Optimization of tree‐shaped flow distribution structures over a disc‐shaped area

In this paper, we review the fundamental problem of how to design a flow path with minimum overall resistance between one point (O) and many points situated equidistantly on a circle centred at O. This is a fundamental problem in energy engineering: the distribution of fluid, energy, electric power, etc., from points to surrounding areas. This problem is also fundamental in heat transfer and electronics cooling: how to bathe and cool with a single stream of coolant a disc‐shaped area or volume that generates heat at every point. This paper outlines, first, a direct route to the construction of effective tree‐shaped flow structures. The starting point is the optimization of the shape of each elemental area, such that the length of the flow path housed by the element is minimized. Proceeding towards larger and more complex structures—from elements to first constructs, second constructs, etc.—the paper develops tree‐shaped flow structures between one point and a straight line, as an elemental problem, and a circle and its centre. We also consider the equivalent tree‐shaped networks obtained by minimizing the pressure drop at every step of the construction, in accordance with geometric constraints. The construction method is applied to a fluid flow configuration with laminar fully developed flow. It is shown that there is little difference between the two methods. The minimal‐length structures perform very close to the fully optimized designs. These results emphasize the robustness of optimized tree‐shaped flows. Copyright © 2003 John Wiley & Sons, Ltd.     

Effect of flow fields and humidification of reactant and oxidant on the performance of scaled‐up PEM‐FC using CFD code

The present study focuses on three‐dimensional two‐phase CFD investigation on scaled‐up proton exchange membrane fuel cell (PEM‐FC) for an active area of 100 cm² with different designs of serpentine and parallel flow configuration. The humidification of hydrogen and oxygen is varied from 10% to 100% to study the PEM‐FC performance. The numerical results of polarization curves predicted in this study have been numerically validated with that of the literature for both parallel and counter serpentine flow channels with active area of 24.8‐cm² PEM‐FC. Further upon validation, the numerical study is extended for scaled‐up PEM‐FC with active area of 100 cm² with different flow path designs to study its performance characteristics namely polarization curves, species concentration distribution, water content in the membrane electrolyte, and proton conductivity to evaluate the fuel cell performance. The three‐dimensional CAD models are created in SOLIDWORKS 10.0 and are discretised hexahedrally using finite volume method. The various governing equations namely conservation of mass, momentum, energy, species concentration, and electrochemical equations are solved numerically with the necessary boundary conditions using the CFD code. The novel design of straight zigzag flow path shows the better performance output over the other designs investigated which is having a higher power density of 0.3711 W/cm² for 100% relative humidity of reactant and oxidant.     

Analysis of two‐dimensional porous fins with variable thermal conductivity

Analysis of porous fins for their higher heat transfer in comparison with solid fins with identical volumes has attracted significant attention. In this paper, a two‐dimensional thermal analysis of a porous fin having variable thermal conductivity coefficient is performed using finite difference method. Heat transfer through porous media is simulated using passage velocity from Darcy's model. The thermal conductivity of the solid phase is considered as a linear function of temperature. It is found that the temperature profile of the fin is completely two‐dimensional even for high Rayleigh and Darcy numbers (Ra = 10³～10⁴, Da = 0.01), because the temperature changes significantly along the transverse axis especially for lower Rayleigh and Darcy numbers. Also, the effects of important nondimensional parameters such as Rayleigh and Darcy numbers, porosity, Nusselt, thermal conductivity, and aspect ratio on the temperature profile are investigated. The results demonstrate that the temperature distribution is strongly dependent on the Rayleigh and Darcy numbers.     

Back‐analyses of in‐situ thermal response test (TRT) for evaluating ground thermal conductivity

In this study, a series of computational fluid dynamics (CFD) numerical analyses was performed in order to evaluate the performance of six full‐scale closed‐loop vertical ground heat exchangers constructed in a test bed located in Wonju, South Korea. The high‐density polyethylene pipe, borehole grouting and surrounding ground formation were modeled using FLUENT, a finite‐volume method program, for analyzing the heat transfer process of the system. Two user‐defined functions accounting for the difference in the temperatures of the circulating inflow and outflow fluid and the variation of the surrounding ground temperature with depth were adopted in the FLUENT model. The relevant thermal properties of materials measured in laboratory were used in the numerical analyses to compare the thermal efficiency of various types of the heat exchangers installed in the test bed. The numerical simulations provide verification for the in‐situ thermal response test (TRT) results. The numerical analysis with the ground thermal conductivity of 4.0 W/m?K yielded by the back‐analysis was in better agreement with the in‐situ TRT result than with the ground thermal conductivity of 3.0 W/m?K. From the results of CFD back‐analyses, the effective thermal conductivities estimated from both the in‐situ TRT and numerical analysis are smaller than the ground thermal conductivity (=4.0 W/m?K) that is input in the numerical model because of the intrinsic limitation of the line source model that simplifies a borehole assemblage as an infinitely long line source in the homogeneous material. However, the discrepancy between the ground thermal conductivity and the effective thermal conductivity from the in‐situ TRT decreases when borehole resistance decreases with a new three pipe‐type heat exchanger leads to less thermal interference between the inlet and outlet pipes than the conventional U‐loop type heat exchanger. Copyright © 2012 John Wiley & Sons, Ltd.     

Influence of Viscous Dissipation on non‐Darcy Mixed Convection Flow of Nanofluid

In this paper, the steady fully developed non‐Darcy mixed convection flow of a nanofluid in a vertical channel filled with a porous medium with different viscous dissipation models is analyzed. The Brinkman‐Forchheimer extended Darcy model is used to describe the fluid flow pattern in the channel. The transport equations for a nanofluid are solved analytically using the seminumerical‐analytical method known as differential transformation method, and numerically with the Runge‐Kutta shooting method. Finally, the influence of pertinent parameters, such as solid volume fraction, different nanoparticles, mixed convection parameter, Brinkman number, Darcy number, and inertial parameter on the velocity and temperature fields are shown graphically. The results show that velocity and temperature are enhanced when the mixed convection parameter, Brinkman number, and Darcy number increases whereas solid volume fraction and inertial parameter decreases the velocity and temperature fields. The obtained results show that the nanofluid enhances the heat transfer process significantly.     

Parametric analysis of space cooling systems based on night ceiling cooling with PCM‐embedded piping

A parametric analysis is conducted for space cooling systems based on cold water flowing, during the night, within regularly arranged pipes embedded in a layer of phase change material (PCM), located among the structural layers of the ceiling. The introduced PCM layer in conjunction with night cooling add to the usual ceiling cooling systems offers the advantages of low energy consumption, high cool storage capacity, operation under reduced night electricity price, smoothing of electricity consumption by eliminating daily peak loads, improved thermal comfort and elimination of ceiling dripping. Our parametric analysis is based on a transient three‐dimensional finite‐difference solution of the related heat‐transfer problem for various values of all the main system parameters. PCM phase change process is simulated by using the effective thermal capacity function, which is determined experimentally for PCM suitable for air‐conditioning applications. Our tests showed that the main parameters of the system are pipe spacing, PCM layer thickness, pipe depth within the ceiling, cooling water inlet temperature, night cooling duration and PCM properties (thermal conductivity, phase change heat and ends of phase change temperature range). The effect of all the above parameters is analysed and suggestions are made for selecting the proper combinations of their values in order to obtain the lowest energy consumption in conjunction with the highest level of thermal comfort. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical simulation of the combustion processes in a W‐shaped boiler furnace under different operating conditions

Numerical simulations of gas–solid flows, heat transfer and gas–particle turbulent combustion have been conducted for a three‐dimensional, W‐shaped boiler furnace. The gas–particle flow, distributions of temperature and concentrations of gaseous constituents, distributions of the rates of heat release, burnout rates of coal particles, and formations of volatiles have been predicted. The results indicate that a steady high‐temperature zone is formed under the arch of the W‐shaped flame boiler, this zone would be of benefit to the ignition and carbon burn‐out and suggest that the W‐shaped flame boiler is suitable for burning low‐quality coals and can operate well under different operating conditions for full and partial loads. Copyright © 1999 John Wiley & Sons, Ltd.     

A three‐dimensional heat transfer model for thermal performance evaluation of ZrCo‐based hydride bed with embedded circular‐shaped cooling tubes

Nowadays, metal hydrides are generally deemed as one of the most potential materials that are in favor of compact hydrogen storage for industrial applications. This work was committed to evaluate the thermal performance of a circular‐shaped‐tube thin double‐layered hydrogen storage reactor using a three‐dimensional model. Finite element simulations were conducted to systematically study the influences of structural geometries, cooling patterns, and material thermophysical properties on the heat diffusion behavior under the framework of convection heat transfer. The results indicate that the proposed model effectively characterizes temperature evolutions during hydrogen absorption process. Moreover, a statistical analysis was performed to reveal the sensitivity sequence of these factors on the total thermal performance, suggesting that decreasing the hydride layer thickness, increasing the number of U‐shaped cooling tubes, accelerating the cooling fluid flow rate, and enhancing the thermal conductivity are more beneficial to the thermal performance improvement. Detailed analysis confirms the possibility of developing the present hydrogen storage tank utilizing metal hydrides for engineering practice.     

Non‐isothermal multi‐phase modeling of PEM fuel cell cathode

In this study, numerical simulation has been carried out for the heat transfer and temperature distribution in the cathode of polymer electrolyte membrane fuel cells along with the multi‐phase and multi‐species transport under the steady‐state condition. The commercial software, COMSOL Multiphysics, is used to solve the conservation equations for momentum, mass, species, charge and energy numerically. The conservation equations are applied to the solid, liquid and vapor phases in the bipolar plate and gas diffusion (GDL) and catalyst layers of a two‐dimensional cross section of the cathode. The catalyst layer is assumed to be a finite domain and the water production in the catalyst layer is considered to be in the liquid form. The temperature distribution in the cathode is simulated and then the effects of the relative humidity of the air stream, the permeability of the cathode and the flow channel shoulder to channel width ratio are investigated. It is shown that the highest temperature change, both in the in‐plane and across‐the‐plane directions, occurs in the GDL, while the highest temperature is reached in the catalyst layer. The distribution of temperature in the bipolar plate is shown to be relatively uniform due to the high thermal conductivity of the plate. A decrease in the inlet relative humidity of the air stream results in the decrease of the maximum temperature due to the absorption of heat during the evaporation of liquid water in the GDL and catalyst layer. The non‐uniformity of the temperature distribution, especially in the catalyst layer, is observed with the increase of the permeability of the cathode. Similarly, the decrease of the channel shoulder to channel width ratio leads to a non‐uniform distribution of temperature especially under the channel areas. Copyright © 2009 John Wiley & Sons, Ltd.     

Factors influencing the lowest refrigerating temperature of the miniature co‐axial pulse tube refrigerator

Experimental studies of the influencing factors on the lowest refrigerating temperature of a miniature co‐axial pulse tube refrigerator have been carried out in this paper. The results show that with the decrease of the mole fraction of hydrogen in the hydrogen‐helium mixture, the lowest refrigerating temperature decreases, and when the mole fraction of hydrogen is below 20%, the lowest refrigerating temperature is close to that obtained using pure helium. In addition, it is also found that the optimum frequency of the compressor is about 16.7 Hz for different hydrogen‐helium mixtures. When the charge pressure of the compressor increases, the lowest refrigerating temperature decreases; however, the decreasing trend gradually slows down with the increase of the charge pressure. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(4): 219–225, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20065     

Transient solution of temperature field of conjugate laminar forced convection heat transfer in functionally graded hollow cylinder

In this study, the numerical analysis of conjugate heat transfer of laminar flow in a functionally graded hollow cylinder (FGHC) made of metal/ceramic for a two‐dimensional fluid and wall conduction subject to Newton boundary condition is considered. The fluid and FGHC energy equations are coupled through the continuity of temperature and heat flux at the inner wall‐fluid interface while the outer surface is subject to convective heat transfer. The continuity, momentum, and energy equations of the fluid are discretized using the finite volume approach. The effects of fluid and functionally graded material parameters, such as volume fraction index, volume composition, time history, wall‐to‐fluid thermal diffusivity ratio, wall‐to‐fluid thermal conductivity ratio, Biot number, Peclet number, and Prandtl number are investigated on the temperature field in the FGHC. The result shows that on account of the inhomogeneity of the material property, the volume fraction index has a significant effect on the other parameters and the temperature variation along the thickness. The lower the volume fraction index, the higher the inner wall (metal side) temperature, and the temperature gradient along the thickness. However, except for the variation in the wall‐to‐fluid thermal conductivity ratio, the lower the volumetric fraction, the lower the outer wall (ceramic side) temperature distribution.     

Coupled radiation‐convection heat transfer of high‐temperature participating medium in heated/cooled tubes

The coupled radiation‐convection heat transfer of high‐temperature participating medium in heated/cooled tubes is investigated numerically. The medium flows in a laminar and fully developed state with a Poiseuille velocity distribution, but the thermal status is developing. By the discrete ordinate method, the nonlinear integrodifferential radiative transfer equation in a cylindrical coordinate form is solved to give the radiative source term in the energy equation of coupled heat transfer. The energy equation is solved by the control volume method. The local Nusselt number and wall heat flux of convection as well as the total wall heat flux are employed to evaluate the influence of radiation heat transfer on convection. The analysis shows that the radiation heat transfer weakens the convection effect, promotes the temperature development, and significantly shortens the tube length with obvious heated/cooled effect. There is an obvious difference between the coupled heat transfer in a heated tube and that in a cooled tube, even though the medium properties are kept constant. The wall emissivity, the medium thermal conductivity and scattering albedo have significant influences on the coupled heat transfer, but the effect of medium scattering phase function is small. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(1): 64–72, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10137     

Numerical investigation of non‐Newtonian nanofluid mixed convection in a two‐opposite direction lid‐driven cavity with variable properties

The mixed convection fluid flow in a square cavity filled with AL₂O₃‐water non‐Newtonian nanofluid is numerically analyzed. The left and right vertical boundaries of the enclosure have been kept in the constant temperature. Remaining walls of the cavity have been considered to have adiabatic boundary condition. Two different cases have been considered. In the first case, left and right side walls have been moved vertically with constant speed V_b in opposite directions. In the second case, the directions of their motions have been reversed. The transport equations, written in terms of the primitive variables for the non‐Newtonian nanofluid, have been solved numerically using the finite volume method. The shear stresses were calculated using the Ostwald‐de Waele model for the shear‐thinning nanofluid. The model introduced by Patel et al was used to obtain the thermal conductivity of the nanofluid. The variation of the fluid flow with respect to the Richardson number and volume fraction of the nanoparticles was investigated through a parametric study. Even though increasing the volume fraction of nanoparticles leads to heat transfer enhancement, for the second case of this study, for Ri = 1, the average Nusselt number initially drops sharply by increasing the volume fraction of nanoparticles, then remains constant.     

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     

Numerical Study of Forced Convection of Nanofluid Flow Over a Backward Facing Step With a Corrugated Bottom Wall in the Presence of Different Shaped Obstacles

In this paper, a numerical study of laminar forced convection of nanofluid flow over a backward facing step with a corrugated bottom wall in the presence of different shaped obstacles placed behind the step was performed. The bottom corrugated wall of the channel downstream of the step is isothermally heated and the other walls of the channel and obstacle surface are assumed to be adiabatic. The governing equations are solved with a finite-element method. The influences of the Reynolds number (between 10 and 200), solid volume fraction of the nanoparticle (between 0 and 0.05), and obstacle type (circular, square, and diamond shaped) on fluid flow and heat transfer are numerically investigated. It is observed that among different obstacles, the diamond shaped obstacle provides better local heat transfer enhancement characteristic in the vicinity of the step compared to the circular or square obstacle at high Reynolds number. Heat transfer enhancement of 6.66% is achieved in terms of maximum values with a diamond shaped obstacle compared to the no-obstacle case of the corrugated channel. Adding an obstacle deteriorates heat transfer in terms of average values for the backward facing step geometry with a corrugated wall. When the solid volume fraction of nanoparticle is increased, maximum and average heat transfer rate increase. Heat transfer enhancements of 7.45%, 7.42%, 6.94%, and 6.64% are obtained for the average values for circle, diamond, square, and no-obstacle cases, respectively, when solid volume fraction of 0.05 is compared to pure fluid.     

Modeling of double diffusive buoyant flow in a solar collector with water‐CuO nanofluid

The behavior of a prism‐shaped solar collector with a right triangular cross sectional area is investigated numerically. The water‐CuO nanofluid is taken as the functioning liquid through the solar collector. The leading differential equations with boundary conditions are solved by the penalty finite element method using Galerkin's weighted residual scheme. The performance of parameters in terms of temperature, mass, velocity distributions, radiative, convective heat and mass transfer, mean temperature and concentration of nanofluid, mid height horizontal‐vertical velocities, and sub‐domain average velocity field are investigated systematically. These parameters include the Rayleigh number Ra and the solid volume fraction φ. The outcome explains that the performance of the solar collector can be enhanced with the largest Ra and φ. The code validation shows excellent concurrence with the hypothetical outcome obtainable in the literature. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21039     

Performance enhancement of direct methanol fuel cell using multi‐zone narrow flow fields

New serpentine and spiral flow field configurations were developed to enhance the performance of direct methanol fuel cells (DMFCs). The new configurations are based on two primary concepts, namely, narrowing the flow field and partitioning the total active area of the fuel cell. Three flow channel heights of 0.8, 0.4, and 0.2 mm were investigated in serpentine and spiral flow fields. The main active area is considered a single zone and is partitioned into two‐ and four‐zone designs while maintaining the total inlet mass flow rate of the reactant and oxidant. To determine the performance parameters of the newly proposed designs, a three‐dimensional single‐phase isothermal model was developed, numerically simulated, and validated through experimental measurements. The findings of the current study indicate that a serpentine flow field configuration with a channel height of 0.2 mm and two zones attains an enhancement of the net power density of 37% compared to a conventional single‐zone design with a flow channel height of 0.8 mm. Similarly, for a spiral flow field design, the maximum net power density increased by 26% using a two‐zone configuration with a channel height of 0.2 mm, in comparison to the conventional design of a single‐zone and a flow channel height of 0.8 mm. The newly developed designs utilize the lower height of the flow fields to decrease the dimensions of the fuel cell stacks and reduce the material costs required.     

Prediction of local heat transfer characteristics of dilute gas‐solid flows through an adiabatic,horizontal pipe

The local heat transfer characteristics of gas‐solid flows through an adiabatic, horizontal pipe are numerically studied using the two‐fluid model of Ansys Fluent 15. First, the model is validated with the experimental results available in the literature for the air temperature and average Nusselt number. Then, the local heat transfer characteristics of gas‐solid flows, such as temperature profiles of gas and solid, gas‐solid Nusselt number, logarithmic mean temperature difference, and effectiveness of gas and solid, are studied by changing different parameters (gas velocities 15‐24 m/s; inlet solid loading ratios 0.1‐1; particle diameters 100‐400 µm). It is observed that increasing the particle diameter and inlet gas velocity increases the gas temperature and decreases the solid temperature, increases the logarithmic mean temperature difference, and decreases the thermal effectiveness of gas and solid. However, increasing the solid loading ratio decreases the gas and solid temperatures, decreases the logarithmic mean temperature difference, and increases the thermal effectiveness of gas and decreases the thermal effectiveness of solid. Moreover, increasing the particle diameter decreases the gas‐solid Nusselt number, whereas increasing the solid loading ratio and inlet gas velocity increase the gas‐solid Nusselt number.     

Thermal conductivity of aluminum foam based on 3‐D stochastic sphere model

To accurately characterize the geometric structure of closed‐cell aluminum foam, a three‐dimensional stochastic sphere model with adjustable porosity and pore size was established, and its thermal conductivity was studied by numerical simulation. A closed‐cell aluminum foam heat conduction experiment was designed to verify the accuracy of the model. Using this model, the thermal conductivity of aluminum foam with different pore sizes and porosity was calculated, and the variation of thermal conductivity was studied. The results show that with the same porosity, the thermal conductivity increases linearly with the pore size. With the same pore size, the thermal conductivity decreases linearly with the porosity. The equivalent thermal conductivity decreases with the increase of porosity. According to the simulation results, the formula of equivalent thermal conductivity of aluminum foam is .     

Numerical study of two‐phase flow of liquid helium in a vertical converging‐diverging nozzle

The fundamental characteristics of the two‐dimensional gas‐liquid two‐phase flow of liquid helium through a vertical converging‐diverging duct near the lambda point are numerically investigated to realize the further development and high performance of new multiphase superfluid cooling systems. First, the governing equations of the two‐phase flow of liquid helium based on the unsteady thermal nonequilibrium multifluid model with generalized curvilinear coordinates system are presented, and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two‐dimensional structure of the gas‐liquid two‐phase flow of liquid helium though vertical converging‐diverging nozzle is shown in detail, and it is also found that the generation of superfluid counterflow against normal fluid flow based on the thermomechanical effect is conspicuous in the large gas phase volume fraction region where the liquid‐ to vapor‐phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(6): 432–448, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20071