A simple model for the simulation of the hydraulic behaviour and heat transfer of a single micro channel is formulated, assessed and optimized. The model is based on a thermally developing flow regime. The results of the optimization show that a reduction of 7.8% in thermal resistance can be achieved using non-uniform channels instead of uniform channels. Furthermore, the assumptions of the simple model are validated by comparing the results with a more accurate, numerical model. It is shown that the simple model is sufficiently accurate to simulate the hydraulic and thermal behaviour of micro channels as such. However, the effective improvement of channel width optimization cannot accurately be determined by the analytical models.

The hydrocarbon mixture of R290/R600a with mass ratio of 50/50 is regarded as a promising long-term refrigerant to replace R12 in domestic refrigerators since it can potentially provide higher COP than R12 system under the same operating conditions. In practical application, the length of the capillary tube should be matched with this alternative mixture; otherwise, the refrigerator system can probably consume more energy than the R12 system. In this paper, a simulation model of adiabatic capillary tube, in which some empirical coefficients are modified due to their inapplicability for R290/R600a, is established to illustrate the influences of the length of the capillary tube on the performance of the refrigerator. During the investigation a domestic refrigerator of 150L is used to test the thermodynamic cycle performances of R290/R600a (50/50) under conditions with different lengths of the capillary tube. The experimental results indicate that the R290/R600a (50/50) mixture with the optimized capillary length, which was obtained from simulation, has the higher energy efficiency and a lower discharge temperature than the original R12 system. The proposed mixture is proven to be a suitable long-term alternative in terms of its excellent thermodynamic cycle performances.

A gas-turbine cogeneration system with a regenerative air preheater and a single-pressure exhaust gas boiler serves as an example for application of CHP Plant. This CHP plant which can provide 30 MW of electric power and 14kg/s saturated steam at 20 bars. The plant is comprised of a gas turbine, air compressor, combustion chamber, and air pre-heater as well as a heat recovery steam generator (HRSG). The design Parameters of the plant, were chosen as: compressor pressure ratio (re), compressor isentropic efficiency (ηac), gas turbine isentropic efficiency (ηgt), combustion chamber inlet temperature (T3), and turbine inlet temperature (T4). In order to optimally find the design parameters a thermoeconomic approach has been followed. An objective function, representing the total cost of the plant in terms of dollar per second, was defined as the sum of the operating cost, related to the fuel consumption. Subsequently, different pars of objective function have been expressed in terms of decision variables. Finally, the optimal values of decision variables were obtained by minimizing the objective function using Evolutionary algorithm such as Genetic Algorithm. The influence of changes in the demanded power on the design parameters has been also studied for 30, 40 MW of net power output.

Using the analogy between heat and mass transfer processes, the recently developed entransy theory is extended in this paper to tackle the coupled heat and mass transfer processes so as to analyze and optimize the performance of evaporative cooling systems. We first introduce a few new concepts including the moisture entransy, moisture entransy dissipation, and the thermal resistance in terms of the moisture entransy dissipation. Thereinafter, the moisture entransy is employed to describe the endothermic ability of a moist air. The moisture entransy dissipation on the other hand is used to measure the loss of the endothermic ability, i.e. the irreversibility, in the coupled heat and mass transfer processes, which consists of three parts: (1) the sensible heat entransy dissipation, (2) the latent heat entransy dissipation, and (3) the entransy dissipation induced by a temperature potential. And then the new thermal resistance, defined as the moisture entransy dissipation rate divided by the squared refrigerating effect output rate, is recommended as an index to effectively reflect the performance of the evaporative cooling system. Meanwhile, a minimum thermal resistance law for optimizing the evaporative cooling systems is developed. In the end, several direct and indirect evaporative cooling processes are analyzed to illustrate the applications of the proposed concepts.

Pyroelectric energy conversion offers a novel approach for directly converting waste heat into electricity. This paper reports numerical simulations of a prototypical pyroelectric energy converter. The two-dimensional mass, momentum, and energy equations were solved to predict the local and time-dependent pressure, velocity, and temperature. Then, the heat input, pump power, and electrical power generated were estimated, along with the thermodynamic energy efficiency of the device. It was established that reducing the length of the device and the viscosity of the working fluid improved the energy efficiency and power density by increasing the optimum operating frequency of the device. Results show that a maximum efficiency of 5.2% at 0.5 Hz corresponding to 55.4% of the Carnot efficiency between 145 and 185°C can be achieved when using commercial 1.5 cst silicone oil. The maximum power density was found to be 38.4 W/l of pyroelectric material.

The heat transfer coefficient of convection from the wall to the flow depends on flow type, on surface temperature distribution in a stream-wise direction, and in transient cases also on time. In so-called conjugated problems, the surface temperature distribution of the wall and flow are coupled together. Thus, the simultaneous solution of convection between the flow and wall, and conduction in the wall is required because heat transfer coefficients are not known. For external and internal flows very accurate approximate analytical expressions have been derived for heat transfer in different kinds of boundary conditions which change in flow direction. Due to the linearity of the energy equation the superposition principle can be adopted to couple with these expressions the surface temperature and heat flux distributions in conjugated problems. In the paper this type of approach is adopted and applied to a number of industrial applications ranging from flat plates of electroluminecence displays to the optimization of heat transfer in fins, fin arrays and mobile phones.

Optimization of heat exchangers (HE), compact heat exchangers (CHE) and micro-heat exchangers by design of their basic structure is the focus of this work. Consistant models are developed to describe transport phenomena in a porous medium that take into account the scales and other characteristics of the medium morphology. Equation sets allowing for turbulence and two-temperature or two-concentration diffusion are obtained for non-isotropic porous media with interface exchange. The equations differ from known equations and were developed using a rigorous averaging technique, hierarchical modeling methodology, and fully turbulent models with Reynolds stresses and fluxes in the space of every pore. The transport equations are shown to have additional integral and differential terms. The description of the structural morphology determines the importance of these terms and the range of application of the closure schemes. A natural way to transfer from transport equations in a porous media with integral terms to differential equations with coefficients that could be experimentally or numerically evaluated and determined is described. The relationship between CFD, experiment and closure needed for the volume averaged equations is discussed. Mathematical models for modeling momentum and heat transport based on well established averaging theorems are developed. Use of a ‘porous media’ length scale is shown to be very beneficial in collapsing complex data onto a single curve yielding simple heat transfer and friction factor correlations. The general transport equations developed for a single phase fluid in a heat exchange medium have many more integral and differential terms than the homogenized or classical continuum mechanics equations. Once these terms are dealt with by closure, the resulting equation set is relatively simple and their solution is obtained using simple numerical methods quickly enough for multiple parameter optimization using Design of Experiment (DOE) or Genetic Algorithms (GA). Current efforts to significantly improve the performance of a HE for electronic cooling, a two temperature problem, and of a finned tube heat exchanger, a three temperature problem, are described.

Heat transfer optimization is ubiquitous because improving heat transfer performance could increase the energy utilization or reduce the weight or size of heat transfer equipments. This article discusses the optimization in heat transfer using the new physical quantity, entransy, in recent years. Entransy describes the heat transfer ability. When heat is transferred from a high temperature to a low temperature and entransy dissipation is produced. Heat transfer is irreversible from the viewpoint of entransy. The entransy transfer efficiency can be defined using the concept of entransy. Definition of entransy, entransy flux, and entransy dissipation are given and the entransy balance equations are derived for conduction, convection and thermal radiation based on the energy equation. The minimum entransy dissipation principle for prescribed heat flux boundary conditions and a maximum entransy dissipation principle for prescribed temperature boundary conditions are investigated. These two principles are called entransy dissipation extreme (EDE) principle. An equivalent or average thermal resistance of a system can be defined based on the entransy dissipation and the EDE principle becomes the minimum thermal resistance principle. These principles can be used to optimize heat transport with constraints and some examples are presented. The relation of entransy with thermomass is discussed and comparison between EDE and entropy generation optimization is made. The essence of the entansy is the energy of thermomass.

The trend towards a better understanding of the fundamentals of nucleate boiling in re-entrant cavities is supported by the variation of the heating surface’s characteristics and the identification of parameters influencing the heat transfer at enhanced tubes. The optimized surface of enhanced evaporator tubes supports the bubble formation by providing stable nucleation sites, which are cavities that trapped the necessary amount of vapor to generate the next bubble. The optimal size of the cavities for bubble formation depends on various thermodynamic properties of the fluid and the wall material. The knowledge of these physical mechanisms is important for the further optimization. The influence of micro- and macrostructures on the overall heat transfer coefficient is investigated with the refrigerant R134a and the hydrocarbon propane (R290) boiling in a wide range of reduced pressures (p* = p s /p c = 0.03 to 0.5) and heat fluxes (0.05 to 100 kW/m 2 ). The measurements are carried out using a standard apparatus and a horizontally positioned, electrically heated surface with various wall materials. Two different materials — copper and mild steel — with the same surface preparation by polishing are investigated. Furthermore, heat transfer measurements are carried out on a plain mild steel tube and on an industrially manufactured surface of the GEWA-PB type. The polished surfaces demonstrate a deterministic microstructure, the roughness parameters depends strongly on the measurement direction. The heat transfer coefficient as function of the heat flux of the polished copper tube can be described by the correlation of the VDI Heat Atlas, while the mild steel surface differ from former investigations due to the deep re-entrant cavities remaining from the drawn surface. The onset of boiling is nearly the same of both materials because of these cavities on the mild steel surface. As presented in the recent years, the heat transfer of nucleate boiling at tubes with subsurface channels can be divided into different domains, each influenced by different parameters like wettability, the product of vapor density and evaporation enthalpy. The identification of parameters influencing the bubble formation is done by heat transfer measurements, high-speed-video recording and photographic documentation. The experimental results of this work are compared to results of the polished surfaces. The heat transfer coefficient increases drastically for the enhanced tube, especially for beginning nucleation. The same α-q-relationship as on plain tubes is observed for higher pressures and heat fluxes but for three times higher values of the heat transfer coefficient α.

In the present paper, we conducted thermal optimization of plate-fin heat sink with fin thickness varying in the vertical direction. The model based on volume averaging theory (VAT) was used for this optimization. It is shown that the thermal resistance of plate-fin heat sink is reduced by allowing the fin thickness to increase in the vertical direction. In the case of water-cooled heat sink, the thermal resistance decreases up to about 20%. The amount of the reduction increases as either pumping power increases or the length of heat sink decreases.

Hydrogen-fuelled internal combustion engines are still investigated as an alternative for current drive trains because they have a high efficiency, near-zero noxious and zero tailpipe greenhouse gas emissions. A thermodynamic model of the engine cycle enables a cheap and fast optimization of engine settings for operation on hydrogen. The accuracy of the heat transfer sub model within the thermodynamic model is important to simulate accurately the emissions of oxides of nitrogen which are influenced by the maximum gas temperature. These emissions can occur in hydrogen internal combustion engines at high loads and they are an important constraint for power and efficiency optimization. The most common models in engine research are those from Annand and Woschni, but they are developed for fossil fuels and the heat transfer of hydrogen differs a lot from the classic fuels. We have measured the heat flux and the wall temperature in an engine that can run on hydrogen and methane and we have investigated the accuracy of simulations of the heat transfer models. This paper describes an evaluation of the models of Annand and Woschni with our heat flux measurements. Both models can be calibrated to account for the influence of the specific engine geometry on the heat transfer. But if they are calibrated for methane, they fail to calculate the heat transfer for hydrogen combustion. This demonstrates the models lack some gas or combustion properties which influence the heat transfer process in the case of hydrogen combustion.

The natural convection cooling capability in a compact item of electronic equipment was investigated quantitatively by experiment and numerical simulation with a simple channel model. The optimization of the channel sizes, especially the clearance between heated walls, was discussed. The channel model, which consists of a vertical duct of rectangular section, was applied as the experimental model of electronic equipment in this study. The channel model consists of two heated copper walls and two transparent acrylic walls. The clearance between the copper walls of the channel was varied from 5 mm to 15 mm. Temperature measurement on the copper wall surfaces and velocity measurement of natural air flow in the channel by using a particle image velocimetry (PIV) were conducted for a few clearances of the channel. Numerical simulation was also carried out, with a model following the experimental setup, for more detailed discussion of various clearances of the channel. The relationship between the clearance and the temperature rise of the walls or velocity profile was investigated. The correlation between the Rayleigh number and the Nusselt number was obtained from measured temperature. The natural cooling capability and the velocity profiles depend on the clearance between the copper walls. When the wall clearances are more than 15 mm, the cooling is not enhanced. On the other hand, in the case that the clearance becomes less than 7 mm, the cooling capability becomes significantly lower. Consequently, it is clarified that the clearance from 8 mm to 10 mm is the best size for natural cooling from the view point of the space and the capability.

Earlier efforts to optimize a simple pin fin heat sink only considered in line or rotated square configurations, a six or seven parameter problem. In this work, a staggered non-square array, two pitch dimensions, with non-circular pin cross-section are added to the heat sink description. The effects of optimizing fin eccentricity and pitch have both been shown to enhance the convective heat transfer as well as to increase the required pumping power thereby contributing to the performance. To optimize, the full conjugate problem must be solved. Volume averaging theory (VAT) is used to rigorously cast the point-wise conservation of energy, momentum and mass equations into a form that represents the thermal and hydraulic properties of the channel morphology. With a VAT based model, multiple heat sinks can be analyzed quickly while being able to change all dimensions. Using commercial software, S-Matrix Corporation’s DOE Fusion, a multi-parameter pin fin heat sink is optimized.

This paper described numerical the procedure used to determine the optimum configuration of two rows of pin fins so that the total heat transfer rate is maximized. The heat transfer across the fins is by laminar forced convection bathed by a free-stream that is uniform and isothermal. The optimization is subjected to fixed volume of fin materials. The dimensions of the optimized configuration are the result of balancing conduction along the fins with convection transversal to the fins. Numerical results on the effect of dimensionless pressure drop and the thermal conductivity ratio on the optimal configuration are reported. Results obtained from numerical analyses are comparable to those in the open literature. The results also show that the flow structure performs best when the fin diameters and heights are non-uniform.

The heat transfer from cylinder to air of a 2-stroke internal combustion finned engine has been simulated. For this purpose, a 2-D model of the block and head has been done. Starting from the dimensions of a real engine, annular cylindrical and spherical symmetric walls and fins have been used to obtain an equivalent simplified geometry, where the heat transfer rate is the same as that in the real engine. The cylinder body, cylinder head (both provided with fins) and piston have been numerically analyzed and optimized in order to minimize engine dimensions. The maximum temperature admissible at the hottest point of the engine has been adopted as the limiting condition. An engine temperature map has been presented as additional information. Cyclically variable inner cylinder conditions (thermodynamic, thermal and chemical) proceed from a previous work; convective and radiative inner boundary conditions and convective external conditions have also been taken into account in this work. A network simulation model (NSM) has been used as the numerical tool in the analysis presented.

The development and testing of a new low-profile, air-cooled heat sink for use in cooling electronic modules are presented. This heat sink consists of a micro-groove surface with a special manifold that generated high heat transfer coefficients but low pressure drops. The optimization of the various geometries that make up a micro-grooved heat sink is discussed, as well as the various CFD simulations that were employed to estimate and optimize the thermal performance of a micro-grooved heat sink. The thermal performance of a prototype micro-grooved heat sink is compared with that of a finned heat sink. Other characteristics of the micro-grooved heat sinks will also be contrasted with the finned heat sink.

In the present paper, geometry specification in the inverse heat conduction problems (IHCP) is applied to detect the location and size of defect in a solid body. A crack or cavity is modeled as a supper-elliptic geometry whose parameters are estimated with inverse heat conduction problems. Both inverse analysis and gradient-based optimization method have been applied to an inverse algorithm that iteratively estimates the defect shape parameters. The inverse analysis is based on recording temperatures data on outer surface of solid domain that determines the objective function in the inverse algorithm with estimated and calculated temperatures. The employed gradient-based optimization method is constructed with the adjoint and sensitivity equations that are used to calculate the gradient of the objective function and the search step size, respectively. An unstructured grid is used and the computational domain is discretized with triangular elements. The finite element method (FEM) is employed to discretize the equations in analysis plus sensitivity and adjoint equations. The effects of different Biot numbers and noisy temperature data are investigated on inverse algorithm and the size and location of crack and complex cavity are calculated. Results show that the estimated shape has good agreement with exact shape of defect. The decrease of noisy data has improve the convergence rate and the increase of Biot numbers causes the estimated shape has the best accuracy in all cases.

The aim of this work is to present a methodology to develop cost-effective thermal management solutions for microelectronic devices, capable of removing maximum amount of heat and delivering maximally uniform surface temperature distributions. The topological and geometrical characteristics of multiple-story three-dimensional branching networks of microchannels were developed using multi-objective optimization. The design variables which will be subject to optimization in this analysis are the geometric parameters of the microchannel network, i.e. the number of network floors in a 3D network, the amount of branching levels per floor, the connectivity of the cooling channels, their cross-sectional areas and lengths. A conjugate heat transfer analysis software package (CHETSOLP) and an automatic 3D microchannel network generator (3DBNGEN) were developed and coupled with a multi-objective particle-swarm optimization (MOPSO) algorithm with a goal of creating a design tool for 3D networks of optimized coolant flow channels. Numerical algorithms in the conjugate heat transfer solution package include a quasi-1D thermo-fluid solver (COOLNET) and a 3D steady heat diffusion solver, which were validated against results from high-fidelity Navier-Stokes equations solver and analytical solutions for basic fluid dynamics test cases. The conjugate heat transfer solution is achieved by simultaneous prediction of the quasi-1D internal flow-field in the microchannel network and 3D internal temperature field in the solid substrate [1]. Minimization of the pumping power requirement and maximization of total heat removal subject to temperature uniformity (at the heated surface) were the objectives. Pareto-optimal solutions demonstrate that thermal loads of up to 400 W/cm 2 can be managed with 3D multi-floor microchannel networks, with pumping power requirements that are up to 50% lower with respect to pumping power requirements in currently used high-performance cooling technologies, such as jet impingement and hybrid impingement-microchannel flow.

This paper presents numerical optimization of a rotating rectangular channel design with the staggered arrays of pin-fins using Kriging meta-modeling technique. In the reference case, the channel aspect ratio (AR) is 4:1, the pin length to diameter ratio (H/D) is 2.0, and the pin spacing to diameter ratio is 2.0 in both the streamwise and spanwise directions. The rotation number is 0.15, while the Reynolds number based on hydraulic diameter is fixed at 10,000. Rotation of the channel slightly reduces the heat transfer on the leading surface and increases it on the trailing surface due to Coriolis effects. Two non-dimensional variables, the ratio of the height to diameter of the pin-fin and the ratio of the spacing between the pin-fins to diameter of the pin-fins, are chosen as design variables. The objective function defined as a linear combination of heat transfer and friction loss related terms with a weighting factor is selected for the optimization. Twenty training points generated by Latin hypercube sampling (LHS) are evaluated by three-dimensional Reynolds-averaged Navier-Stokes (RANS) analysis with the shear stress transport (SST) model for the turbulence closure. The predictions of objective function by Kriging meta-modeling at optimum point show reasonable accuracy in comparison with the values calculated by RANS analysis. The results of optimization show that the cooling performance of the optimized shape is enhanced significantly through the optimization.

The relative inverse admittance is used to obtain the geometry of the optimum longitudinal rectangular fin of a set of fins of the same volume that radiate to free space. With this information a set of new universal curves that permits direct optimization of 1-D and 2-D practical fins. To ensure a dissipation effect, lines of constant effectiveness are introduced in the optimization graph. Examples are shown.