Sohail R. Reddy

Multi-Objective Optimization of Micro Pin-Fin Arrays for Cooling of High Heat Flux Electronics with a Hot Spot

ABSTRACT This article presents fully three-dimensional conjugate heat transfer analysis and a multi-objective, constrained optimization to find sizes of pin-fins, inlet water pressure, and average speed for arrays of micro pin-fins used in the forced convection cooling of an integrated circuit with a uniformly heated 4 × 3 mm footprint and a centrally located 0.5 × 0.5 mm hot spot. Sizes of micro pin-fins having cross sections shaped as circles, symmetric airfoils, and symmetric convex lenses are optimized to completely remove heat due to a steady, uniform heat flux of 500 W cm−2 imposed over the entire footprint (background heat flux) and a steady, uniform heat flux of 2000 W cm−2 imposed on the hot spot area only (hot spot heat flux). The two simultaneous objectives are to minimize maximum substrate temperature and minimize pumping power, while keeping the maximum temperature constrained below 85°C and removing all of input thermal energy by convection. The design variables are the inlet average velocity and size of the pin-fins. A response surface is generated for each of the objectives and coupled with a genetic algorithm to arrive at a Pareto frontier of the best trade-off solutions. Numerical results show that, for a specified maximum temperature, optimized arrays with pin-fins having symmetric convex lens shapes create the lowest pressure drop, followed by the symmetric airfoil and circular cross-section pin-fins. An a posteriori three-dimensional stress–deformation analysis incorporating hydrodynamic and thermal loads shows that Von-Mises stress for each pin-fin array is significantly below the yield strength of silicon, thus, confirming structural integrity of such arrays of micro pin-fins.

Multi-Winglets: Multi-Objective Optimization of Aerodynamic Shapes

Various configurations of aircraft wing tip devices have been investigated by performing 3D aerodynamics analysis. The wing tip device in this study was derived from the wing tips of a soaring bird, featuring three smoothly blended elements. Each multi-winglet configuration was integrated into a complete wing-tail-body aircraft configuration. Geometry of each of the three elements in the multi-winglet was defined using 11 parameters, totaling 33 parameters defining a complete multi-winglet geometry. The current design methodology utilized a second order, 3D geometry generation algorithm based on locally analytical smoothly connected surface patches. This algorithm allows for creation of vastly diverse 3D geometries with minimal number of specified design parameters. A 3D, compressible, turbulent flow, steady state analysis was performed using a Navier-Stokes solver on each configuration to obtain the objective function values. Each configuration was analyzed at a free stream Mach number of 0.25 and at an angle of attack of 11 degrees to mimic the takeoff conditions of a passenger aircraft. Multi-objective optimization was carried out using modeFRONTIER utilizing a radial basis function response surface approximation coupled with a genetic algorithm. Maximizing coefficients of lift and lift-todrag ratio, while minimizing coefficients of drag and the magnitude of the coefficient of moment were the four simultaneous objectives. The multi-winglet concept was shown to have superior performance at subsonic and transonic speeds.

Multi-Objective Optimization of Micro Pin-Fin Arrays for Cooling of High Heat Flux Electronics With a Hot Spot

The ability of various arrays of micro pin-fins to reduce maximum temperature of an integrated circuit with a 4 × 3 mm footprint and a 0.5 × 0.5 mm hot spot was investigated numerically. Micro pin-fins having circular, symmetric airfoil and symmetric convex lens cross sections were optimized to handle a background uniform heat flux of 500 W cm−2 and a hot spot uniform heat flux of 2000 W cm−2. A fully three-dimensional conjugate heat transfer analysis was performed and a multi-objective, constrained optimization was carried out to find a design for each pin-fin shape capable of cooling such high heat fluxes. The two simultaneous objectives were to minimize maximum temperature and minimize pumping power, while keeping the maximum temperature below 85 °C. The design variables were the inlet average velocity and shape, size and height of the pin-fins. A response surface was generated for each of the objectives and coupled with a genetic algorithm to arrive at a Pareto frontier of the best trade-off solutions. Stress–deformation analysis incorporating hydrodynamic and thermal loads was performed on the three Pareto optimized configurations. Von-Mises stress for each configuration was found to be significantly below the yield strength of silicon.Copyright

Inverse determination of spatially varying material coefficients in solid objects

Abstract Material properties such as thermal conductivity, magnetic permeability, electric permittivity, modulus of elasticity, Poissons ratio, thermal expansion coefficient, etc. can vary spatially throughout a given solid object as it is the case in functionally graded materials. Finding this spatial variation is an inverse problem that requires boundary values of the field quantity such as temperature, magnetic field potential or electric field potential and its derivatives normal to the boundaries. In this paper, we solve the direct problem of predicting the spatial distribution of the field variable based on its measured boundary values and on the assumed spatial distribution of the diffusion coefficient using radial basis functions, the finite volume method and the finite element method, whose accuracies are verified against analytical solutions. Minimization of the sum of normalized least-squares differences between the calculated and measured values of the field quantity at the boundaries then leads to the correct parameters in the analytic model for the spatial distribution of the spatially varying material property.

Inverse Design of Cooling of Electronic Chips Subject to Specified Hot Spot Temperature and Coolant Inlet Temperature

Most methods for designing electronics cooling schemes do not offer the information on what levels of heat fluxes are maximally possible to achieve with the given material, boundary and operating conditions. Here, we offer an answer to this inverse problem posed by the question below. Given a micro pin-fin array cooling with these constraints:- given maximum allowable temperature of the material,- given inlet cooling fluid temperature,- given total pressure loss (pumping power affordable), and- given overall thickness of the entire electronic component,find out the maximum possible average heat flux on the hot surface and find the maximum possible heat flux at the hot spot under the condition that the entire amount of the inputted heat is completely removed by the cooling fluid. This problem was solved using multi-objective constrained optimization and metamodeling for an array of micro pin-fins with circular, airfoil and symmetric convex cross sections that is removing all the heat inputted via uniform background heat flux and by a hot spot. The goal of this effort was to identify a cooling pin-fin shape and scheme that is able to push the maximum allowable heat flux as high as possible without the maximum temperature exceeding the specified limit for the given material. Conjugate heat transfer analysis was performed on each of the randomly created candidate configurations. Response surfaces based on Radial Basis Functions were coupled with a genetic algorithm to arrive at a Pareto frontier of best trade-off solutions. The Pareto optimized configuration indicates the maximum physically possible heat fluxes for specified material and constraints.Copyright

Multi-Objective Optimization of Micro Pin-Fin Arrays for Cooling of High Heat Flux Electronics

The thermal management capability of various candidates of micro-pin fin arrays is investigated. An integrated circuit having a footprint of 4 × 3 mm with micro-pin fin array having circular, airfoil and convex cross-section is considered. The three pin fin cross-sections along with the cooling schemes are optimized to handle a uniform heat flux of 500 W/cm2 applied to the top surface of the electronic chip. A fully three-dimensional, steady-state conjugate heat transfer analysis was performed on each cooling configuration and a constrained multi-objective optimization was carried out for each of the three micro-pin fin shapes to find pin fin designs configurations capable of cooling such high heat fluxes. The design variables were the geometric parameters defining each pin fin cross section, height of the chip and inlet speed of the coolant. The two simultaneous objectives were to minimize maximum temperature and pressure drop (pumping power), while keeping the maximum temperature below 85°C. A response surface was constructed for each objective function and was coupled with a genetic algorithm to arrive at a Pareto frontier of the best trade-off solutions. Stress-deformation analysis incorporating the hydrodynamic and thermal loads was performed on each of the three optimized configurations. The maximum displacement was found to be on the nano-level, and the Von-Mises stress for each configuration was found to be significantly below the yield strength of Silicon.Copyright

Conjugate Analysis of Thin Film Heat Spreaders to Reduce Temperature at Hot Spots

The effects of thin film coating on maximum temperature of integrated electric circuits are investigated. A fully three-dimensional conjugate heat transfer analysis was performed to investigate the effects of thin film material and thickness on the temperature of a hot spot. Two different materials, diamond and graphene nano-platelets were simulated as materials for thin films. The thin film heat spreaders were applied to the top wall of the three optimized arrays of micro pin-fins having circular, airfoil and convex cross sections. The electronic chip with a 4 × 3 mm footprint featured a 0.5 × 0.5 mm hot spot located on the top wall which was exposed to a uniform high-level background heat flux. The effective area of coverage of the thin films was also investigated computationally. It was found that thin film heat spreaders significantly reduce the hot spot temperature, allowing for increased thermal loads and therefore increased performance. Furthermore, it was found that thickness of the thin film heat spreader does not have to be greater than a few tens of microns.Copyright

Analysis of anisotropic graphene platelet heat spreaders to reduce hot spot temperature and temperature non-uniformity

This work investigates the effect of thin film graphene heat spreaders on the maximum temperature of integrated electric circuits. An electronic chip with a 4 × 3mm footprint featured a centrally located 0.5 × 0.5mm hot spot located on the top wall. The remainder of the top wall was exposed to a uniform background heat flux. The graphene heat spreaders were applied to the top wall of an optimized cooling array of micro pin-fins having airfoil cross-sections. A fully 3D conjugate heat transfer analysis was performed to investigate the effects of different heat spreader thicknesses on the temperature of the hot spot and the temperature distribution on the hot surface. Both isotropic and anisotropic thermal conductivities of heat spreaders were considered. The conjugate heat transfer analysis also incorporated thermal contact resistance.

INVERSE DETERMINATION OF SPATIALLY VARYING HEAT CAPACITY AND THERMAL CONDUCTIVITY IN ARBITRARY 2D OBJECTS

A methodology for non-destructive simultaneous estimation of spatially varying thermal conductivity and heat capacity in 2D solid objects was developed that requires only boundary measurements of temperatures. The spatial distributions were determined by minimizing the normalized sum of the least-squares differences between measured and calculated values of the boundary temperatures. Computing time was significantly reduced for the entire inverse parameter identification process by utilizing a metamodel created by an analytical response surface supported by an affordable number of numerical solutions of the temperature fields obtained by the high fidelity finite element analyses. The minimization was performed using a combination of particle swarm optimization and the BFGS algorithm. The methodology has shown to accurately predict linear and nonlinear spatial distributions of thermal conductivity and heat capacity in arbitrarily shaped multiply-connected 2D objects even in situations with noisy measurement data thus proving that it is robust and accurate. The current drawback of this method is that it requires an a priori knowledge of the general spatial analytic variation of the physical properties. This can be remedied by representing such variations using products of infinite series such as Fourier or Chebyshev and determining correct values of their coefficients.

Effect of cooling fluids on high frequency electric and magnetic fields in microelectronic systems with integrated TSVs

A fully 3D conjugate numerical analysis was performed to reveal the effects of air, R134a refrigerant and water on electromagnetic fields of electronic cooling designs made of arrays of micro pin-fins with integrated Through-Silicon-Vias (TSVs). The integrated TSV cooling configuration included 8 cylindrical TSVs with 150m diameter each and 200m height. The external dimensions of the silicon substrate were 900700280m. Each TSV encapsulated four equally spaced copper vias each having a diameter of 40m. The impacts of the presence of the stationary cooling fluids without heat transfer on TSVs electric and magnetic fields were examined for five different frequencies; 100MHz, 500MHz, 1GHz, 5GHz and 10GHz. Then, separately, the effects of moving cooling water with temperature-dependent physical properties were studied while exposing the cooled micro pin-fin array to a uniform heat flux of 500Wcm2. For the case of stagnant and moving cooling fluids it was found that water influences the electric field twice as much as either R134a or air and that this influence decreases only negligibly with the increase in frequency of the electric current passing through the TSVs. The influence of the presence of the stagnant and moving cooling fluids on the magnetic field is orders of magnitude smaller and reduces rapidly with the increased frequency. The effects of three different cooling fluids (air, R134a and water) on the magnetic and electric fields of arrays of micro pin-fins having integrated TSVs were studied at five different frequencies using fully 3D conjugate heat transfer/electro-magneto-hydrodynamics analyses.The coolant can have significant impact on the electric field of such micro-electronic packages.