dimensional cellular topologies limited only by paste flow and die manufacturability. Wall thicknesses and cell diameters as small 1025