Temperature-Constrained Topology Optimization of Transient Heat Conduction Problems

A regional temperature measure model is constructed to obtain a small number of temperature constraints for local transient temperature control. The temperature sensitivity is derived using the adjoint variable method. The multiple temperature criteria and three-phase topology optimization are further investigated for transient heat conduction design. The material layout design of transient heat conduction is replaced by a static optimization problem, which is subsequently solved by the method of moving asymptotes. Finally, several numerical examples are provided to demonstrate the feasibility and validity of the proposed topology optimization for transient heat conduction problems.     

Solution of the inverse heat conduction problem described by the Poisson equation for a cooled gas-turbine blade

The presented paper describes a method of solving the inverse problems of heat conduction, consisting in solving the Poisson equation for a simply connected region instead of the Laplace equation for a multiply connected one, like a gas-turbine blade provided with cooling channels. The considered method consists in determining unknown values of the source (heat sink) power in the cooling channels for a given external heat transfer situation to achieve as close as possible an isothermal outer surface. Afterwards the temperature and heat flux distributions at the cooling channel walls are determined. Since the unknown source power is sought, the problem is an inverse one. Taking into account the sought values the method is reckoned among the class of the fictitious source methods and presents an optimization scheme. Using an exemplary gas turbine blade cooling configuration, the results of the calculation obtained with this method have been compared to the results achieved with an inverse method using the boundary element method for a multiple connected region.The results obtained with both methods within the optimization scheme approximated each other. Nevertheless, the results for the inverse method shown in the present paper gave nearly no oscillations, which is important in case of the blades with other geometric features of the cooling channels.     

Topology optimization of convection-dominated,steady-state heat transfer problems

The current push in the topology optimization community is to apply topology optimization to mechanics problems beyond typical structural design to other physical domains. Here, a framework for topology optimization of nonlinear steady-state heat transfer with conduction, convection, and radiation without explicitly accounting for fluid motion is evaluated. Convection-dominated diffusion problems are susceptible to numerical instabilities that, unless they are handled properly in the analysis, can severely affect the optimization. This numerical instability issue is the focus of this work, its origin is discussed in the context of density-design-variable-based topology optimization, and a method for avoiding such instabilities is described. Several design examples demonstrate the approach.     

Vascularization with line-to-line trees in counterflow heat exchange

Here we report the heat and fluid flow characteristics of counterflow heat exchangers with tree-shaped line-to-line flow channels. The flow structures of the hot and cold sides are sequences of point-to-line trees that alternate with upside-down trees. The paper shows under what conditions the tree vascularization offers greater heat flow access than corresponding conventional designs with parallel single-scale channels. The analytical part is based on assuming fully developed laminar flow in every channel and negligible longitudinal conduction in the solid. The numerical part consists of simulations of three-dimensional convection coupled with conduction in the solid. It is shown that tree vascularization offers greater heat flow access (smaller global thermal resistance) than parallel channels when the number of pairing levels increases and the available pumping power or pressure drop is specified. When the solid thermal conductivity increases, the heat transfer effectiveness decreases because of the effect of longitudinal heat conduction. The nonuniformity in fluid outlet temperature becomes more pronounced when the number of pairing levels increases and the pumping power (or pressure drop number) increases. The nonuniformity in outlet fluid temperature decreases when the solid thermal conductivity increases.     

Laminar conjugate mixed convection in a vertical channel with heat generating components

Conjugate mixed convection arising from protruding heat generating ribs attached to substrates (printed circuit boards) forming channel walls is numerically studied. The substrates with ribs form a series of vertical parallel plate channels. Assuming identical disposition and heat generation of the ribs on each board, a channel with periodic boundary conditions in the transverse direction is considered for analysis. The governing equations are discretised using a control volume approach on a staggered mesh and a pressure correction method is employed for the pressure–velocity coupling. The solid regions are considered as fluid regions with infinite viscosity and the thermal coupling between the solid and fluid regions is taken into account by the harmonic thermal conductivity method. Parametric studies are performed by varying the heat generation based Grashof number in the range 10⁴–10⁷ and the fan velocity based Reynolds number in the range 0–1500, with air as the working medium. Results are obtained for the velocity and temperature distributions, natural convection induced mass flow rate through the channel, the maximum temperatures in the heat sources and the local Nusselt numbers. The natural convection induced mass flow rate in mixed convection is correlated in terms of the Grashof and Reynolds numbers. In pure natural convection the induced mass flow rate varies as 0.44 power of Grashof number. The maximum dimensionless temperature is correlated in terms of pure natural convection and forced convection inlet velocity asymptotes. For the parameter values considered, the heat transferred to the working fluid via substrate heat conduction is found to account for 41–47% of the heat removal from the ribs.     

Experimental study on heat transfer and flow resistance in improved latticework cooling channels

Characteristics of heat transfer and flow resistance of the latticework （vortex） cooling channel with ribs truncated at their two ends were theoretically and experimentally studied compared with regular and smooth channels of the same configuration. The results showed： the heat transfer efficiency of the latticework channel with two slots was better than those of regular and smooth channels of the same configuration, its flow resistance situation in the slotted channel becomes quite complex; The flow resistances of 2 mm- and 4 mm-slotted channels were obviously lower than that of the regular channel, but they are still much higher than that of the smooth channel; Compared with the regular channel, the total heat transfer efficiencies of the slotted channels were pretty improved, among them the 4-mm slotted channel has the biggest enhancement. From the experimental results, it is obvious that the latticework channel with proper slots has a great prospect in the design of the inner cooling channels of turbine blades.     

Topological design of channels for squeeze flow optimization of thermal interface materials

Performance of thermal interface materials (TIMs) used between a microelectronic device and its associated heat spreader is largely dependent on the bulk thermal conductivity of the TIM, but the bond-line thickness (BLT) of the applied material as well as the interfacial contact resistances are also significant contributors to overall performance. Hierarchically Nested Channels (HNCs), created by modifying the surface topology of the chip or the heatsink with hierarchical arrangements of microchannels in order to improve flow, have been proposed to reduce both the required squeezing force and the final BLT at the interfaces. In the present work, a topological optimization framework that enables the design of channel arrangements is developed. The framework is based on a resistance network approximation to Newtonian squeeze flow. The approximation, validated against finite element (FE) solutions, allows efficient, design-oriented solutions for squeeze flow in complex geometries. A comprehensive design sensitivity analysis exploiting the resistance network approximation is also developed and implemented. The resistance approximation and the sensitivity analysis is used to build an automated optimal channel design framework. A Pareto optimal problem formulation for the design of channels is posed and the optimal solution is demonstrated using the framework.     

Numerical study on heat transfer enhancement of a proton exchange membrane fuel cell with the dimpled cooling channel

As the power density of a proton exchange membrane fuel cell (PEMFC) increases, the problems of internal heat accumulation and non-uniform temperature distribution are becoming significant. In this paper, a novel cooling channel with dimple structures is designed and a three-dimensional PEMFC numerical model is established. When comparing to the conventional channels, the heat transfer performance of dimpled channel is 10% higher than the smooth one, and the pressure loss is almost 13% lower than that of wavy channel. In addition, the optimization of dimple structure parameters is investigated based on the index of uniformity temperature (IUT) and performance evaluation criteria (PEC) of heat transfer. It is found that a diameter-to-depth ratio of 4 is recommended when the dimple diameter is less than 0.80 mm. Furthermore, the clock-wise vortex observed inside the dimple is considered to be the main reason affecting heat exchange. This study will contribute to the design of cooling channels for high-power density PEMFCs in the future.     

A numerical method for natural convection and heat conduction around and in a horizontal circular pipe

Natural convection around a horizontal circular pipe coupled with heat conduction in the solid structure is numerically investigated using a preconditioning method for solving incompressible and compressible Navier–Stokes equations. In this method, fundamental equations are completely reduced to an equation of heat conduction when the flow field is static (zero velocity). Therefore, not only compressible flows but also very slow flows such as natural convection in a flow field and heat conduction in a static field can be simultaneously calculated using the same computational algorithm. In this study, we first calculated the compressible flow around a NACA0012 airfoil with conduction in the airfoil and then simulated natural convections around a horizontal circular pipe with a different heat conductivity. Finally, we numerically investigated the effect of heat conductivity of the pipe on natural convection.     

The effect of axial conduction on heat transfer in a liquid microchannel flow

Analysis is presented for conjugate heat transfer in a parallel-plate microchannel. Axial conduction in the fluid and in the adjacent wall are included. The fluid is a constant property liquid with a fully-developed velocity distribution. The microchannel is heated by a uniform heat flux applied to the outside of the channel wall. The analytic solution is given in the form of integrals by the method of Green’s functions. Quadrature is used to obtain numerical results for the local and average Nusselt number for various flow velocities, heating lengths, wall thicknesses, and wall conductivities. These results have application in the optimal design of small-scale heat transfer devices in areas such as biomedical devices, electronic cooling, and advanced fuel cells.     

Numerical study of fluid flow and heat transfer in microchannel cooling passages

Numerical investigation was conducted for fluid flow and heat transfer in microchannel cooling passages. Effects of viscosity and thermal conductivity variations on characteristics of fluid flow and heat transfer were taken into account in theoretical modeling. Two-dimensional simulation was performed for low Reynolds number flow of liquid water in a 100 μm single channel subjected to localized heat flux boundary conditions. The velocity field was highly coupled with temperature distribution and distorted through the variations of viscosity and thermal conductivity. The induced cross-flow velocity had a marked contribution to the convection. The heat transfer enhancement due to viscosity-variation was pronounced, though the axial conduction introduced by thermal-conductivity-variation was insignificant unless for the cases with very low Reynolds numbers.     

Fluid and thermal analysis of a microchannel electronics cooler using computational fluid dynamics

Fluid flow and heat transfer of a microchannel electronics cooler is analyzed using computational simulation and experimental validation. The microchannel cooling technique appears to be a viable solution to high heat rejection requirements of today’s high-power electronic devices, such as diode lasers. The thermal design of these small electronics cooling devices is a key issue that needs to be optimized in order to keep the system temperatures at certain levels. However, this optimization should balance the heat transfer with pressure drop through the system by modifying the geometrical design. This technique is used in optimizing the performance of a microchannel cooler for high-power semiconductor diode laser applications in this study. The results show that symmetrical design modifications improve both pressure drop and heat transfer significantly, while resizing the channels may affect slightly.     

Objective function proposed for optimization of convective heat transfer devices

In this work, a general method using exergy analysis has been proposed to achieve a compromise between heat transfer effectiveness and pressure loss in heat transfer optimization problems involving internal channels. The proposed method is applied to the design optimization of a channel roughened by staggered arrays of dimples for heat transfer augmentation. Optimization is performed using surrogate-based optimization techniques and three-dimensional Reynolds-averaged Navier–Stokes analysis. Three nondimensional design variables are defined using the dimpled channel height, dimple print diameter, dimple spacing, and dimple depth. The objective function is defined as the net exergy gain considering the exergy gain by heat transfer, and exergy losses generated by friction and heat transfer. Twenty design points are generated using Latin hypercube sampling, and the Kriging model is used as a surrogate model to approximate the objective function values in the design space. Through optimization, the objective function is successfully improved with respect to the reference geometry.     

Topology optimization for thermal conductors considering design-dependent effects,including heat conduction and convection

In structural designs considering thermal loading, in addition to heat conduction within the structure, the heat convection upon the structure’s surface can significantly influence optimal design configurations. In this paper, we focus on the influence of design-dependent effects upon heat convection and internal heat generation for optimal designs developed using a topology optimization scheme. The method for extracting the structural boundaries for heat convection loads is constructed using a Hat function, and heat convection shape dependencies are taken into account in the heat transfer coefficient using a surrogate model. Several numerical examples are presented to confirm the usefulness of the proposed method.     

A Global Heat Compliance Measure Based Topology Optimization for the Transient Heat Conduction Problem

For topology optimization with transient loads, heat compliance varies with transient heat analysis. The peak value of the transient heat compliance should be minimized. Thus, this article proposes a global heat compliance measure to handle this kind of topology optimization for the transient heat conduction problem. The optimization model is then constructed by the global heat compliance measure. The finite-element, equivalent static loads, and continuum shape based sensitivity analyses are derived using the adjoint variable method. Through case studies, the effectiveness of the proposed global heat compliance measure for the transient heat conduction topology optimization is validated.     

Effect of cooling channel geometry on re-cooled cycle performance for hydrogen fueled scramjet

Developing fuel with higher heat sink is widely carried out to meet the cooling requirement for an airbreathing hypersonic vehicle. However, a Re-Cooled Cycle has been newly proposed for a regeneratively cooled scramjet to reduce the fuel flow for cooling. Fuel heat sink (cooling capacity) is repeatedly used to indirectly increase the fuel heat sink. Parametric sensitivity analysis of Re-Cooled Cycle of a hypersonic aircraft is explored. An analytical fin-type model for incompressible flow in smooth-wall rectangular ducts in terms of hydrodynamic, thermal, power balance and Mach number constraints is proposed. Based on this model, the difference of the cooling channel structure design between Re-Cooled Cycle and regenerative cooling is discussed, and a new optimization index is introduced for Re-Cooled Cycle. The sensitivity of the cycle performance to cooling channel geometry is investigated, and the optimal performance of a Re-Cooled Cycle is obtained by satisfying constraints. The differences of the effect of channel design variables between Re-Cooled Cycle and regenerative cooling are also discussed.     

Enhancement of heat transfer from hot water by co-flowing it with mercury in a mini-channel

The present study is a numerical investigation on the flow and heat transfer in a mini-channel where both hot liquid water and mercury co-flow together in a direct contact manner. Results show that the presence of a high thermal conductivity liquid metal such as mercury enables the hot water to lose much more of its initial thermal energy content, than when only water alone flows in the channel. However, too unjustified excessive mercury co-flowing with the hot water can lead to adverse effects in regards to the heat loss from the hot water. The reason behind the enhanced heat transfer between the two liquids is due to the initiation of high temperature gradients sites inside the channel, especially in the region of the interface between the two liquids, in addition to the high thermal conductivity of mercury, as compared to water thermal conductivity. These two effects lead to effective conduction cooling in the transverse direction over the whole length of the channel. These aspects are quantified in this study.     

Shape optimization of steady‐state heat‐conduction fields considering temperature dependency of thermal conductivity coefficient

This paper presents a numerical analysis method for shape optimization of domains with steady‐state heat‐conduction fields considering the temperature dependence of the thermal conductivity coefficient. In this paper, we formulate two shape optimization problems, namely, maximization of thermal dissipation on heat transfer boundaries and minimization of heat‐conduction fields. The shape gradient functions for these shape optimization problems are derived theoretically using the Lagrange multiplier method and formulae of the material derivative. Reshaping is accomplished using the traction method proposed as a solution to the shape optimization problems. The proposed method is validated from the results of two‐dimensional numerical analysis. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20374     

Combined Heat Transfer by Natural Convection – Conduction and Surface Radiation in an Open Cavity Under Constant Heat Flux Heating

Combined heat transfer by natural convection-conduction and surface radiation in an open cavity heated by constant flux is studied here. The laminar flow is solved numerically by employing the SIMPLE algorithm with QUICK scheme. The numerical results show that both radiation and solid conduction increase the average total Nusselt number. The average total Nusselt number is a linear increasing function of emissivity when emissivity is larger than 0.2. The heat conduction of a conductive wall increases the total cooling effect, but its effect is close to a limit when the conductivity ratio exceeds 100. The increase due to radiation ranged from 54.1% to 64.0%.     

某发动机单缸冷却腔室CFD优化分析

对某发动机单缸冷却腔室的流动特性进行CFD分析,得到其流速和导热分布情况。由此对流速与压降异常部位进行优化设计。分析结果表明:优化后的冷却腔室结构的流动特性得到改善,保证了气缸单元具有良好的流动状态和较小的压降。