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Fundamental Experiment and Numerical Analysis of a Modular Microcombustor with Silicon Carbide Porous Medium K. J. Chua,*,†,‡ W. M. Yang,† and W. J. Ong‡ †

Department of Mechanical Engineering and ‡Engineering Science Programme, National University of Singapore, 9 Engineering Drive 1, Singapore 117576 S Supporting Information *

ABSTRACT: The use of porous media in combustion processes has been widely researched and investigated. In this paper, the effect of employing porous media on microcombustion was studied using numerical simulation. Simulated results demonstrated good agreement with the experimental results, and thus validated the model. Analysis has been carried out with dimensional analysis and basic theorem which incorporates the Biot number in an attempt to fundamentally understand the effects brought about by equivalence ratio, thermal conductivity of the solid matrix and mass flow rate on microthermophotovoltaic (TPV) performance. One of the key results has demonstrated that the higher the equivalence ratio of the fuel/air mixture, the higher will be the mean wall temperature. A peak-shift phenomenon has been observed, where the position of maximum flame temperature shifts downstream away from the inlet at lower equivalence ratio. Results from the Biot number analysis has indicated that the higher the thermal conductivity of the wall is, the more uniform the wall temperature distribution will be. A lower mean wall temperature is obtained when the thermal conductivity of the solid matrix is installed at 50 W/mK, whereas higher mean wall temperatures can be achieved for either small (5 W/mK) or very large (500 W/mK) thermal conductivity. It is clearly evidenced that the performance of microcombustors can be markedly enhanced by incorporating a thermally effective porous medium. The theoretical understanding gained from the present research will facilitate the design of more energy efficient, stable and better controllable portable TPV on-field power systems.

1. INTRODUCTION Among the microscaled power generators, the micro TPV system has the potential to be a clean and quiet source with virtually zero moving components.1,2 A TPV unit, as seen in Figure 1, consists

higher energy photons, and thereby higher power output. Within the system, the microcombustor is perceived as the key component which is responsible for the main source of radiation energy. Therefore, the design of the combustor and the quality of the fuel deployed are paramount factors that govern the performance of the TPV system. Several microcombustor designs have been developed and studied as portrayed in Table 1. Among them, the development of the micro modular system using planar combustors, as shown in Figure 2, holds many advantages.

Figure 1. Schematic of a TPV unit.

of three primary components − a heat source, an emitter (or radiator) and low bandgap photovoltaic cells. During the combustion process, a large amount of thermal energy is transferred to the emitter. As the emitter reaches a sufficiently high temperature, photons are emitted from the external wall to the surroundings. Photons with energy higher than the bandgap energy of the photovoltaic (PV) cells, i.e., GaSb (0.72 eV) or GaInAsSb (0.55 eV) will evoke free electrons and generate electricity under the action of a PN junction.3 On the other hand, photons with energy less than the bandgap energy of the PV cell will be absorbed, resulting in destructive thermal loading, which in turn reduces the conversion efficiency of the cells. In line with the Stefan−Boltzmann law, it is clear that a higher emitter surface temperature leads to the emission of © 2012 American Chemical Society

Figure 2. Schematic of modular micro-TPV system.

They include (1) simplification of fabrication and assembly of the system; (2) inclusion of a recuperator to improve the efficiency of the system; (3) potential use of liquefied fuel; and (4) facilitates the adjustment of the number of TPV units required.4 Received: Revised: Accepted: Published: 6327

December 22, 2011 March 23, 2012 April 16, 2012 April 16, 2012 dx.doi.org/10.1021/ie203017g | Ind. Eng. Chem. Res. 2012, 51, 6327−6339

Industrial & Engineering Chemistry Research

Article

Figure 3. Schematic of the experimental setup.

creating high volumetric heat release rates and high effective flame speed.14 Besides, the addition of porous matrix in the burner serves to extend the lean flammability limits of the mixture as well as allowing the use of fuels with low energy content. One of the key advantages of including porous medium in a microcombustor stems from the high conductivity of the solid matrix, which is believed to increase the rate of heat transfer from the reaction zone to the wall and give rise to more uniform wall temperature. However, there are practical issues such as flame stabilizing within the matrix structure as well as durability of the materials, which tend to degrade and crack upon repeatedly long periods of thermal cycling. Extensive experimental data in porous medium are presently not available. This is primarily due to the measurement difficulty arising from the presence of the solid matrix which limits the access of temperature probes. Furthermore, modeling remains a challenge because of limited knowledge in the transport phenomena within the porous medium. Chou et al.15 were the pioneering researchers to incorporate porous medium in a numerical microcombustor model. They investigated the effect of inert porous medium on the wall temperature of a cylindrical microcombustor involving combustion of hydrogen and oxygen, and found a remarkable improvement of up to 81% in the amount of useful radiation. In this work, a numerical model has been constructed to study the combustion of premixed hydrogen and air in a planar porous medium incorporated microcombustor. The combustion process was modeled as species transport based chiefly on the detailed mechanism used by Li et al.16 To facilitate a fundamental analysis of the porous medium incorporated TPV, a sufficiently detailed model of microcombustor with inert porous media was studied. This approach enables a deeper understanding on the intrinsic properties that may affect the wall temperature of the combustor. Although the performance of porous media combustion may be governed by many

Because of the difficulties in measuring key parameters such as velocity and temperature within a microcombustor, numerical simulation is often relied on as a cost-effective approach to study the microcombustion mechanism. Norton and Vlachos5 conducted a two-dimensional Computational Fluid Dynamics (CFD) simulation to analyze the stability of premixed CH4/air flames in a microcombustor comprising two parallel wide plates of length 1 cm separated by a short distance. Choi et al.6 applied numerical simulation to investigate hydrogen/air flame propagation near extinction condition in a microcombustor. As the H2/air reaction mechanism constitutes the main transport phenomena within the microcombustor, it plays a prominent role in the performance of the microcombustor. Therefore, it is crucial that a detailed and well-validated microcombustion mechanism is developed from numerical modeling. The kinetics of hydrogen oxidation and its behavior under different environmental conditions has been studied extensively by Giovangigli and Smooke,7 Tien and Stalker,8 Mueller et al.,9 and Yetter et al.10 More recently, O’Conaire et al.11 modified the reaction mechanism proposed by Mueller et al.9 to evolve a more consistent model that is valid over a wider range of physical conditions. The incorporation of inert porous media to a microcombustor has yielded promising results. Due to its high heat capacity, high thermal conductivity and high emissivity of the solid matrix, incorporating a porous medium to a microcombustor offers an alternative pathway in achieving high power density and low emission of pollutants such as NOx and CO.12 The structure of the porous matrix allows premixed fuel and air to be heated up as they pass through the interstitial voids in the matrix. This mixture, in turn, is heated by two transport mechanisms - radiation emitted upstream from the reaction zone and conduction through the solid matrix.13 These two feedback mechanisms upstream from the reaction zone to the unburned gas enhance the laminar flame speed, thereby 6328

dx.doi.org/10.1021/ie203017g | Ind. Eng. Chem. Res. 2012, 51, 6327−6339


Article

Figure 4. (a) Photograph of the microcombustor; and (b) design feature of the planar microcombustor and flow connector (units in mm).

reference from the baseline of the wall, a total of 18 temperature readings were recorded for each experiment. The fuel−air ratio fa is typically determined on a mass basis and can be found directly from the measurements of the fuel and air mass flow rates. The fuel−air ratio can be normalized by the stoichiometric ratio to yield a quantity known as equivalence ratio:

parameters, only the impact of several key parameters on combustor performance was investigated. They included the equivalence ratio, thermal conductivity and mass flow rate. It is worthy to highlight that the chief aim of this article is to facilitate the fundamental understanding of these key parameters that may influence the wall temperature distribution. Both experiments and numerical approaches were adopted for the presentation of the results in this work.

ϕ=

2. MATERIAL AND METHODS The experimental setup for microcombustion is shown in Figure 3. The entire system was operated at room condition with ambient temperature spanning 295 to 300 K. The system consisted of two mass flowmeters, a flow controller and readout, a plenum, a microcombustor, an infrared (IR) thermometer mounted on a height gauge, a PC display and connection tubes. Supply air was provided by an air compressor. The flow rates of hydrogen and air were adjusted using Brooks Mass Flowmeters (Model 5850E) which are capable of controlling flow rates with accuracy up to 1%. The plenum was designed and fabricated carefully to prevent any flash back. In addition, Swagelok stainless steel tube fittings were used for all tubing connections from the plenum to the microcombustor. The microcombustor and flow connector used in the experiments were made of stainless steel 316 in order to withstand high temperatures without physical degradation. Figure 4 shows the features of the planar microcombustor and the flow connector. Fine stainless steel wire mesh was used at the combustor inlet to achieve uniform flow. Using a Vernier caliper, the diameter of the wire was found to be 0.1 mm with an interval distance of 0.23 mm. The porous media employed is a product of ERG Materials and Aerospace Corporation - a piece of 100 PPI Silicon Carbide (SiC) foam of 85% porosity with dimensions 10 mm × 1 mm × 17 mm. The wall temperature was measured using a high-performance RAYTEK Infrared Thermometer (Model MA2SCCF) with an accuracy of up to ± (0.3% T + 1) K. The measuring spot has a size of around 1 mm in diameter when the distance from the lens to the microcombustor is at 300 mm (optical resolution of 300:1). In order to obtain accurate temperature readings, the thermometer was mounted on a high-precision Mitutoyo Height Gauge which is accurate to 0.01 mm. Taking

fa,actual fa,stoichiometric

(1)

The fuel-air mixture can then be classified as lean, stoichiometric and rich if the equivalence ratio is less than 1, equal to 1 and more than 1, respectively. The temperature of a combustion reaction usually peaks when the equivalence ratio is close to unity and decreases when the mixture becomes leaner or richer. This is primarily due to the unreacted constituents absorbing some of the heat released from the reaction. When complete combustion of hydrogen in air takes place, the overall chemical equation can be written as 2H 2 + O2 + 3.76N2 → 2H 2O + 3.76N2

(2)

This is based on the assumption that air contains 21% oxygen and 78% nitrogen by volume. From the chemical equation, the stoichiometric ratio can be computed to give ⎛ ṁ H ⎞ fa,stoichiometric = ⎜ 2 ⎟ ⎝ ṁ air ⎠stoic =

2 × 2 × 1.00794 2 × 15.9994 + 3.76 × 2 × 14.0067

= 0.029358

(3)

and eq 1 can be written as ϕ=

fa,actual 0.029368

=

⎛ ṁ H2 ⎞ 1 ⎜ ⎟ 0.029368 ⎝ ṁ air ⎠

(4)

The flow rates for H2 and air can be determined by first considering the conservation of mass within the plenum. At the combustor inlet, it can be observed that n H2 + nair = nmixture (5) 6329



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Figure 5. (a) Three-dimensional view of the microcombustor; and (b) boundary conditions of numerical model.

on microcombustion is negligible, even though the mean free path of the gases increases due to high temperature. Thus, no-slip conditions are employed at the fluid-wall interfaces. In casting the present model, the following assumptions were made: (1) no Dufour effects;19 (2) no gas radiation;5,20 (3) no work done by pressure and viscous forces; (4) inert wall with no surface reactions; (5) steady-state combustion; (6) detailed reaction mechanism applies; (7) the incorporated porous medium is isotropic and homogeneous; and (8) body forces are neglected. The governing equations of continuity, momentum, species and energy in the porous medium are written for the microcombustor. For continuity conservation:

By applying ideal gas law and adopting the assumption of constant pressure and temperature in the plenum, eq 5 can be written as ṁ H2 ṁ + air = u inA in ρH ρair (6) 2 The mass flow rates equations for H2 and air can be obtained by substituting eq 6 into eq 3, yielding: 1 ṁ H2 = u inletA in /( 1 + ) ρH

2

0.029368ϕρair

(7)

and ṁ air =

u inletA in

⎛ 0.029368ϕ ⎜ + ⎝ ρH2

1 ⎞ ⎟ ρair ⎠

∇·(ρu ̅ ) = 0

(9)

For momentum conservation: (8)

⎛ ⎡⎛ ⎞⎤⎞ 2 ρ(u ⃗ ·∇u ⃗) = −∇p + ∇·⎜μ⎢⎜∇u ⃗ + (∇u ⃗)T − ∇·uI⃗ ⎟⎥⎟ ⎠⎦⎠ 3 ⎝ ⎣⎝ ⎤ ⎡ ρ − ⎢μ(D̅ ·u ⃗) + || u ⃗ || C̅ ·u ⃗ ⎥ ⎦ ⎣ (10) 2

3. COMPUTATIONAL METHODS 3.1. Mathematical Model and Boundary Conditions. The planar combustor used in this study has internal dimensions of 10 mm × 1 mm × 17 mm with 0.5 mm wall thickness. The origin is fixed at the center of the inlet plane. z depicts the axial or downstream distance, whereas x and y represent the distance in the transverse directions from the centerline of the combustor, respectively. Because of symmetry of the computational domain and the need to trim simulation time, only a quarter of the combustor as shown in Figure 5a is modeled. The pretreatment process installed on the numerical model can be partitioned into different stages which include (a) making essential assumptions to simplify the transport processes; (b) defining the governing equations; (c) analyzing the fluid dynamics involved within the porous medium; (d) analyzing the chemical kinetics within the microcombustor; and (e) defining the boundary conditions. The fluid medium can be regarded to be in continuum as the Knudsen number is less than unity. That is the characteristic lengths of the models used are sufficiently large compared to the mean free path of air or hydrogen molecules.13,17 Recently, Li et al.18 found that the effect of slip-wall boundary condition

where the fourth and fifth terms on the right-hand side are the viscous loss term and inertia loss term, respectively. These two momentum sink terms contribute to the pressure gradient in the porous media, creating a pressure drop that is proportional to the fluid velocity.21 For energy conservation: ⎡ ∇·[u ⃗(ρEf + p)] = ∇· ⎢keff ∇T − (∑ hiJi ⃗ ) ⎢⎣ i ⎛ ⎡ ⎤⎞ ⎤ 2 + ⎜μ⎢(∇u ⃗ + (∇u ⃗)T ) − ∇· uI⃗ ⎥⎟·u ⃗ ⎥ + Sfh ⎦⎠ ⎥⎦ ⎝ ⎣ 3 (11)

where keff = εkf + (1−ε)ks and term. For species conservation:

Shf

∇·(ρuY ⃗ i ) = −∇·Ji ⃗ + R i + Si 6330

is the fluid enthalpy source

(12)



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Table 1. Experimental Studies on Micro-combustors with Simple Geometries3 author(s)

fuel-oxidizer

Zamashchikov17

C3H8/Air CH4/Air H2/Air CH4/O2 CH4/Air

Prakash et al.18 Fan et al.19

combustor geometry

combustor size

cylindrical tubes

D = 2.7 mm

rectangular slots radial microchannels

H = 0.75 mm H = 0.5−3 mm

(13)

The energy equation for the wall is given by ∇·(k w ∇T ) = 0

(14)

The Reynolds number for flow within a porous media is defined as Red =

ρu p̅ d ̅ μ

stainless steel ceramic quartz alumina quartz

sections are below that critical value, hence, laminar flow model is adopted. The flow behavior within a porous medium is governed by the momentum equation which includes the viscous and inertia loss terms. These terms are intrinsic properties of the solid matrix as they are material and geometry dependent. To better reflect the flow field within the porous medium, it is necessary to obtain the values of these terms through measurements. A simple experiment was conducted to determine the pressure drop across the porous medium within a microcombustor over different flow velocities of air. Figure 6 shows the pressure change for different flow speeds.

where Ri is the net rate of production of species i by chemical reaction, Si is the rate of creation by addition from the dispersed phase, and Ji⃗ is the diffusion flux of species i which is given by Ji ⃗ = −ρDi·m∇Yi

combustor material

(15) 22

Equation 15 was defined by Dybbs and Edwards after examining the velocity distribution through hexagonal packing of spheres and complex arrangements of cylinders. In that study, each bubble structure in the porous foam typically consists of 14 reticulated windows or facets and the pores are of two or three different characteristic sizes and shapes.23 To simplify the analysis of pore structures and their effects on flow distribution, it is assumed that eq 15 is valid for the porous media employed in this work. The four distinct flow regimes described by Dybbs and Edwards are defined as follows: (i) Darcy or creeping flow regime: Red < 1, (ii) inertial flow regime: 1 to 10 < Red < 150; (iii) unsteady laminar flow regime: 150 < Red < 300; and (iv) unsteady and chaotic flow regime: Red > 300. The average pore velocity can be described by the inlet velocity or filter velocity using up = uin/ε. Furthermore, the Reynolds number can be computed using Table 2 for fuel/air

Figure 6. Measured pressure drop against inlet velocity through SiC foam.

A linear regression line was obtained to fit the data points, yielding a relationship between the change in pressure and the inlet velocity as described by the following equation:

Table 2. Density of H2/air mixture at different equivalence ratio equivalence ratio, Φ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

air density at 300 K H2 density at 300 (kg/m3) K (kg/m3) 1.184 1.184 1.184 1.184 1.184 1.184 1.184 1.184 1.184 1.184 1.184

0.0826 0.0826 0.0826 0.0826 0.0826 0.0826 0.0826 0.0826 0.0826 0.0826 0.0826

Δp = 0.4989u in2 + 0.5172u in

(16)

We employed a detailed mechanism of chemical kinetics as provided in Table 3 that comprises 9 species (H, H2, HO2, H2O, H2O2, O, O2, OH, and N2) and 19 reversible reactions to account for the H2/air combustion. The inlet boundary condition is defined based on the values of the mass flow rates and the temperature measured in the experiment. The mass fraction of the species at the inlet plane can be derived from the fuel-air equivalence ratio and composition of air. From eqs 7 and 8, the mass fraction for H2 and O2 are derived as ṁ H2,in = (ṁ H2)/(ṁ H2+ṁ air) and ṁ O2,in = (ṁ air × 0.23)/ (ṁ H2+ṁ air), respectively. A specified pressure outlet condition is applied at the exit of the combustor. At the fluid-wall interface (inner wall), nonslip boundary condition and zero diffusive flux of species are specified. The heat loss flux from the external wall to the surroundings is given by

average density at 300 K (kg/m3) 1.184 1.14 1.098 1.061 1.025 0.992 0.962 0.933 0.907 0.881 0.858

mixtures with different inlet equivalence ratio. For an inlet flow velocity of 6 m/s with ϕ = 1.0, Red ≅ 85. This value falls within the inertia flow regime, where there is dominance of inertia forces over viscous forces. A simple computation has revealed that the flow remains laminar for inlet velocities of up to 21 m/s. The flow velocities for all simulations discussed in subsequent

qw = h(Tw − To) + εw σ(Tw4 − To4)

(17)

where h is the natural convective heat transfer coefficient from the external wall to the surroundings with a value of 10 W/m2K. 6331



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where Prad is net radiation power emitted by the emitter, Hfuel is the heat value of fuel, SE is the emission area of the emitter, λ is wavelength, T is the temperature of the emitter, ε is the emissivity of the emitter and Wb(λ,T) = (c1)/(λ5(ec2/λT − 1)) is the spectral distribution of emissive power of a blackbody. The fraction of power loss through convection is defined as the ratio of convective heat loss through the wall to the total input energy, which can be calculated by

Table 3. Gas-Phase Reaction Mechanism for Hydrogen− Aira 22,27 reactions

Ak (m, kmol, s)

βk

× × × × × × × × × × × × × × × × × × ×

−0.82 1.00 1.30 1.30 0.00 −2.60 0.50 0.50 −1.00 −1.42 −1.42 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1. O2 +H = OH + O 2. H2 + O = OH + H 3. H2 + OH = H2O + H 4. OH + OH = H2O + O 5. H2 + O2 = OH + OH 6. H + OH + M = H2O + Mb 7. O2 + M = O + O + M 8. H2 + M = H + H + Mc 9. H + O2 + M = HO2 + Md 10. H + O2 + O2 = HO2 + O2 11. H + O2 + N2 = HO2 + N2 12. HO2 + H = H2 + O2 13. HO2 + H = OH + OH 14. HO2 + O = OH + O2 15. HO2 + OH = H2O + O2 16. HO2 + HO2 = H2O2 + O2 17. H2O2 + M = OH + OH + M 18. H2O2 + H = H2 + HO2 19. H2O2 + OH = H2O + HO2

5.10 1.80 1.20 6.00 1.70 7.50 1.90 2.20 2.10 6.70 6.70 2.50 2.50 4.80 5.00 2.00 1.20 1.70 1.00

1013 107 106 105 1010 1020 108 109 1012 1013 1013 1010 1011 1010 1010 109 1014 109 1010

Ek (J/kmol) 6.91 3.70 1.52 0.00 2.00 0.00 4.001 3.877 0.00 0.00 0.00 2.90 7.90 4.20 4.20 0.00 1.905 1.57 7.50

× 107 × 107 × 107 × 108

ηwall,conv =

× 108 × 108

× × × ×

(20)

where, h is the free convective heat transfer coefficient, A is the surface area of the combustor wall, Twall is the wall temperature of the combustor, T0 is the room temperature. The heat conduction loss through the connection tube is then obtained as

106 106 106 106

ηheat loss,cond = 1 − ηexhaust − ηwall,rad − ηwall,conv

(21)

3.2. Numerical Method and Grid Independence. The governing equations are discretized and solved using the finite volume method. First-order upwind schemes are used to solve all the governing equations as they yield faster convergence than higher-order schemes. The governing equations are solved implicitly using a pressure-based double-precision segregated solver with an under-relaxation method. The pressure-velocity coupling is solved using the SIMPLE algorithm where the momentum equations are solved first, followed by the continuity equation, before the pressure and velocity are updated. Iterations are then performed and monitored until a converged solution is obtained. The criterion of convergence is determined from the residuals of the conservation equations, which are defined to be 1 × 10−3 for continuity, 1 × 10−3 for velocity, 1 × 10−6 for energy and 1 × 10−3 for species concentration. The gas viscosity, specific heat and thermal conductivity are calculated as a mass-fraction-weighted average of all species. Numerical convergence is generally difficult due to the inherent stiffness of the matrix − a result of strong coupling between temperature, pressure and velocity within the computational domain. Depending on the complexity of the model, the computational time required can vary from 30 h to a few days. In order to determine the number of mesh points required, a grid independence test was conducted by meshing the model using structured hexahedral grid of various sizes. Figure 7 shows the temperature profiles of various mesh sizes

× 108 × 107 × 106

Rate constants are given in the form k = AkTβk exp(−Ek/RT) Enhancement factors: H20 = 20.0. cEnhancement factors: H20 = 6.0, H = 2.0, H2 = 3.0. dEnhancement factors: H20 = 21.0, H2 = 3.3, O2 = 0.0, N2 = 0.0. a b

Unlike convective heat transfer coefficient, the wall emissivity is a significant parameter as radiation is the dominant heat transfer mechanism.16 Due to repeated experiments at high temperature, the external surface of the microcombustor is often oxidized to a large extent; thereby leading to the formation of thin-layered oxides such as Cr2O3 and MnCr2O4.24 Numerous studies have been conducted to determine the thermal properties of Cr2O3.25,26 One study revealed that the total normal emissivity of Cr2O3 could reach up to 0.9 at 1370 K.27 On the other hand, information on MnCr2O4 is not readily available. In this work, εw is assigned with a value of 0.9 to account surface oxidation based on the thermal conditions of the wall (∼1370 K) during combustion. And Cr2O3 is considered as the main oxide layer that forms on the surface.28 The thermal conductivity value for stainless steel type-316 has been found to be approximately 30 W/mK at 1300 K.29,30 However, it is believed that repeated combustion experiments have led to changes in the thermal properties of the wall. As such, a smaller value of 25 W/mK has been assigned as the thermal conductivity of the wall while the thermal conductivity for the solid matrix is set to be 50 W/mK.23 The fraction of the power loss through the exhaust is calculated as ηexhaust =

hA(Twall − T0) Hfuelṁ

c p2T2 − c p1T1 Hfuelṁ

(18)

where T2 is the temperature of the exhaust gas and T1 is the temperature of fresh gas at the inlet. The fraction of the power loss through radiation is defined as the ratio of radiation energy to the total input energy, which can be calculated by ∞

ηwall,rad

∫ Wb(λ , T )εSEdλ P = rad = 0 Hfuelṁ Hfuelṁ

(19)

Figure 7. Temperature profile along center axis for different mesh size. 6332



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4. RESULTS AND DISCUSSION 4.1. Model Validation. To determine the validity of the model, there is a need to compare between the results from numerical simulations and experiments. The error associated with each experimental measurement is taken to be 5% of the measured value. This value is higher than the results obtained from an uncertainty analysis as there may be other errors unaccounted for. Panels a and b in Figure 8 shows the wall

the contact between the porous medium and the wall. This contact is affected by the combustion taking place due to the different thermal expansion rates experienced by stainless steel and SiC. A reduced heat transfer from the porous media to the wall is anticipated. The eventual result is that the wall temperature drops faster. In our present model, we assume a seamless perfect contact between the porous medium and the combustor wall. This explains the slight degree of variability but still within the confine of the experimental errors. 4.2. Effect of Equivalent Ratio on Microcombustion. Equivalence ratio is a key parameter that affects the performance of the TPV system. Here, we will look at how changes in ϕ affect the microcombustor’s performance under the conditions where uin = 6 m/s and ks = 50 W/mK. Figure 9a

Figure 8. Comparison of experimental and numerical results for the wall temperature for (a) fixed inlet velocity and varying ϕ; and (b) fixed ϕ and varying inlet velocity.

Figure 9. (a) Temperature profile along the centerline of the wall; and (b) temperature along center axis of combustor at different ϕ.

temperature along the centerline the wall temperature for fixed inlet velocity and varying ϕ and fixed ϕ and varying inlet velocity, respectively. As depicted, the numerical results are generally in good agreement with the experimental result, thereby confirming the validity of the model. It is noteworthy that the experimental temperature data are only marginally higher than numerical curves for the front portion of the combustor; in this case for the distance up to 4 mm (reference from combustor flow entrance). If we consider the embedded variability of the data due to experimental errors, it is apparent the prediction of the numerical curve is still within the confine of the calculated experimental errors. Toward the later section of the combustor (about 12 mm beyond the reference inlet), we noted lower wall temperatures in contrast to numerical predictions. This observation may be attributed to

shows the temperature profile of the wall for different ϕ where the maximum temperature increases as ϕ increases. The mean wall temperature values are 1094, 1120, 1156, 1176, and 1187 K for mixtures of ϕ = 0.6, 0.7, 0.8, 0.9, and 1.0, respectively. As ϕ represents the amount of the fuel available, a higher value corresponds to more H2 available for reaction. This in turn leads to more energy being released during combustion. Therefore, close to the inlet where the flame is contained within the combustor, higher wall temperature can be observed. In addition, the maximum flame temperature can be observed to be a nonlinear function of ϕ, where the values are found to be 1192, 1252, 1316, 1360, and 1386 K for mixtures of ϕ = 0.6, 0.7, 0.8, 0.9, and 1.0, respectively. The equivalence ratio affects the location where the peak temperature occurs. As ϕ increases, the location of the maximum flame temperature is shifted

along the center axis of the microcombustor. A mesh size of 0.075 mm was selected for all models as there was little difference in the results generated from mesh sizes of 0.075 mm and 0.07 mm. This selection leads the computational domain to be meshed into 272992 nodes.

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upstream toward the inlet from 1.9 mm at ϕ = 0.6 to 0.7 mm at ϕ = 1.0 (Figure 9b). Similar shift has also been observed by Li et al.31 on a planar microcombustor with porous medium inserted halfway through the combustor. However, they did not provide further insights on the peak-shift phenomenon. One possible explanation for this observed trend is based on the length scale of the reaction. Employing a dimensional analysis, we obtain the length scale of the reaction, as depicted in eq 21. This parameter can be interpreted as a ratio of the inlet velocity over the reaction rate. When ϕ decreases, the concentration of H2 molecules and, hence, reaction rate reduces. This in turn gives rise to the need for a longer length scale. u l′c ≈ in R′c (22)

However, there may be other underlying reasons to explain the occurrence. One possible reason could be attributed to the shift in the combustion zone. Higher ϕ values reflect shorter reaction length scales. To understand the principles behind this effect, we judiciously anticipate a competition between the main transport mechanisms within the combustor, i.e. heat loss from the core to the wall, convective heat loss through the outlet as well as heat available for preheating. A flame that is positioned further downstream from the inlet allows the flame core to be positioned further from the inlet than that to the wall. Greater amount of heat would be absorbed by the wall and hence less heat would be available for preheating. This direct impact is a lower flame temperature that delays flame ignition. In contrast, a flame that is positioned closer to the inlet leads to more avail heat for preheating and possibly to ignite the incoming reactants. The combustor wall may not necessary be able to absorb the same proportion of heat. Therefore, an optimal position exits where the heat losses are balanced. This insight explains why higher ηheat cond, loss values are obtained when the equivalence ratio increases as illustrated in Figure 11. The power distribution at different equivalence ratio is also illustrated in Figure 11. It can be seen that convective losses are minimal and can be neglected. In addition, ηwall,rad is relatively constant across for different values of ϕ, while ηexhaust reduces from 51% to 41% and ηheat cond, loss increases from 24% to 35% as ϕ increases from 0.6 to 1.0. In sum, ϕ appears to be the parameter that controls both the flame location as well as the distribution between preheat and exhaust power. 4.3. Varying Solid Matrix Thermal Conductivity. During combustion, heat is transferred rapidly from the flame throughout the entire solid matrix by both conduction and interfacial convection. Since radiation is not employed and is, therefore, not a feature in the model, its effects are not considered here. To determine which transport phenomena dominates within the medium, the ratio of the thermal penetration time into the solid phase to the residence time in the pore, ((d̅2)/(αs))/(d̅/εuin) = εuin (d̅)/(αs) = (εPeαf)/(αs) is computed,32 where αs is the thermal diffusivity term and is defined asαs=ks/ρscp,s. Given the flow conditions where uin = 6 m/s and ks = 50 W/mK, the ratio is obtained to be approximately 102. The high ratio obtained has indicated conduction to be the dominant mechanism among the thermal transport processes within the porous medium. Consequently,

Li et al.31 found that the maximum efficiency of a emitter with porous medium did not occur concurrently with a stoichiometric mixture, but instead at ϕ = 0.8. Similar outcome was also observed in Figure 10, where a maximum emitter efficiency of

Figure 10. Emitter efficiency at different ϕ.

20% was obtained when ϕ = 0.8. In their work, Li et al.31 attributed heat loss to the flange connection as the main reason for a low emitter efficiency as ϕ increases from 0.8 to 1.0.

Figure 11. Power distribution at different ϕ. 6334



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For the range of ks tested, the scale of Bi is in the order of 1 to 10−2. As ks increases, Bi becomes smaller, thus producing a flatter temperature profile along the center axis of the solid matrix. When ks is reduced, the maximum temperature in the flame core increases and the flame core was observed to have shifted upstream toward the combustor’s inlet. From Figure 12b, a localized region of high temperature can be seen for ks = 5 W/mK. This effect can be explained by the concept of thermal diffusivity which relates to the rate of heat propagation. For a porous medium with ks = 5 W/mK, αs is on the order of 1 × 10−7, which is one order lower than that of the wall. This indicates that the rate at which heat is being transferred from the inner surface of the combustor wall to the external surface is faster than conduction of heat downstream. In other words, heat is conducted more rapidly from the porous medium to the wall than downstream along the medium, or simply, heat is lost at a faster rate in the transverse direction as compared to the axial direction. The temperature distribution along the wall is, therefore, steeper. Additionally, the overall rate of heat release through combustion is faster than the rate of heat loss, implying the containment of heat is within only a small region. Figure 13a shows the emitter efficiency for different ks values under the same flow conditions. Because of effective and rapid

thermal dispersion effects can be ignored in the following discussions. The effect of the solid matrix thermal conductivity on the performance of the TPV is studied with uin = 6 m/s and ϕ = 1.0. The profiles of the wall temperature are illustrated in Figure 12a for different thermal conductivities of the solid

Figure 12. (a) Temperature profile along the centerline of the wall; and (b) temperature profile along the center axis for different ks.

matrix. It is apparent that a higher ks value results in a flatter temperature profile. From the graph, the mean wall temperatures and maximum wall temperatures for ks = 5, 50, and 500 W/mK are found to be 1230, 1187, 1332, and 1521, 1350, and 1391 K, respectively. The temperature profiles along the center axis of the combustor are given in Figure 12b, where the peak temperatures are 1984, 1386, and 1398 K for ks = 5, 50, and 500 W/mK, respectively. This phenomenon of flatter temperature profile has been discussed by Hua et al.33 on a cylindrical microcombustor without porous medium, where similar trend in their results were obtained for various wall thermal conductivity values. They observed that small Biot number leads to more uniform temperature distribution. Similar explanation also holds for combustion in porous media. According to Dukhan,34 the Biot number for a porous medium is given by hσ L2 Bi = s ks

Figure 13. (a) Emitter efficiency for different ks; and (b) mole fraction of H2O at a distance of 0.5 mm from internal wall. (23)

By using scaling analysis, the Biot number becomes (10 × 104 × (10−2)2)/(ks) ≈ (10)/(ks).

heat transfer from the flame core to the internal wall surface, higher emitter efficiency is obtained when ks increases beyond a 6335



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Figure 14. Power distribution for different ks.

certain order of magnitude. Similarly, high emitter efficiency is obtained when ks is small. A low efficiency is observed when ks = 50 W/mK. This phenomenon is attributed to the competing mechanisms in terms of conduction losses along the transverse and axial directions. A comparison between the thermal diffusivity of the porous medium and emitter wall has revealed that the rate of heat propagation across the wall is approximately twice of that across the porous medium. It is postulated that the flame size is smaller in this state as compared to flames in other conditions. When αs is close to that of the wall, heat released from reaction is lost through the wall rapidly, such that only a small portion of heat is confined at the flame core. The flame can then be considered to be thin and reactants flowing within the quenching distance from the wall to the flame do not undergo effective combustion. This can be readily observed from Figure 13b which shows the mole fraction of H2O at a distance of 0.5 mm from the wall. Less energy is released and the flame core temperature is accordingly reduced. When ks is large, the flame zone widens as the rate of heat loss is restricted by the combustor wall. When ks is low, the flame zone is confined to a region close to the inlet as the rate of heat loss is limited by the medium. The accumulation of heat favors complete combustion within the region. The ratio of αs/αw can be thought to be somewhat analogous to the resonance effect based on the ratio of oscillating frequency to the natural frequency. The difference is that this phenomenon is more complex because of the associated coupling between chemical kinetics, fluid dynamics, and heat transfer. The power distribution for combustors with different ks values is illustrated in Figure 14. At ks values of 5, 50, and 500 W/mK, ηexhaust are computed to be 42, 45.5, and 47%, respectively. It appears that for higher ks values result in greater ηexhaust. Nonetheless, there is an upper limit for ηexhaust. By considering adiabatic temperature of H2 (2382 K)35 at the outlet, the maximum ηexhaust value can be found to be 51.3% for the stoichiometric mixtures. The lowest ηheat cond, loss value occurs at ks = 500 W/mK with a value of 18%, thereby confirming that heat is conducted mainly in the axial direction, i.e., downstream away from the inlet before they are transferred to the wall. 4.4. Effect of Mass Flow Rate on Microcombustion. The effect of mass flow rate on wall temperature distribution is also investigated under the conditions where ϕ = 1.0 and ks = 50 W/mK. As shown in Figure 15a, higher mean wall temperatures are observed as uin increases from 6 to 15 m/s.

Figure 15. (a) Mean wall temperature; and (b) emitter efficiency under different inlet velocities.

The phenomenon of increasing wall temperature with increasing flow velocity has also been observed in planar31,36,37 as well as cylindrical16,38 microcombustors. At higher flow velocity, and hence, mass flow rate, more fuel will be available for combustion. This enhances the heat transfer rate between the wall and the combustion products, and in turn produces higher mean wall temperature. The increase in the mean wall temperature is noted to be smaller as uin becomes larger. As uin increases from 6 to 9 m/s, the mean increase in wall temperature is about 126 K. When uin increases from 12 to 15 m/s, the temperature rise is only 58 K. This trend indicates the presence of a peak mean temperature as uin reaches a critical 6336



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Figure 16. Power distribution for different uin..

value. The key concern with microcombustors is the small length scale which limits the residence time. Intuitively, there is a limit to uin as it is inversely proportional to the residence time. To sustain the flame within the combustor becomes an issue if uin increases beyond that value. The existence of maximum wall temperature for different flow velocities has been confirmed by experiments on microcombustors without porous media inserts.28 In Figure 15b, we observed higher emitter efficiency when the inlet velocity increases until the point where uin = 9 m/s, yielding a peak efficiency of 19.8%. This suggests that the maximum efficiency of the emitter occurs within the range from 6 to 12 m/s. Moreover, the power available at the exhaust as uin increases (Figure 16). For flow through porous medium, the average Nusselt number is found to increase almost linearly as the Reynolds number increases.39,40 Therefore, increased uin allows more heat to be convected from the flame zone to the end of the combustor. Accordingly, ηexhaust increases linearly from 45% to 51% when uin increases from 6 to 12 m/s. The same reason may be applied to explain the drop in efficiency as well as the reduction in ηheat cond, loss.

higher mean wall temperatures are obtained when the thermal conductivity values are small (5 W/mK) or very large (500 W/mK). The ratio αs/αw reveals important information about the combustion process. When it is close to unity, the emitter efficiency is low as combustion is less complete. The results indicate that the performance of microcombustors can be improved if porous medium with very high ks value is used. (3) Higher inlet flow velocity gives rise to higher wall temperature but lower emitter efficiency. Higher inlet velocity also enables higher ηexhaust. With a prescribed range of velocities, ηexhaust increases linearly with uin.

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ASSOCIATED CONTENT

* Supporting Information S

This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel. + 65 6516 2558. Fax: + 65 6779 1459. E-mail: mpeckje@ nus.edu.sg. Notes

5. CONCLUSIONS This work describes the fundamental findings derived from a numerical model constructed to understand the combustion process within a planar microcombustor that is filled with a porous medium. This attempt is believed to be the first among the emerging fields of micropower generation. Key findings that have emerged from this work can be summarized as follows: (1) Higher equivalence ratios of the fuel/air mixture induce higher mean wall temperatures. A peak-shift phenomenon is observable where the position of maximum flame temperature shifts downstream away from the inlet at lower equivalence ratio. The maximum emitter efficiency is obtained at ϕ = 0.8, which is the result of a downstream flame core. The equivalence ratio is an important parameter that has the capacity to control both the position of the flame core and the distribution between exhaust and conduction heat loss. (2) From the Biot number obtained, it is sufficiently apparent that the higher the thermal conductivity of the wall is, the more uniform the wall temperature distribution will be. A lower mean wall temperature can be observed when the thermal conductivity of the solid matrix is 50 W/mK, whereas

The authors declare no competing financial interest.

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NOMENCLATURE Ain Inlet area, m2 C2 Inertia resistance factor, m−1 d̅ Characteristic length scale for the pore, m Di,m Diffusion coefficient for species i in mixture, m2/s Ef Total fluid energy, J/kg fa Fuel−air ratio h Heat transfer coefficient, W/mK hi Enthalpy of species i, J/kg Hfuel Higher heating value of fuel, J/kg keff Effective bulk thermal conductivity of porous medium, W/mK kf Thermal conductivity of fluid, W/mK Thermal conductivity of solid matrix, W/mK ks kw Thermal conductivity of wall, W/mK l′C Length scale associated with reaction, m L Height of the wall, m ṁ air Mass flow rate of air, kg/s 6337


Industrial & Engineering Chemistry Research ṁ H2 ṁ H2,in ṁ O2,in ni qw Q̇ exhaust Q̇ gen Q̇ in Q̇ out Q̇ preheat Q̇ wall,rad Q̇ wall,conv Ri R′C S Si Shf Tin Tw To uin u ̅p Vi Yi Δn ΔT

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Mass flow rate of H2, kg/s Mass fraction of H2 at inlet Mass fraction of O2 at inlet Number of moles of compound i, mol Heat flux through the wall, W/m2 Power loss through outlet, W Power generated through combustion, W Power input into combustor, W Power output from combustor, W Power loss through a series of mechanisms but predominantly in the preheating of reactants, W Power loss through radiation from the wall to surroundings, W Power loss through convection from the wall to surroundings, W Net rate of production of species i by chemical reaction, kg/m3s Reaction rate, s−1 Momentum sink term Rate of creation of species i by addition from the dispersed phase, kg/m3s Fluid enthalpy source term, W/m3 Inlet temperature, K Wall temperature, K Ambient temperature, K Inlet velocity, m/s Mean pore velocity, m/s Volume of compound i, m3 Local mass fraction of species i Thickness of porous medium, m Average temperature difference between inlet and outlet, K Permeability of porous medium, m2 Thermal diffusivity of fluid, m2/s Thermal diffusivity of solid matrix, m2/s Thermal diffusivity of wall, m2/s Porosity Emissivity of wall Emitter efficiency Fraction of power loss through the outlet Fraction of power loss through conduction Fraction of power loss through convection Fraction of power loss through radiation Viscosity of fluid, Pa·s Density of fluid, kg/m3 Stefan−Boltzmann constant, 5.67 × 10−8 W/m2K4 Surface area per unit volume, m−1 Equivalence ratio

Subscripts

f s w C̅ D̅ Ji⃗ u̅

REFERENCES

(1) Yang, W. M.; Chou, S. K.; Shu, C.; Xue, H.; Li, Z. W. Development of microthermophotovoltaic system. Appl. Phys. Lett. 2002, 81, 5255−5257. (2) Yang, W. M.; Chou, S. K.; Li, J. Microthermophotovoltaic power generator with high power density. Appl. Therm. Eng. 2009, 29, 3144− 3148. (3) Yang, W. M.; Chou, S. K.; Shu, C.; Xue, H.; Li, Z. W.; Li, D. T.; Pan, J. F. Microscale combustion research for application to micro thermophotovoltaic systems. Energy Convers. Manage. 2003, 44, 2625− 2634. (4) Yang, W. M.; Chou, S. K.; Pan, J. F.; Li, J.; Zhao, X. Comparison of cylindrical and modular micro combustor radiators for micro-TPV system application. J. Micromech. Microeng. 2010, 20, 085003. (5) Norton, D. G.; Vlachos, D. G. Combustion characteristics and flame stability at the microscale: a CFD study of premixed methane-air mixtures. Chem. Eng. Sci. 2003, 58, 4871−4882. (6) Kwon, H. C.; Han, B. N.; Lee, D. H.; Kwon, S. Numerical simulation of flame propagation near extinction condition in a microcombustor. Microscale Therm. Eng. 2004, 8, 71−89. (7) Giovangigli, V.; Smooke, M. D. Extinction of stained premixed laminar flames with complex chemistry. Combust. Sci. Technol. 1987, 53, 23−49. (8) Tien, J. H.; Stalker, R. J. Release of chemical energy by combustion in a supersonic mixing layer of hydrogen and air. Combust. Flame 2002, 130, 329−348. (9) Mueller, M. A.; Kim, T. J.; Yetter, R. A.; Dryer, F. L. Flow reactor studies and kinetic modeling of the H2/O2 reaction. Int. J. Chem. Kinet. 1999, 31, 113−125. (10) Yetter, R. A.; Dryer, F. L.; Rabitz, H. A comprehensive reaction mechanism for carbon monoxide/hydrogen/oxygen kinetics. Combust. Sci. Technol. 1991, 79, 97−128. (11) Connaire, M. O.; Curran, H. J.; Simmie, J. M.; Pitz, W. J.; Westbrook, C. K. A comprehensive modeling study of hydrogen oxidation. Int. J. Chem. Kinet. 2004, 36, 603−622. (12) Zhou, X. Y.; Pereira, J. C. F. Numerical study of combustion and pollutants formation in inert non-homogeneous porous media. Combust. Sci. Technol. 1997, 130, 335−364. (13) Kaviany, M. Principles of Heat Transfer in Porous Media;Ling, F. F., Ed.; Mechanical Engineering Series; Springer-Verlag: New York, 1995 (14) Howell, J. R.; Hall, M. J.; Ellzey, J. L. Combustion of hydrocarbon fuels within porous inert media. Prog. Energy Combust. 1996, 22, 121−145. (15) Chou, S. K.; Yang, W. M.; Li, J.; Li., Z. W. Porous media combustion for micro thermophotovoltaic system applications. Appl. Energy 2010, 87, 2862−2867. (16) Li, J.; Chou, S. K.; Yang, W. M.; Li., Z. W. Experimental and numerical study of the wall temperature of cylindrical micro combustors. J. Micromech. Microeng. 2009, 19. (17) Jennings, S. G. The mean free path in air. J. Aerosol Sci. 1988, 19, 159−166. (18) Li, J.; Chou, S. K.; Li, Z. W.; Yang, W. M. Combust. Theor. Model. 2008, 12, 325−347. (19) Williams, F. A., Combustion Theory: Fundamental Theory of Chemical Reacting Flow Systems, 2nd ed.; Benjamin/Cummings: Menlo Park, 1985. (20) Norton, D. G.; Vlachos, D. G. A CFD study of propane-air microflame stability. Combust. Flame 2004, 138, 97−107. (21) Fluent 6.3 User’s Guide; ANSYS: Canonsburg, PA, 2006. (22) Dybbs, A. Edwards, R.V. A New Look at Porous Media Fluid Mechanics−Darcy to Turbulent. In Fundamentals of Transport Phenomena in Porous Media; Bear, J., Corapcioglu, M. Y., Eds.; Martinus Nijhoff Publishers: Hague, The Netherlands, 1984; pp 199− 254. (23) ERG, Duocel Foam Properties. http://www.ergaerospace.com/ foamproperties/introduction.htm (accessed August 2011).

Greek Symbols

α αf αs αw ε εw ηemitter ηexhaust ηheat cond, loss ηwall,conv ηwall,rad μ ρ σ σs ϕ

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Fluid Solid matrix Wall Inertia resistance, m−1 Viscous resistance, m−2 Diffusion flux of species i, kg/m2s Velocity vector, m/s

Dimensionless Numbers

Bi Biot number Pe Peclet number Red Reynolds number at pore scale 6338



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(24) Guillamet, R.; Lenglet, M.; Gazin, L.; Hannoyer, B.; Lopitaux, J. Influence of surface preparation on oxidation of stainless steels at high temperature. Surf. Interface Anal. 1993, 20, 15−20. (25) Neuer, G.; Jaroma-Weiland, G. Spectral and total emissivity of high-temperature materials. Int. J. Thermophs.y 1998, 19, 917−929. (26) Lasday, S. B. Nature of ceramic coatings and their benefits in thermal processes. Ind. Heat 1982, 49, 49−52. (27) Cockeram, B. V.; Measures, D. P.; Mueller, A. J. , The development and testing of emissivity enhancement coatings for themophotovoltaic (TPV) radiator applications. Thin Solid Films 1999, 355, 17−25. (28) Guillamet, R.; Lopitaux, J.; Hannoyer, B.; Lenglet, M. Oxidation of stainless steels (AISI 304 and 316) at high temperature. Influence on the metallic substratum. J. Phys−Paris IV 1993, 3, 349−356. (29) Chawla, T. C.; Graff, D. L.; Borg, R. C.; Bordner, G. L.; Weber, D. P.; Miller, D. Thermophysical properties of mixed oxide fuel and stainless steel type 316 for use in transition phase analysis. Nucl. Eng. Des. 1981, 67, 57−74. (30) Leibowitz, L.; Blomquist, R. A. Thermal conductivity and thermal expansion of stainless steels D9 and HT9. Int. J. Thermophys. 1988, 9, 873−883. (31) Li, J.; Chou, S. K.; Li, Z. W.; Yang, W. M. A potential heat source for the micro-thermophotovoltaic (TPV) system. Chem. Eng. Sci. 2009, 64, 3282−3289. (32) Li, Z. W.; Chou, S. K.; Shu, C.; Yang, W. M. Effects of step height on wall temperature of a microcombustor. J. Micromech. Microeng. 2005, 15, 207−212. (33) Hua, J.; Wu, M.; Kumar, K. Numerical simulation of the combustion of hydrogen-air mixture in micro-scaled chambers. Part I: Fundamental study. Chem. Eng. Sci. 2005, 60, 3497−3506. (34) Dukhan, N. Developing nonthermal-equilibrium convection in porous media with negligible fluid conduction. J. Heat Transfer 2009, 131, 1−3. (35) Glassman, I. Combustion, 4th ed.; Academic Press: New York, 2008. (36) Li, J.; Chou, S. K.; Li, Z. W.; Yang, W. M. Experimental investigation of porous media combustion in a planar microcombustor. Fuel 2010, 89, 708−715. (37) Yang, W. M.; Chou, S. K.; Chua, K. J.; Li, J.; Zhao, X. Research on modular micro combustor-radiator with and without porous media. Chem. Eng. J. 2011, 168 (2), 799−802. (38) Li, J.; Chou, S. K.; Huang, G.; Yang, W. M.; Li, Z. W. Study on premixed combustion in cylindrical micro combustors: Transient flame behavior and wall heat flux. Exp. Therm. Fluid Sci. 2009, 33, 764−773. (39) Calmidi, V. V.; Mahajan, R. L. Forced convection in high porosity metal foams. J. Heat Transfer 2000, 122, 557−565. (40) Venugopal, G.; Balaji, C.; Venkateshan, S. P. Experimental study of mixed convection heat transfer in a vertical duct filled with metallic porous structures. Int. J. Therm. Sci. 2010, 49, 340−348.

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