Numerical simulation of conjugate,turbulent mixed convection heat transfer in a vertical channel with discrete heat sources

This paper presents the results of a comprehensive numerical study to analyze turbulent mixed convection in a vertical channel with a flush-mounted discrete heat source in each channel wall. The conjugate heat transfer problem is solved to study the effect of various parameters like the thermal conductivity of the wall material (k_s), the thermal conductivity of the flush-mounted discrete heat source (k_c), Reynolds number (Re_s), modified Richardson number (Ri⁎) and the aspect ratio of the channel (AR). The standard k–ε turbulence model, modified by including buoyancy effects, without wall functions, has been used for the analysis. The two-dimensional governing equations are discretised on a semi-staggered, non-uniform grid, using the finite volume method. The asymptotic computational fluid dynamics (ACFD) technique has been then applied to obtain a correlation for the non-dimensional maximum temperature θ¯_max, which can be used for a wide range of parameters.     

Determination of hot spots on a heated wavy wall in channel flow

The present study deals with the effects of wall geometry on the fluid flow and heat transfer in a channel with a wavy wall heated with constant heat dissipation. The waviness is characterized by wave amplitude and period. A detailed parametric numerical investigation of the effect of waviness on the local heat transfer parameters is performed for different turbulent flow conditions and compared with the literature.The effect of flow and geometry parameters is assessed quantitatively. Generalization is done based on the Reynolds number, Re_A, which uses doubled wave amplitude, or height, A = 2a, as the characteristic length, and on the geometry parameter, A/λ, which essentially is the amplitude-to-wavelength ratio. A dimensionless location of the hottest spot on the wavy wall is shown to be dependent on these two dimensionless parameters. A correlation which encompasses the hottest spot locations for all the cases studied in the work is suggested.In order to obtain generalization for the hottest spot temperature, the Nusselt number is introduced based on the constant (uniform) heat flux and variable temperature difference, with wave amplitude as the characteristic length. It is shown that, for all cases studied herein, the hottest temperature is represented as Nu_A,min(Re_A, A/λ). Accordingly, a correlation for the minimum Nusselt number is suggested. A further generalization for the hottest spot temperature is attempted for the conjugate problem with a conducting wall. It includes wall-to-fluid thermal conductivity ratio, k_s/k_l, as the additional dimensionless parameter which determines the Nusselt number.     

Conjugate-mixed convection heat transfer in a lid-driven enclosure with thick bottom wall

Conjugate heat transfer by mixed convection and conduction in lid-driven enclosures with thick bottom wall has been studied by a numerical method. The enclosure is heated from the bottom wall isothermally. Temperature of the top moving wall, which has constant flow speed, is lower than that of the outside of bottom wall. Vertical walls of the enclosure are adiabatic. Governing parameters are solved for a wide range of Richardson numbers (0.1 ≤ Ri ≤ 10), ratio of height of bottom wall to enclosure height (0.1 ≤ h/H ≤ 0.5) and thermal conductivity ratio (0.01 ≤ λ_f/λ_s ≤ 10). Obtained results showed that heat transfer decreases with increasing of λ_f/λ_s ratio, Richardson number and thickness ratio of the wall. Flow strength is affected for only higher values of λ_f/λ_s ratio.     

Shape design for a cylinder with uniform temperature distribution on the outer surface by inverse heat transfer method

Performance of the inverse heat transfer method in application to the shape design for the heat convection problems has been evaluated. The approach is constructed by combining curvilinear grid generation scheme, direct problem solver, conjugate gradient optimization method, and redistribution method. Shape design for the outer surface profile of a solid medium in a crossflow that contains a heating element and features an isothermal outer surface has been carried out. Practical cases under different combinations of the dominant physical parameters, including Reynolds number (Re), thermal conductivity ratio (k_f/k_s), desired outer surface temperature (θ_d), and Prandtl number (Pr), are studied to evaluate the effects of the physical parameters on the shape design.     

An optimized nickel phosphate/carbon composite electrocatalyst for the oxidation of formaldehyde

The electrocatalytic performance of highly conducting Nickel phosphate (NiPh)/carbon composite catalyst is investigated for the oxidation of formaldehyde in alkaline solution. The NiPh nanoparticles are synthesized by a cost-effective one-pot method, which is based on refluxing nickel and phosphate precursors at 90 °C. Inks of the composite catalyst are produced by mixing NiPh nanoparticles with carbon conductive additives (CCA) and Nafion oil. Then, the ink is cast then dried on the glassy carbon electrode. Systematic study is performed to investigate the effect of varying the CCA loading on the electrochemical oxidation of formaldehyde. The best catalytic performance is obtained for NiPh/CCA composite catalyst containing 20 wt% of CCA (NiPh/CCA-20 wt%). The physicochemical properties of the composite catalysts are investigated and analyzed by field-emission scanning electron microscopy (FE-SEM), Energy Dispersive x-ray Spectroscopy (EDX) and X-ray diffraction (XRD). Also, the N₂ adsorption/desorption isotherms are recorded and the Brunauer–Emmett–Teller (BET) and Barrett-Joyner-Halenda (BJH) methods are used to calculate the specific surface area and pore size distribution. The electrocatalytic performance of the NiPh/CCA composite was compared to the pristine NiPh for the oxidation of formaldehyde in alkaline solution. Electrochemical impedance spectroscopy technique is used to study the electrical conductivity of the composite catalysts. Additionally, cyclic voltammetry and chronoamperometry techniques are used to calculate key parameters such as surface coverage (Γ) of Ni²⁺/Ni³⁺ species, the diffusion coefficient of the formaldehyde (D) and the catalytic rate constant (k_cat). Ã, D and k_cat values for the NiPh/CCA-20 wt% catalyst are 5.95 × 10⁻⁵ mmol cm⁻², 1.08 × 10⁻⁴ cm² s⁻¹ and 2.59 × 10⁷ cm³ mol⁻¹ s⁻¹ respectively. Both Γ and k_cat parameters are used to identify the optimum composition of the catalyst.     

Computation of Thermal Fracture Parameters for Inclined Cracks in Functionally Graded Materials Using J k -Integral

This article describes the formulation and implementation of the J _k -integral for the analysis of inclined cracks located in functionally graded materials (FGMs) that are subjected to thermal stresses. The generalized definition of the J _k -integral over a vanishingly small curve at the tip of an inclined crack is converted to a domain independent form that consists of area and line integrals defined over finite domains. A numerical procedure based on the finite element method is then developed, which allows the evaluation of the components of the J _k -integral, the modes I and II stress intensity factors and the T-stresses at the crack tips. The developed procedure is validated and the domain independence is demonstrated by providing comparisons to the results obtained by means of the displacement correlation technique (DCT). Detailed parametric analyses are conducted by considering an inclined crack in an FGM layer that is subjected to steady-state thermal stresses. Numerical results show the influences of the thermal conductivity and thermal expansion coefficient variation profiles and the crack inclination angle on the mixed-mode fracture parameters.     

Lattice Boltzmann method modeling and experimental study on liquid water characteristics in the gas diffusion layer of proton exchange membrane fuel cells

Water transport through the gas diffusion layer (GDL) is vital to proton exchange membrane fuel cells (PEMFCs), especially under flooding conditions. In this paper, a two-dimensional (2D) lattice Boltzmann method (LBM) is applied to reveal the water dynamic characteristics in GDL, and the computational domain is reconstructed based on the experiment. In-situ experiments, including I–V performance and electrochemical impedance spectroscopy (EIS) tests under flooding conditions, are carried out and analyzed. It is found that the porosity distribution inside the GDL is a crucial factor in water dynamic behavior research. The horizontal liquid water saturation (HS_w) under the channel of real GDL (with porosity distribution) at 0.4 relative thickness are 3.2 times, 2.1 times and 3.4 times higher than the ideal GDL (without porosity distribution) in the case of 0.8 mm, 1.2 mm and 2.0 mm, respectively. The numerical simulation and experimental study show that water dynamic characteristics under the rib influence cell performance directly. In our LBM model, the GDL water distribution inconsistency (Var_w) under 2.0 mm width rib is 43.1% and 28.0% higher than that under the 0.8 mm and 1.2 mm rib, respectively. With the rib wider from 0.8 mm to 2.0 mm, some parts of cell impedance such as R_mt, R_ct, and L_mt increase 64.22%, 98.89%, and 47.46%, respectively. However, GDL under the channel shows no influence on water transport process.     

Investigation of tungsten carbide supported Pd or Pt as anode catalysts for PEM fuel cells

In this contribution, we present results of electrochemical characterization of prepared tungsten carbide supported palladium and platinum and Vulcan XC-72 supported palladium. These catalysts were employed as anode catalysts in PEMFC and results are compared to commercial platinum catalyst. Platinum seems to be irreplaceable as a proton exchange membrane fuel cell (PEMFC) catalyst for both the anode and the cathode, yet the high price and limited natural resources are holding back the commercialization of the PEMFCs. Tungsten carbide is recognized as promising catalyst support having the best conductivity among interstitial carbides. Higher natural resources and significantly lower price make palladium good candidate for replacement of the platinum catalyst. The presented results show that all prepared catalysts are very active for the hydrogen oxidation reaction. Linear sweep voltammetry curves of Pd/C and Pd/WC show existence of peaks at 0.07 V vs. RHE, which is assigned to absorbed hydrogen. H₂|Pd/WC|Nafion117|Pt/C|O₂ fuel cell has almost the same efficiency and similar power output as commercial platinum catalyst.     

Fractal model for prediction of effective thermal conductivity of gas diffusion layer in proton exchange membrane fuel cell

The process of heat transfer within porous media is usually considered as a transport through large numbers of straight channels with uniform pore sizes. For the prediction of effective thermal conductivity of gas diffusion layer (GDL), morphological properties such as the tortuosity of channels and pore-size distribution of this porous layer should be considered. Thus in this article, novel parallel and series-parallel prediction models of effective thermal conductivity for the GDL in proton exchange membrane fuel cell (PEMFC) have been derived by fractal theoretical characterization of the real microstructure of GDL. The prediction of fractal parallel model for carbon paper, a basal material of the GDL, is in good agreement with the reference value supplied by Toray Inc. The prediction results from the proposed models are also reasonable because they are distributed between the upper and lower bounds. Parametric effect has been investigated by using the presented models in dimensionless formalism. It can be concluded that dimensionless effective thermal conductivity (k^′eff${k^{\prime }}_{\text{eff}}$) has a positive correlation with effective porosity (?) or the pore-area fractal dimension (D_p) when k_s/k_g < 1; whereas it has a negative correlation with ? or D_p when k_s/k_g > 1 and with tortuous fractal dimension (D_t) whether k_s/k_g < 1 or not. Furthermore, these fractal models have been modified by considering the effect of polytetrafluoroethylene (PTFE) incorporated into the pore spaces of carbon paper, and the corresponding model prediction shows that there is an increase in the effective thermal conductivity due to the filling of PTFE that has high thermal conductivity.     

Wall heat recirculation and exergy preservation in flow through a small tube with thin heat source

Theoretical studies have been made on heat transfer and exergy analysis of flow through a narrow tube with heat recirculating wall and embedded thin heat source. Heat transfer analysis is based on numerical solution of conservation equations of mass, momentum and energy, while the exergy analysis is based on flow exergy balance and entropy transport equation. It has been observed that the ratio of heat recirculation to heat loss (Q_R/Q_L) increases with increase in the ratio of thermal conductivity of solid wall to that of working fluid (k_s/k_g) and Peclet number of flow (Pe), while it decreases with an increase in external Nusselt number (Nu_E). The ratio Q_R/Q_L has a maximum with the ratio of wall thickness to tube radius (t_w/R). The optimum value of t_w/R depends only on k_s/k_g and reduces from a value of 0.2 at k_s/k_g = 330 to a value of 0.125 at k_s/k_g = 850, and then remains almost constant for any further increase in k_s/k_g. The volumetric entropy generation rate in the fluid flow reaches a maximum at a radial location close to the inner surface of the wall, while the entropy generation in solid wall, being more than that of the fluid, is radially uniform. The volumetric entropy generation is found to be confined within the upstream region of the heat source. Second law efficiency increases with a decrease in t_w/R and Nu_E, but with an increase in Pe. It remains almost constant with k_s/k_g.     

Proton conducting solid oxide fuel cells with layered PrBa0.5Sr0.5Co2O5+δ perovskite cathode

BaZr_0.1Ce_0.7Y_0.2O_3−δ (BZCY7) exhibits adequate protonic conductivity as well as sufficient chemical and thermal stability over a wide range of SOFC operating conditions, while layered perovskite PrBa_0.5Sr_0.5Co₂O_5+δ (PBSC) has advanced electrochemical properties. This research fully takes advantage of these advanced properties and develops a novel protonic ceramic membrane fuel cell (PCMFC) of Ni–BZCY7|BZCY7|PBSC. Experimental results show that the cell may achieve the open-circuit potential of 1.005 V, the maximal power density of 520 mW cm⁻², and a low electrode polarization resistance of 0.12 Ωcm² at 700 °C. Increasing operating temperature leads to the decrease of total cell resistance, among which electrolyte resistance becomes increasingly dominant over polarization resistance. The results also indicate that PBSC perovskite cathode is a good candidate for intermediate temperature PCMFC development, while the developed Ni–BZCY7|BZCY7|PBSC cell is a promising functional material system for SOFCs.     

Improving cell performance for anion exchange membrane fuel cells with FeNC cathode by optimizing ionomer content

To improve the performance of anion exchange membrane fuel cells (AEMFCs) with platinum-group-metal (PGM)-free cathode, significant efforts are still needed. Herein, we prepare high oxygen reduction reaction activity FeNC catalyst and integrate such catalyst into AEMFCs with different ionomer/catalyst (I/C) ratios from 0.1 to 1.0. We show that suitable quaternary ammonia poly (methyl-piperidine-co-p-terphenyl) (QAPPT) ionomer content can provide better catalyst layers (CLs) microstructure, in which the transfer efficiency of electron and charge can be improved so as to decrease the active polarization. High ohmic resistance is caused by either low or excess ionomer which leads to inconsecutive ionic network of CLs or high coverage of non-electronic conductor. In addition, mass-transfer polarization is also brought out by excess QAPPT ionomer which fills up the gas–liquid transport pores inside FeNC/QAPPT aggregates. With the I/C ratio of 0.7, AEMFC with FeNC cathode exhibits the best cell performance achieving a peak power density of 660 mW cm^?2 at 1500 mA cm^?2 under H₂/air (CO₂-free). To verify the feasibility of FeNC cathode in realistic applications, an AEMFC stack with 29 cells of 270 cm² MEAs was assembled with a power output of 508 W under H₂/air.     

Conjugate heat transfer with viscous dissipation in a microtube

Hydrodynamically developed, thermally developing, steady, laminar conjugate heat transfer of a liquid flow in the entrance region of a microtube is studied numerically. The finite volume method is used. The effects of the thermal conductivity ratio, the diameter ratio, the channel length and the viscous dissipation on the Nusselt number as well as on the temperature and the interface heat flux distribution are examined in detail. In the entrance region, large reductions are observed in the Nusselt number with increasing k_s/k_f and d_o/d_i. This is considered to be due to the axial conduction, which also extends to the exit region. The results also show that the Nusselt number decreases with increasing viscous dissipation for fixed values of k_s/k_f and d_o/d_i.     

Influence of catalyst layer polybenzimidazole molecular weight on the polybenzimidazole-based proton exchange membrane fuel cell performance

The catalyst layer (CL) of a polybenzimidazole (PBI) membrane electrode assembly (MEA) consists of Pt–C (Pt on a carbon support), PBI, and H₃PO₄. Two series of catalyst ink solutions each containing Pt–C, N,N′-dimethyl acetamide, and PBIs comprising four different molecular weights (MWs) (i.e., M_w = 1.1 × 10⁴, 4.4 × 10⁴, 9.0 × 10⁴, and 17.4 × 10⁴ g mol⁻¹) are used to fabricate CLs. One catalyst ink solution series is mixed with LiCl, while the other solution series lacks LiCl. We demonstrate that the CL prepared using a lower MW PBI has a higher electrochemical surface area, lower charge transfer resistance, and higher fuel cell performance. The addition of LiCl enhances the dispersion of the high MW PBIs in the catalyst ink solution and acts as a foaming agent in CL, thus improving fuel cell performance. However, LiCl exerts small influence on the fuel cell performance of the MEAs fabricated using low MW PBIs.     

Analysis of the effective thermal conductivity of fractal porous media

Several types of fractals are generated to model the structures of porous media, and heat conduction in these structures is simulated by the finite volume method (FVM). The influences of the thermal conductivity of solid k_s, the thermal conductivity of fluid k_f, the porosity ε, the size and spatial distribution of pores on the effective thermal conductivity k_e of these structures are analysed in detail. The calculated results indicate that the relation of effective thermal conductivity k_e with thermal conductivity of solid k_s and thermal conductivity of fluid k_f conforms to a power function, and the relation of effective thermal conductivity k_e with porosity ε conforms to an exponential function. The porosity ε is the most important factor that determines the effective thermal conductivity of fractal porous media, but the size and spatial distribution of pores, especially the spatial distribution of the bigger pores, do have substantive influence. The numerical results are analysed by comparing with the available empirical formulas from literatures, and provide verification of these empirical formulas.     

Forced Convection of Metallic Foam Heat Sink under Laminar Slot Jet Confined by Parallel Wall

This investigation numerically explores the fluid flow and heat transfer characteristics of the metallic foam heat sink under the laminar slot jet confined by a parallel wall. The Prandtl number is 0.7, and the range of Reynolds numbers is 100–500. The parameters of interest in this work are the porosity (?), pore density (PPI), effective solid conductivity (k _s *), jet nozzle width (W), ratio of the porous sink length to the jet nozzle width (L/W), ratio of the jet-to-sink distance to the jet nozzle width (C/W), and ratio of the porous sink height to the jet nozzle width (H/W). The simulation data reveal that the Nusselt number of the system with a metallic porous heat sink was much better than that of the system without a porous sink, for a given volumetric flow rate and value of (C+H)/W. The porous properties (such as ? and k _s *) and the system configurations (such as L/W and H/W) strongly influenced the cooling performance. The effect of the PPI, W, and C/W values on the heat transfer characteristics of the system was negligible. The effect of the fluid flow on the thermal results was examined. Finally, the correlations of the stagnation Nusselt number and the average Nusselt number were also determined using the numerical data for a system with the size of a common multi-chips module.     

Prediction of the effective conductivity of Nafion in the catalyst layer of a proton exchange membrane fuel cell

In a previous study, a simple acid catalyzed reaction (esterification) was found to predict excellently conductivity of a membrane contaminated with NH₄⁺ or Na⁺. Since measurement of the conductivity of Nafion in a catalyst layer is problematic, being able to predict this conductivity for various formulations and fuel cell conditions would be advantageous. In this study, the same methodology as before was used to examine the proton availabilities of supported Nafion (Nafion on carbon and on Pt/C), as exists in the catalyst layer used in a PEMFC, during impurity exposure (e.g., NH₃) as a means for prediction of its conductivity. It was found that the effect of NH₃ exposure on the proton composition (yH+) of supported Nafion was similar to that of N-211 under the same conditions. Determined values of yH+ were then used to estimate the effective conductivity of an ammonium-poisoned cathode layer using the correlation developed and the agglomerate model. The predicted conductivities were matched with the results available in the literature. This technique would be useful for the optimization of catalyst design and for fuel cell simulation, since it provides many benefits over conventional performance test procedures.     

Forced convection heat transfer in microchannel heat sinks

This paper presents an analysis of forced convection heat transfer in microchannel heat sinks for electronic system cooling. In view of the small dimensions of the microstructures, the microchannel is modeled as a fluid-saturated porous medium. Numerical solutions are obtained based on the Forchheimer–Brinkman-extended Darcy equation for the fluid flow and the two-equation model for heat transfer between the solid and fluid phases. The velocity field in the microchannel is first solved by a finite-difference scheme, and then the energy equations governing the solid and fluid phases are solved simultaneously for the temperature distributions. Also, analytical expressions for the velocity and temperature profiles are presented for a simpler flow model, i.e., the Brinkman-extended Darcy model. This work attempts to perform a systematic study on the effects of major parameters on the flow and heat transfer characteristics of forced convection in the microchannel heat sink. The governing parameters of engineering importance include the channel aspect ratio (α_s), inertial force parameter (Γ), porosity (ε), and the effective thermal conductivity ratio (k_r). The velocity profiles of the fluid in the microchannel, the temperature distributions of the solid and fluid phases, and the overall Nusselt number are illustrated for various values of the problem parameters. It is found that the fluid inertia force alters noticeably the dimensionless velocity distribution and the fluid temperature distribution, while the solid temperature distribution is almost insensitive to the fluid inertia. Moreover, the overall Nusselt number increases with increasing the values of α_s and ε, while it decreases with increasing k_r.     

Assessing the effects of soil grading on the moisture content-dependent thermal conductivity of stabilised rammed earth materials

New data for both the dry-state and the moisture content-dependent thermal conductivity of cement-stabilised rammed earth (SRE) materials is presented. For highly compacted SRE materials, no correlation was found between thermal conductivity and dry density or void ratio. The thermal conductivity of SRE materials increases linearly with the saturation ratio, S_r of the material and can be expressed as λ¹, the moisture content-dependent thermal conductivity. The sensitivity of λ¹ to an increase in the saturation ratio of SRE materials varies according to soil grading. The influence of grading parameters on λ¹ can cause material variations of approximately 0.8 m² K/W. The experimental data has been applied to standard SRE wall design configurations and the effect of wall moisture content on the total thermal resistance has been shown. The R-value of an SRE wall irrespective of cavity insulation can vary by as much as 0.13 m² K/W.