Simulation of conjugate heat transfer in a microchannel system by a hybrid algorithm

Microchannels are of current interest for use in heat exchangers where very high heat transfer performance is desired. Microchannels provide very high heat transfer coefficients because of their small hydraulic diameters. In this study, an investigation of fluid flow and heat transfer in microchannels is conducted. A review of the literature published regarding fluid flow and heat transfer in microchannels is provided in this study. A thorough background on the theory of internal convective heat transfer is provided as well. A critical analysis of some of the published heat transfer experiments on microchannels is also given. It was found that some of the experimental methods published recently employ experimental and data reduction techniques which may result in errors for reported Nusselt numbers. A brief computational fluid dynamics (CFD) investigation into the heat transfer and fluid flow performance of some channels with designed bumps is also presented. It was found that designed channels offer enhanced Nusselt numbers in the turbulent regime at the cost of a higher friction factor when compared to a plain channel. Fluid flow and heat transfer experiments were conducted on a copper microchannel heat exchanger (MHE). An experimental method of imposing a constant surface temperature to the MHE was used. A description of the experimental apparatus and procedure is provided. The friction factor results from the experiments agree fairly well with theoretical correlations. The experimental Nusselt number results agree with theory very well in the transition/turbulent regime, but the results show a higher Nusselt number in the laminar regime than predicted by theoretical correlations. A full description of the data reduction and analysis of the experimental data is given. A CFD model was created to simulate the fluid in the inlet plenum and the microchannels. The results from these simulations are presented, and they show good agreement with the experimental data in the transition/turbulent regime as well as with theoretical correlations for laminar and turbulent flow.

In order to study the fundamental physical mechanisms of fluid flow and heat transfer in microchannels, many effects should be taken into account. The effect of axial heat conduction on heat transfer in microchannels is one of the hottest topics. Experimental investigation was carried out to analyze heat transfer characteristics of methanol flowing through microchannel heat sink, which consists of 10 parallel triangular microchannels. Experimental results show that the temperature distribution on the heated wall do not change linearly along the channel, which mainly caused by the axial heat conduction in the wall. The ratio of the power due to the axial heat flux to the Joule heating in the heater, and the axial heat conduction number were used to evaluate the heat conduction effect in the wall. Many factors play important roles in the axial heat conduction, including geometric configuration, material of the wall, and Reynolds number. The experimental study reveals that the axial heat conduction effect is gradually strengthened as the Reynolds number decreases.

Simulation and experimental investigation of pressure loss and heat transfer in microchannel networks containing bends and T-junctions

There is a growing interest for applications of heat and mass transfer in microchannels. Consequently, several numerical and experimental studies related to transport phenomena in microchannels have been carried-out. The flow problem in microchannels is different from the macro-scale problems due to rarefaction effects, surface roughness, viscous dissipation heating as well as other effects. As a result, a number of studies have been proposed for investigating the micro-flow problem and how each of these phenomena affect heat and mass transfer characteristics. Naturally, there is particular focus on how the observed micro-scale phenomena differ from the traditionally known macro-scale effects. In the realm of simulation studies for heat transfer in micro-sized channels, this paper proposes a comparison between hybrid solution strategies for solving steady heat transfer problems within microchannels. The Generalized Integral Transform Technique (GITT) is employed as the main solution methodology; however, different solution approaches are investigated in order to determine advantages and drawbacks of each alternative. The presented results can serve as guidance for choosing an optimum solution methodology for thermally developing heat transfer in microchannels using GITT implementations.

Many problems in fluid dynamics and heat transfer are defined by nonlinear equations. In this paper steady state convection-diffusion-reaction (SSCDR) equations are solved by dual reciprocity boundary element method (DRBEM). DRBEM is employed to transform the domain integrals into the boundary only integrals by employing the fundamental solution of the Laplace Equation. The linear Radial Basis Functions (RBFs) is used in the dual reciprocity technique. To verify the accuracy of the approach, the numerical results of an examples is calculated and compared with the analytical solution. The comparison demonstrates the usefulness of the approach for diffusion-dominated problems with low velocity values.

The present paper is devoted to experimental investigations of the flow and the associated heat transfer in two-dimensional microchannels. Scaling laws pertaining to the hydrodynamics and heat transfer in microchannels are not yet clearly established. The published results are affected by a significant scatter, owing to the various conditions used in the experiments, and, most likely, owing to the difficulty of measurements at micronic scales. The present facility was designed to modify easily the channel height e. It was then possible to investigate hydrodynamics and heat transfer in channels of height ranging from 1 mm, which corresponds to conventional size, up to 0.1 mm, where size effects are expected. Size effects were therefore tested in the same set-up and with the same channel walls for all the experiments, which were carried out with demineralized water. Measurements of the overall friction coefficient and of local Nusselt numbers show that the classical laws of hydrodynamics and heat transfer are verified for e>0.4 mm. For lower values of e, a significant decrease of the Nusselt number is observed whereas the Poiseuille number keeps the conventional value of laminar developed flow. The transition to turbulence is not affected by the channel size.

The paper presents both three and two-dimensional numerical analysis of convective heat transfer in microchannels. The three-dimensional geometry of the microchannel heat sink followed the details of the experimental facility used during a previous research step. The heat sink consisted of a very high aspect ratio rectangular microchannel. Two channel heights, namely 1mm and 0.3mm (0.1mm), were used for 3D (2D) numerical model respectively. Water was employed as the cooling liquid. The Reynolds number ranged from 200 to 3000. In the paper, the thermal entrance effect is analyzed in terms of heat transfer efficiency. Finally, the comparison between measured and computed heat flux and temperature fields is presented. Contrary to the experimental work, the numerical analysis did not reveal any significant scale effect in heat transfer in microchannel heat sink up to the smallest size considered (0.1 mm).

The paper presents both three and two-dimensional numerical analysis of convective heat transfer in microchannels. The three-dimensional geometry of the microchannel heat sink followed the details of the experimental facility used during a previous research step. The heat sink consisted of a very high aspect ratio rectangular microchannel. Two channel spacings, namely 1 mm and 0.3 mm (0.1 mm), were used for three-dimensional (two-dimensional) numerical model, respectively. Water was employed as the cooling liquid. The Reynolds number ranged from 200 to 3000. In the paper, thermal entrance effects and conduction/convection coupling effects are considered both for the test case of uniform channel inlet conditions and the complete geometry of the experiment. Finally, the comparison between measured and computed heat flux and temperature fields is presented. Contrary to the experimental work, the numerical analysis did not reveal any significant scale effect on heat transfer in microchannel heat sink down to the smallest size considered (0.1 mm).

Convective heat transfer during laminar fluid flow through channels is an important technological problem. The literature provides much research data on heat transfer phenomena occurring during fluid flow through channels of different dimensions and shapes based on theoretical analysis, numerical calculations and experimental investigations. Theoretical analysis has attempted to solve the problem of convective heat transfer in channels of basic shape in simplified conditions of fluid flow. Laminar convective heat transfer in pipes where the fluid velocity profile was parabolic was described by Graetz (Graetz, 1885). His solution to this classical problem was further developed by Sellars, Tribus and Klein (Sellars et al., 1956). Alternatively, Levěque (Levěque, 1928) investigated heat transfer in the entrance region of pipes where hydraulic stabilisation occurs. All these works offer an analytical solution to the problem. Numerical investigation of heat transfer in the entrance region of pipes was initiated by Kays (Kays, 1955) who provided the results of numerical calculations for three types of gas flow conditions: uniform wall temperature, uniform heat flux and uniform difference between wall and fluid temperature. On the other hand, the work of Sider and Tite (Sider and Tite, 1936) is an example of an early experimental investigation where an empirical formula for the heat transfer coefficient calculations, regardless of the fluid being heated or cooled, is provided. The above-mentioned works were followed by further research on the laminar convective fluid flow in channels. Particularly, heat transfer in channels of small hydraulic diameters was extensively investigated. It turned out that heat transfer and fluid flow in small diameter channels often differed from those in channels of conventional dimensions. Mathematical equations describing heat transfer cannot always be applied to minior microchannels. Hence some researchers (Adams et al., 1998), (Tso and Mahulikar, 2000), (Owhaib and Palm, 2004), (Lelea et al., 2004), (Celata et al., 2006), (Kandlikar et al., 2006), (Yang and Lin, 2007), (Yarin et al., 2009) examined liquid and gas convective heat transfer in circular miniand micro-channels using experimental methods, mostly the thermal balance method. However, the surface and fluid temperature measurements using this method are difficult to obtain due to the small size of the channels tested. Application of mass transfer investigations and the mass/heat transfer analogy makes it possible to avoid the problem as it excludes temperature measurements. In this chapter application of the mass/heat transfer

Advanced Microsink Design Utilizing Disruptive Structures

Numerical simulation of laminar heat transfer in microchannels with rough surfaces characterized by fractal Cantor structures

Recently, we have proposed a robust and computationally efficient numerical algorithm for the optimization of 2-D and 3 -D catalysts distributions in Proton Exchange Membrane Fuel Cells (PEMFCs) using a gradient-based technique [1-3]. The algorithm is based on the computation of the catalyst sensitivity functions of the cell current and cell voltage by using the adjoint method. This method was initially developed by the applied mathematics community to solve optimization problems in fluid dynamics, climate, and heat transfer problems and, later, by other research groups to solve optimization problems in magnetics, model parameter determination, and semiconductor devices [4-6]. It was only recently that COMSOL, a popular finite element solver, has introduced the adjoint method, which has started to be used by the electrochemical community for calculation of sensitivities of platinum distribution in PEMFCs [7,8]. In this presentation we analyze the cell current, cell voltage, and spectral electrochemical impendence properties of PEMFCs by using the catalyst sensitivity functions of cell voltage, γPt(r). These functions show how much the cell voltage is increasing by adding 1 unit amount of platinum at a given location inside the catalyst layer (and assuming the cell is operating at the same current density). For instance, the figure below shows the 2-D catalysis sensitivity functions of the cell voltage for two cells with membrane thicknesses of 60 mm and 25 mm, in which the catalyst is distributed uniformly inside the cell. It is apparent from these figures that in order to increase the cell voltage and consequently the power of the cell, one needs to increase the concentration of Pt particles in the regions under the oxygen openings. As it will be shown at the conference the optimum catalyst distribution also depends on the operating temperature, catalyst and gas diffusion layers porosities, Nafion content, and cell current. In addition to the above analysis, we will also introduce a technique for the analysis of variability of polarization curves induced by the randomness of pore sizes and pore shapes in the catalyst and gas diffusion layers in PEMFCs. The technique is based on the evaluation of sensitivity functions of the cell voltage and can also be extended to the analysis of variability induced by the random platinum distribution in the catalyst layers (which is assumed to have a uniform random distribution). More details about the method for the analysis of variability effects, as well as about the numerical implementation of the adjoint method in the case of finite element simulations and its computational efficiency will be presented at the conference. [1] J. Lamb, G. Mixon, and P. Andrei, “Optimization of polymer electrolyte membrane fuel cells with a large number of degrees of freedom”, ECS 231Meeting, New Orleans, LA, 2017. [2] J. Lamb, G. Mixon, and P. Andrei, “Mathematical optimization of the spatial distribution of platinum particles in the catalyst layer of PEMFCs”, PRIME 2016 Meeting, Honolulu, HI, 2016. [3] P. Andrei, G. Mixon, M. Mehta, and V. Bevara, “Design of the catalyst layers in PEMFCs using an adjoint sensitivity analysis approach”, ECS Transactions 66(8), 91-128, 2015. [4] D. Cacuci, M. Ionescu-Bujor and M. N. Ionel, Sensitivity and Uncertainty Analysis, Volume 2: Applications to Large-Scale Systems, Chapman & Hall/CRC (2005) [5] W. K. Anderson and V. Venkatakrishnan, “Aerodynamic design optimization on unstructured grids with a continuous adjoint formulation”, Computers & Fluids, 28, 443 (1999). [6] P. Andrei, I. Mayergoyz, “Quantum mechanical effects on random oxide thickness and random doping induced fluctuations in ultrasmall semiconductor devices”, Journal of Applied Physics, 94, 7163-7172 (2003). [7] COMSOL Multiphysics Software, https://www.comsol.com. [8] F. C. Cetinbas, S. G. Advani and A. K. Prasad, “Three dimensional proton exchange membrane fuel cell cathode model using a modified agglomerate approach based on discrete catalyst particles”, Electrochimica Acta, 174, 787 (2015). Figure 1

The presence of a balance between heat transfer rate and pressure drop is an important issue in designing passages of coolant flows to repel high heat flux. This kind of heat transfer is excessively used in cooling microprocessor chips. Application of microchannels leads to an increase in heat transfer and higher efficiency; however, one main challenge of using these channel kinds is the pressure drop, as well as high power requirement for pumping. One effective way of reducing pressure drop is to substitute some parts of the microchannels surface with hydrophobic surfaces. In the present study, a microchannel, with a rectangular cross-section, was modeled by two kinds of hydrophilic/hydrophobic patterns. Governing equations, including continuity, momentum and energy equations, are solved by the use of computational fluid dynamics. The model under investigation includes two transversal and longitudinal patterns. The fluid flow is three-dimensional and incompressible. In addition, hydrophilic surfaces act as rips of flow and, owing to possessing no-slip condition, have an effect on the resultant heat transfer. Comparisons between longitudinal and transversal models show that in the presence of longitudinal models, the pressure drop decrease is 1.5 times more than transversal ones. According to results, using a longitudinal hydrophobic pattern on one of the walls leads to a 12% decrease of mean velocity in a fully developed region. Also, outcome results indicated that the use of hydrophobic models could reduce the required power fluid pump up to 69% and increases heat flux up to 15%.

Aerodynamic characteristics of a guided rocket projectile are numerically simulated. Simulations are performed in a range of flight conditions using a commercial CFD software FLUENT, and variations of lift coefficients and drag coefficients with Mach numbers and angles of attack were demonstrated. The numerical results also indicate that the angle of canard deflection has significant influence on the flow field near tailfins.

The solution of the conjugate problem of convective-conductive heat transfer in the channels of power plants is presented. The problem of convective heat transfer in the gas phase is solved by the integral theory of heat transfer. A one-dimensional problem of conductive heat transfer in the material of the wall is solved by the finite-difference method. Relative laws of heat and mass transfer and friction are obtained by numerical integration with respect to the boundary-layer thickness. The effect of the material and geometry of the wall on the level of problem “conjugation” is studied.