Modelling of solid fuel stoves

Fuel 89 (2010) 782–791

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Modelling of solid fuel stoves Shankar B. Kausley, Aniruddha B. Pandit * Chemical Engineering Division, UICT, Matunga, Mumbai 400 019, India

a r t i c l e

i n f o

Article history: Received 18 May 2008 Received in revised form 17 August 2009 Accepted 17 September 2009 Available online 14 October 2009 Keywords: Stove Solid fuel Biomass Modelling Suction

a b s t r a c t This work presents a detailed theoretical study of solid fuel combustion in a domestic stove (make Harsha, RRL, Bhubaneswar, India). In this work different steady state as well as unsteady state combustion models have been formulated, which include the description of all the chemical and physical processes taking place during the solid fuel combustion inside the stove. Steady state models involve the calculation of effective maximum flame temperature, suction of combustion air created by hot flue gases inside the stove and the propagation of ignition front inside the stove. Unsteady state mathematical model involves all the processes occurring simultaneously or sequentially during the solid fuel combustion such as moisture evaporation, devolatilization, pyrolysis and homogeneous and heterogeneous combustion reactions. This unsteady state model gives the temperature profiles at different locations inside the stove and fuel mass loss (combustion) rate, which can be further used to calculate the power delivery by the stove during combustion. The model shows good agreement with the experimental results. These models can be used to find the effect of stove geometry and fuel properties on the stove performance parameters such as effective maximum flame temperature, suction created inside the stove, propagation of ignition front inside the stove, and fuel burn rate, which play an important role in the design of such stoves for maximum thermal efficiencies. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Solid fuel stoves used traditionally, are known to have low thermal efficiencies. The design of these stoves can be improved if various phenomena occurring in the stove are better understood. Present work deals with a detailed theoretical study including steady state and unsteady state of fuel particle and particle bed combustion models. Steady state models involve the calculation of effective maximum flame temperature, suction created by the hot flue gases inside the stove and propagation of ignition front inside the stove. These models are used to find the effect of stove geometry and fuel properties on the effective maximum flame temperature, excess air required to sustain the combustion, suction created by hot flue gases inside the stove, and propagation of the ignition front inside the fuel bed. Unsteady state heterogeneous combustion mathematical model has been developed including all the processes occurring during the biomass combustion inside the stove such as drying, devolatilization, homogeneous and heterogeneous combustion. The model is validated using the experimental results. 1.1. Experimental set-up Experiments are carried out with Harsha domestic stove developed by RRL Bhubaneswar [1]. It consists of a corrugated grate, ash * Corresponding author. Tel.: +91 22 4145616; fax: +91 22 4145614. E-mail address: [email protected] (A.B. Pandit). 0016-2361/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.fuel.2009.09.019

scrapper, perforated combustion chamber and air jacket for flow of air in primary and secondary streams as shown in Fig. 1a and b. The combustion air is preheated through the hot surfaces of the stove before it is drawn into the stove by natural drafts during the burning of the various solid fuels. In order to measure the performance of stove in terms of thermal efficiency, power delivery, flame temperature and bed temperatures, entire stove with cooking pot above it, is placed on a weighing platform. Seven K type thermocouples (T1–T7) are placed at different locations: at the bottom near the grate (T1), at a distance 10 mm (T2) and 60 mm (T3) above the grate, three thermocouples in the flame (T4–T6) (average temperature of these three thermocouples is reported as flame temperature) and inside the material (water) in the pot (T7). The entire stove, the pot and weighing balance are enclosed in a chamber with inlet port for air and chimney for the escape of flue gases as shown in Fig. 1b. Velocity of air at inlet port and flue gas velocity at chimney exit are measured by using fan type anemometer, placed in inlet and exit ports.

2. Steady state calculations 2.1. Calculations of effective maximum flame temperature and excess air 2.1.1. Effective maximum flame temperature Effective maximum flame temperature which has a close scientific resemblance to adiabatic flame temperature is the maximum

S.B. Kausley, A.B. Pandit / Fuel 89 (2010) 782–791

783

Nomenclature a A B Bi0 C cp Cw,s Cw,g d D g h H J k kc kd kdev k0 keff keff,0 KR L m M mf n P pO2 ;g pO2 ;s Pr q Qc Q 00 Q Qlg Qls r rc R Re Sc Sh

specific surface area (m1) area (m2) breadth (m) modified Biot number () species concentration (mol m3, kg m3) specific heat capacity (J mol1 K1, J kg1 K1) concentration of moisture at the solid fuel particle surface (kg m3) concentration of moisture in the gas phase (kg m3) diameter (m) molecular diffusivity (m2 s1) acceleration due to gravity (m s2) convective heat transfer coefficient between solid and gas (W m2 K1) and enthalpy (J kg1) height (m) Colburn J factor thermal conductivity (W m1 K1) char reaction rate constant (Pa1 s1) mass transfer coefficient (m s1) rate constant of devolatilization (s1) overall char combustion reaction rate constant (Pa1 s1) effective thermal conductivity (W m1 K1) thermal conductivity for no fluid flow (W m1 K1) radiation coefficient length (m) gas or air mass flux (kg m2 s1) molecular weight (kg mol1) fuel mass (kg) moles of individual gas species (mol) pressure (Pa) partial pressure of O2 in the gas phase (Pa) partial pressure of O2 at the solid fuel particle surface (Pa) Prandtl number heat flux (W m2) heat liberated during combustion (J) volumetric heat generation or loss (J m3 s1) energy per unit volume (J m3) heat loss by gas phase along the bed wall heat loss by solid phase along the bed wall reaction rate (mol m3 s1 or kg m3 s1) and radial distance (m) ratio of CO/CO2 ideal gas constant (J mol1 K1) Reynolds number Schmidt number Sherwood number

temperature reached when fuel is burning at a steady rate and there are also heat losses to the surrounding. Usually adiabatic temperatures are not obtained in practice due to heat losses (heat lost in flue gases, heat lost in evaporation of moisture, radiation losses from the surface of combustor, heat lost in excessive air) or due to incomplete combustion resulting from inadequate air supply. Hence actual flame temperatures are lower than adiabatic flame temperatures. Greater the effective maximum flame temperature, higher is the rate of heat flux because of increased temperature gradients. A steady state energy balance equation for combustion of fuel (wood) can be written as

S t T Tsg u wig x y Y

suction created by flue gases (Pa) time (s) temperature (K) average gas phase and solid phase temperature (K) superficial gas velocity (m s1) ignition velocity (m s1) coordinate along bed height (m) moisture content (dry basis) mass fraction of the species

Greek symbols a mass fraction of gas during devolatilization a decay coefficient (m1) b mass fraction of tar during devolatilization ci mass ratio of different species during wood pyrolysis w percentage excess air (%) DH heat of reaction (J kg1) DP pressure drop in packed bed (Pa) e bed voidage / sphericity k latent heat of vaporization of water (J kg1) l viscosity (Pa s) q density (kg m3) r Stefan Boltzmann constant (W m2 K4) U stoichiometric ratio for the char combustion Subscripts 0 ambient 1 far from ignition front b bed c char and Combustion chamber dev devolatilization eff effective evp evaporation f flame and fuel g gas ig ignition i ith species j jth species j O2 and N2 in the incoming air m moisture p particle port port r reference s solid tar tar v volatiles w water

Heat liberated by complete combustion of wood ðQ c Þ ¼ Heat in flue gases ðincluding O2 and N2 from elemental analysis of fuelÞ þ Heat required to heat the incoming combustion air to flame temperature þ Heat required to heat the fuel to its ignition temperature   Z Tf Z T f X  w Qc ¼ ðnj cp;j ÞdT þ mf cp;f ðT ig  T r Þ ni cp;i dT þ 1 þ 100 T ig Tr

ð1Þ ð2Þ

where, i represent the individual species in the flue gas including O2 and N2 from elemental analysis of fuel. j represent the O2 and N2 in the incoming air. f represents the fuel. m represents the mass (kg), n represent the moles of individual species of the solid fuel, Tf, Tig, and

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a

ing the suction developed by the flue gas, which in turn depend on the rate of suction of air. As shown in Fig. 1b, if flue gases are at a temperature Tf, suction (draught) created by flue gases inside the stove is given by the driving pressure, which is;

Suction ðdraughtÞ created by flue gases inside the stoveðSÞ ¼ Pressure head due to ambient air column of height ðH þ H1 Þ  Pressure drop across the bed of height H  Pressure head due to flue gases over height H1 S ¼ qair ðT amb ; PÞ g ðH þ H1 Þ  DP  qg ðT f ; PÞ gH1

ð3Þ ð4Þ

Pressure drop across the packed fuel bed of height H filled with solid fuel particle is given by the following expression [2].

Schematic of Harsha stove [1]

!

b

luð1  eÞ2 qu2 ð1  eÞ H DP ¼ 150 þ 1:75 2 3 2 dp e3 / dp e /

Exit port (Chimney)

ð5Þ

Suction created by flue gases = kinetic head of incoming air.

Cooking pot

H1

ρg (Tf, P) PA

T7

T4-T6

Thermocouples

x=H H

x x= x0

Suction created by flue gasesðSÞ ¼

T3 PB Fuel bed u

Weighing platform

T2 T1

Inlet port

dport

Fig. 1. Schematic of (a) Harsha domestic stove, and (b) Harsha domestic stove and cooking pot enclosed in the chamber.

Tr represents the effective maximum flame temperature, ignition temperature and reference temperature, respectively (K), w is the percentage excess air (during theoretical air requirement, w = 0), Qc is the heat liberated by complete combustion of fuel (J) and cp represent the specific heat of individual species (J/kg mol K or J/ kg K). Details for heat liberated by complete combustion of wood and specific heat are given in Eqs. (B.1.2) and (B.1.4) respectively (Appendix B). 2.1.2. Excess air In actual practice, the amount of air supplied during the combustion of fuel is greater than the theoretical air requirement. In calculation of excess air it is assumed that, the excess air has taken the heat off the flame and reduced the effective maximum flame temperature (actual measured temperature). Eqs. (2) and (B.1.4) are solved iteratively by varying the percentage excess air (w) to match the effective maximum flame temperature to actual measured flame temperature (average temperature of thermocouples T4–T6). 2.2. Calculations of suction (draught) created by hot flue gases Flue gases leaving the stove are at a high temperature compared to the ambient air. Due to the density difference between the column of flue gases and the ambient air, suction (draught by chimney effect) is developed and air is sucked inside the stove which is further used for the combustion of the fuel. Flame temperature and pressure drop across fuel bed are important parameters affect-

 2 1 1 Ac q u2port ¼ q u2 2 2 Aport

ð6Þ

Flame temperature is the measured temperature (about 860 °C), bed temperature is calculated as an average of flame temperature and inlet air temperature (ambient temperature). Air is sucked inside the stove through grate, passes through the bed and then mix and burn with volatiles in the flame. Temperature of air, changes from ambient to bed and finally to the flame temperature. Air density (calculated at ambient, bed and flame temperatures respectively) is used to calculate the pressure driving force terms in Eqs. (4) and (5). Solving Eqs. (4)–(6) iteratively, with some initial value of superficial air velocity (u), gives the suction created by flue gases inside the stove, at any instant depending on the location of the ignition front and the height of the hot air column created due to the hot flue gases. 2.3. Propagation of combustion front inside the stove Understanding of propagation of combustion front in the stove is very important, as it determines the fuel burn rate and power delivery. In Harsha domestic stove, when fuel is ignited at the top, ignition front starts to propagate in the downward direction, even though the air is moving in the upward direction. During the propagation of the ignition front, heat is transferred from flame to fresh layers of fuel beneath it (conduction and radiation). As soon as the temperature of the layer below increases to ignition temperature (for wood it is 650 K), pyrolysis of fuel occurs with the release of volatiles. These volatiles react (combust) within themselves and with the oxygen in the incoming air from grate as well as perforated side walls, with the release of heat. This heat is further utilized for the propagation of ignition front in the downward direction, and further pyrolyses the fuel layer beneath it. During the propagation of ignition front in the downward direction, released volatiles and char combust with the primary air (from grate) as well as with secondary air (from stove wall perforations of combustion chamber), hence homogeneous (volatile combustion) and heterogeneous combustion (char combustion) occur simultaneously. When ignition front reaches the bottom of the stove all volatiles as well as char is burnt and the stove extinguishes. Thus, the ignition front velocity gives a good indication of fuel mass loss rate due to combustion. In order to get a clear picture, ignition mass flux (ignition velocity, m/s  bulk density, kg/m3) can be used as a measure of fuel mass loss rate and power delivery with the knowledge of calorific value of the fuel.

S.B. Kausley, A.B. Pandit / Fuel 89 (2010) 782–791

Since homogeneous and heterogeneous combustion occurs simultaneously in Harsha domestic stove (side-wall perforated combustion chamber), compared to sequential homogeneous and heterogeneous combustion in a tall packed solid fuel bed where the combustion air is supplied only at the bottom. Model developed earlier by Saastamoinen et al. [3] for the propagation of ignition front (volatile release rate) in packed bed wood combustion is used here for the prediction of propagation of combustion front (overall fuel burn rate in this work is a combination of homogeneous and heterogeneous combustion). Saastamoinen et al. [3] derived an analytical equation for the prediction of ignition front velocity. The ignition front velocity can be defined as the ratio of heat flux to the energy per unit volume required to evaporate the water and heat the solids to the ignition temperature.

Hence; wig ¼ qig =Q 00 Q 00 ¼ ð1  eÞqs ½cp;s ðT igT 1 Þ þ ym ðk þ cp;w ÞðT w  T 1 Þ

ð7Þ

Heat flux at ignition front is given by

qig ¼ K R r T 4f

ð8Þ

In this model, the geometrical factors (size, shape, porosity, packing arrangement or random orientation of fuel particles) and emissivity are lumped to the experimental radiation coefficient KR. The following correlations for KR and Tf (flame temperature) are used in Eq. (8) when fuel moisture (wet basis) is below 30%.

K R ¼ a0  a1 mg T f ¼ b0  b1 mg  b2 m2g

ð9Þ ð10Þ

where, mg is the air mass flux (kg/m2 s). Saastamoinen et al. [3] have given the values of coefficients (a0, a1, b0, b1 and b2) for different solid fuels. In the present case, values of these coefficients are optimized in such a way that air flow rate at which the maximum ignition velocity occur should be equal to the theoretical air requirement, calculated by effective maximum flame temperature model. Values of these coefficient used in the calculations are thus worked out as: a0 = 0.2, a1 = 2, b0 = 903, b1 = 5547 and b2 = 11,626. The coefficient KR can be evaluated from Eq. (8) by using measured values of wig and Tf. Values of cp,s = 2000 J/kg K, T1 = 300 K and Tig = 650 K are used in the calculation. 3. Unsteady state heterogeneous combustion mathematical model The solid fuel (Biomass wood chips, pellets etc.) combustion process involves four successive or overlapping sub-processes: evaporation of moisture, volatile release/char formation, burning of volatiles, and the oxidation (combustion) of char particles. Unsteady state heterogeneous combustion mathematical model has been developed assuming stove as a packed bed equivalent to porous media or a bed with voidage and air quantity equivalent to that of suction created by flue gases. It is flowing from grate through the packed bed in the upward direction as shown in Fig. 1b. In this model transient combustion in the fuel bed is considered. Based on fuel mass loss rate, power delivery values are estimated. Freeboard combustion and heat transfer to cooking pot is not considered (in this work). The temperature distribution in the particle is an important parameter, which will determine the rates of different reaction fronts (drying, pyrolysis, homogeneous and heterogeneous combustion) during combustion. The Biot number is the measure of uniformity of temperature distribution. Yang et al. [4] have defined the modified Biot number for packed bed of wood particle combustion, considering radiation from the flame can only penetrate the bed through voids. The modified Biot number is given by

0

Bi ¼ e

hdp ks

785

ð11Þ

The value of modified Biot number for the given system is 1.55, which is reasonably close to 1 and particles can be considered as thermally thin (uniform temperature distribution inside the particle). Since the ratio of time required for thermal wave to propagate inside the centre of individual particle to the time required to reach at the bottom of bed is 0.075 (Table A1, Appendix A), which is very small and hence the overall performance will not affect significantly and particles can be treated as thermally thin (uniform temperature distribution inside the particle). The main assumptions involved in this model are: (1) (2) (3) (4) (5)

The system is one-dimensional. Gas is described as an ideal gas. Fuel particles used are of same size and shape. Bed voidage is constant and remains so. Gas-phase species included in the model are CO, CO2, H2O, O2, H2, CH4, higher hydrocarbons, tar and N2. (6) Since the bed size is small, gaseous combustion reactions are controlled by kinetics without any mixing limitations. (7) Particles are thermally thin (uniform temperature distribution inside the particle). Mathematical description of sub-processes occurring during the solid fuel combustion is as follows: 3.1. Moisture evaporation Biomass usually contains moisture either as liquid water stored in the fuel particle pores due to capillary forces or as water bound to the cellulosic structure of the biomass by intra-molecular forces. In some cases, the process is assumed to take place instantaneously [5] or to be a diffusion limited process [6–8]. The later treatment together with a Clausius–Clapeyron expression for vapor pressure at the solid surface is used for describing the rate of moisture release from the solids [9].

H2 OðlÞ ! H2 OðgÞ revp ¼ kd ap M w ðC w;s  C w;g Þ

ð12Þ ð12aÞ

3.2. Pyrolysis Biomass is characterized by a higher content of volatile matter. The volatiles are composed mainly of CO, CO2, CH4, H2, higher hydrocarbons (CxHy), tar (CHmOn) and other trace compounds. Wood (Biomass) pyrolysis may be simply described as a one-step global reaction:

Wood ! Char þ Volatiles

ð13Þ

Volatiles ¼ a  gas þ b  tar gas ¼ c1 CO þ c2 CO2 þ c3 Cx Hy þ c4 H2 þ c1 CH4 The rate of formation of volatiles is given by following expression [10]:

rdev ¼ kdev qv

ð14Þ

3.3. Combustion of the volatiles Combustion of volatiles, particularly tar, is an important process in biomass combustion. Tar is a complex mixture of condensable hydrocarbons. The amount and composition of tar that form from biomass pyrolysis depend on: type and properties of biomass and pyrolysis conditions. For simplification, tar is modelled as hydro-

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carbons CH1.84O0.96, with molecular weight equal to 95 [10]. The tar is oxidized to produce CO and H2O:

CH1:84 O0:96 þ 0:48O2 ! CO þ 0:92H2 O

ð15Þ

The kinetic rate for tar oxidation is obtained from Bryden and Ragland [11] as;

r tar ¼ 2:9  105 T sg expð9650=T sg ÞC 0:5 CH1:84 O0:96 CO2

ð16Þ

The kinetic rates for H2, CH4, CxHy (non-methane hydrocarbons for e.g. C2H6) are as follows:

2H2 þ O2 ! 2H2 O r H2 ¼ 51:8  T

3=2

ð17Þ

expð3420=T g Þ C H1:52 CO2

CH4 þ 1:5O2 ! CO þ 2H2 O

ð18Þ ð19Þ

0:8 r CH4 ¼ 1:6  1010 expð  24157=T g ÞC 0:7 CH4 C O2

ð20Þ

C2 H6 þ 2:5O2 ! 2CO þ 3H2 O

ð21Þ

r C2 H6 ¼ 2:7  108  T 0:5 g expð  2013=T g Þ C C2 H6 C O2

ð22Þ

3.4. Char oxidation The char forms, as the volatiles escape from the biomass particles. The primary products of char combustion are CO and CO2. The char oxidation reaction is:

Cþ

    1 2 O2 ! 2 1   1 CO2 CO þ

1

U

U

U

ð23Þ

where U is the stoichiometric ratio for char combustion, U = (1 + 1/ rc)/(1/2 + 1/rc), rc is the ratio of CO–CO2 formation rate; which can be estimated by [12]:

rc ¼

CO ¼ 12 expð3300=T s Þ CO2

ð24Þ

The char combustion rate is controlled by mixed gas film diffusion and chemical reaction. The film diffusion is taken into account with a correlation for gas flow through packed beds in terms of the Colburn J factor [13]:

0:765

eJ ¼

Re0:82 p

þ

0:365

! ð25Þ

Re0:368 p

where e is the bed voidage, Rep is the particle Reynolds number, Rep = qgudp/lg, qg is the gas density calculated at gas phase temperature at a particular location in the bed (kg/m3), u is the superficial gas velocity (m/s), dp is the diameter of wood particle (m), lg is the gas viscosity (Pa s). The J factor is defined as J = Sh/(Sc1/3Rep), Sh is the Sherwood number, Sh = kddp/D, kd is the mass transfer coefficient (m/s), D is the molecular diffusion coefficient of O2 in air (m2/s) and Sc is the Schmidt number, Sc = lg(qgD). Char combustion rate under diffusion controlled reaction is then written as;

r char;diff ¼ kd ap

ðpo2 ;g  po2 ;s Þ UMc ; RT

ð26Þ

Rate of char combustion under chemical reaction control regime is given by the following equation [14];

r char;k ¼ kc qchar po2 ;s ;

kc ¼ 8620 expð15900=T s Þ

ð27Þ

k0 ¼ q

1

char RTs

1

UM c ap kd

þ k1c

For a stationary bed, mass and energy balance equations for gas and solid phases can be written as follows: The continuity equations for the gas phase.

e

@ qg @ qg u ¼ rg þe @x @t

ð28Þ ð29Þ

ð30Þ

where t is the time (s), x is the coordinate along the bed height (m), x = 0 at the bottom of the bed, as shown in Fig. 1b, e is the bed voidage. The source term rg is the conversion rate from solid to gas due to moisture evaporation (Eq. (12a)), devolatilization (Eq. (14)), combustion of volatiles (Eqs. (16), (18), (20), and (22)) and char combustion (Eq. (28)). For the given stove geometry axial diffusion is very small and can be neglected. Then the equivalent equation for individual gas species is:

e

@ðqg Y i Þ @ðqg Y i uÞ þ ¼ er i @t @x

ð31Þ

where i represents the individual species (i = CO, CO2, H2, CH4, C2H6, H2O, O2 and tar (gas)). Yi is the mass fraction of the species. The source term ri represents the rate of mass production of individual species during moisture evaporation (Eq. (12a)), devolatilization (Eq. (14)), combustion of volatiles (Eqs. (16), (18), (20), and (22)) and char combustion (Eq. (28)). The conservation equation for the stationary solid phase is:

@ qs ¼ r g @t

ð32Þ

Solid species balance can be written as

qs

@Y j ¼ rj @t

ð33Þ

where qs is the bulk density of the solid phase (kg/m3), j represents individual solid phase species (volatile matter, char, and ash), Yj is the mass fraction of individual species. The energy equation for the solid phase (which is treated as a bed with fixed voidage) is:

  @ðqs hs Þ @ @T s þ hc ap ðT g  T s Þ þ Q H2 O þ Q s þ Q ls ¼ keff @t @x @x

ð34Þ

where hs is the solid phase enthalpy, hs = cp,s(Ts  T0), cp,s is the specific heat of solid phase, keff is the effective thermal conductivity of the solid phase (W/m K), hc is the gas–solid heat transfer coefficient (W/m2 K). The second term on the right hand side of Eq. (34) represents convective heat transfer between the gas and the solid phase. The source term Q H2 O is the enthalpy loss due to moisture evaporation. Q H2 O ¼ revp  k. revp is the rate of moisture evaporation given by Eq. (12a) and k is the latent heat of vaporization of water. Qs is the heat generation due to char combustion (W/m3). Q s ¼ rchar  DHchar . rchar is the rate of char combustion reaction given by Eq. (28). DHchar is the heat of char combustion reaction. Heat produced by the char combustion reaction is assumed to first get delivered to the solid phase. Qls is the enthalpy loss, along the bed wall. Qls = (1  e)(k/L) (Ts  T0)/Dl, k is the heat conductivity coefficient of bed wall, L is the length/height (bed dimension), T0 is the ambient temperature, and Dl is the wall thickness. The effective thermal conductivity can be expressed as [15].

keff ¼ keff;0 þ 0:5kg PrRep =e

Overall char combustion rate, thus be written as

r char ¼ k0 qchar po2 ;g

3.5. Governing equations for the gas and solid phases

ð35Þ

where keff,0 is the thermal conductivity for no fluid flow, kg is the thermal conductivity of gas phase, Pr is the Prandtl number, Pr = lgcp,g/kg and Rep is the particle Reynolds number defined in Eq. (25).

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For the given stove geometry thermal diffusion is very small and can be neglected. Then the energy equation for the gas phase is:

Tg ¼ Ts ¼ T0 qs;i ¼ yi qs;0 ; i = wood, moisture and char. t > 5 s and x ¼ H (At the top of fuel bed)

@ðq hg Þ @ ðuqg hg Þ ¼ hc ap ðT s  T g Þ þ Q g þ Q lg e g þ @t @x

dqg;i dz dqs;i dz

ð36Þ

where hg is the gas phase enthalpy (J/kg), hg = cp,g(Tg  T0), cp,g is the specific heat of gas phase (J/kg K). hc is the gas–solid heat transfer coefficient (W/m2 K). The second term on the right hand side of Eq. (36) represents convective heat transfer between the gas and the solid phase. The source term Qg is the heat gain of the gas phase P due to combustion. Qg = i ri(DHi). ri is the rate of ith gas phase reaction (Eqs. (16), (18), (20), and (22)). DHi is the heat of reaction of ith reaction. Qlg is the enthalpy loss, along the bed wall. Qlg = e (k/L) (Tg  T0)/Dl, k is the heat conductivity coefficient of bed wall, L is the length/height (bed dimension), T0 is the ambient temperature, and Dl is the wall thickness.

¼

dT g dz

¼ 0;

i ¼ CO; CO2 ; CH4 ; C2 H6 ; C1:84 H0:96 O;H2 and H2 O

s ¼ dT ¼ 0; i = wood, moisture and char dz

The solution scheme for Eqs. (30)–(36) is discussed further in Section 4.2. 4. Results and discussion In Harsha domestic stove 1–1.5 kg of wood can be burnt efficiently in 1 h. Detailed theoretical study of this stove including steady state as well as unsteady state models are as follows. 4.1. Steady state models

3.6. Initial and boundary conditions Initial conditions are as follows: the burning process is initiated at the top of the fuel bed. Therefore, at the top of the bed surface, both the gas and solid phase temperatures are set as 1100 K (ignition source temperature, which is actually the measured approximate temperature required to observe and obtain sustained combustion) and these temperatures are maintained for a period of 5 s (assuming flame front travels with maximum possible velocity which is about 0.038 mm/s (calculated using model for propagation of ignition front (Eq. (7))), after 5 s, flame front has propagated a distance of 0.19 mm, that means ignition front has propagated a distance of 1.3% in all particles (15 mm cubes) in the upper layer, which is sufficient to propagate ignition front in the downward direction). Temperature at all other locations (near the grate and in the fuel bed) is 300 K. The mass fractions of O2 and N2 are 23.3% and 76.7%, respectively. 3.6.1. Initial conditions t = 0 and x = 0 (At the bottom of fuel bed) qg;i ¼ 0; i ¼ CO;CO2 ; CH4 ; C2 H6 ; C1:84 H0:96 O;H2 and H2 O qg;i ¼ yi qg;0 ; i ¼ O2 and N2 Tg ¼ Ts ¼ T0 qs;i ¼ yi qs;0 ; i ¼ wood; moisture and char t ¼ 0 and x ¼ H ðAt the top of fuel bedÞ qg;i ¼ 0; i ¼ CO; CO2 ; CH4 ; C2 H6 ; C1:84 H0:96 O;H2 and H2 O qg;i ¼ yi qg;0 ; i ¼ O2 and N2 T g ¼ T s ¼ 1100 K qs;i ¼ yi qs;0 ; i ¼ wood; moisture and char

3.6.2. Boundary conditions For the gas phase, air temperature and velocity at the bottom of the bed are given by the operating conditions. At the top surface of the fuel bed, gradients in the gaseous concentration and temperature beyond the time of 5 s are assumed to be zero. For the solid phase, the temperature gradient beyond the time 5 s is set as zero at the bed surface, while temperature at the bottom (the grate temperature) is assumed to be equal to the inlet air temperature (ambient) due to intensive heat transfer between the entering air and the solid phases at the point of entry. t>5s

and

x ¼ 0 (At the bottom of fuel bed)

qg;i ¼ 0; i ¼ CO;CO2 ; CH4 ; C2 H6 ; C1:84 H0:96 O; H2 and H2 O qg;i ¼ yi qg;0 ; i ¼ O2 and N2

4.1.1. Effective maximum flame temperature and excess air Effective maximum flame temperature is calculated by solving Eqs. (2) and (B.1.4) in iterations (w = 0). In the present case, when 1 kg of wood with the elemental composition C = 52.9%; H2 = 6.3%, N2 = 0.1%, O2 = 39.7% and Ash 1% [16] is burnt completely, effective maximum flame temperature is 1622 °C (Appendix B) and theoretical air requirement is about 4.87 m3/kg fuel (0.0014 m3/s over a period of 1 h). Average flame temperature measured in Harsha domestic stove is about 860 °C. Effective maximum flame temperature is available only when the incoming air is equal to theoretical oxygen (air) requirement (w = 0). If the incoming oxygen (air) in the stove is less than the theoretical oxygen (air) requirement, incomplete combustion of wood occurs, with the release of CO and unburnt hydrocarbons in the flue gases, and the heat released is less compared to complete wood combustion under theoretical air requirement. If the incoming oxygen (air) in the stove is more than the theoretical oxygen (air) requirement, excess air carries the heat from the flame. As a result, flame temperatures in actual combustion are less compared to theoretical combustion (oxidation) based effective maximum flame temperatures. Considering the pollution angle, combustion under excess air is preferred as it will ensure no CO at an expense of some loss of thermal efficiency. In Harsha domestic stove air is sucked inside, from the bottom grate as well as perforated side walls. To get the actual flame temperature of 860 °C, calculated air requirement is about 12.77 m3/kg fuel (0.0035 m3/s for a period of 1 h) i.e. 162% of excess air (over and above the theoretical air requirement of 4.87 m3/kg fuel (0.0014 m3/s over a period of 1 h)) is being sucked inside the stove. Though in calculations it is assumed that all the heat lost from the flame is due to excess air, in reality along with this there is a heat loss in radiation cooling, heat loss in evaporation of moisture and radiation losses from the surface of combustor resulting into temperature much lower than the effective maximum flame temperature, thus it is quite likely that the excess air may be overestimated by this method. The solid fuel boilers are known to use 30–50% excess air and hence this estimate appears reasonable. Flue gas composition (mass percent) under adiabatic condition is CO2 – 17.82%, H2O – 12.73%, and N2 – 69.45% and during actual condition (with 162% excess air) is CO2 – 7.35%, H2O – 5.25%, O2 – 12.34% and N2 – 75.06%. Inlet air velocities measured at the inlet port of chamber (Fig. 1b) are found to be 0.05 to 0.25 m/s. Assuming inlet air is uniformly distributed across the cross sectional (c/s) area and air resistance is negligible, a maximum of 35% (stove grate c/s area to chamber c/s area) of sucked air is likely to go through packed bed of fuel and would be actually used for combustion. The air requirement (0.0035 m3/s) calculated based on the measured temperature, matches reasonably with the

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Suction created by flue gases (N/m2)

1.4

Flame temperature (600°C) Flame temperature (800°C)

1.2 1 0.8 0.6 0.4 0.2 0 0.1

0.08

0.06

Bed height (m)

Ignition velocity (mm/s)

Fig. 2. Effect of bed height and flame temperature on suction created by flue gases.

0.045 0.04 0.035 0.03 0.025 0.02 0.015 0.01 0.005 0

10% moisture 20% moisture 30% moisture

0

0.0005

0.001 0.0015 0.002 Air flow rate (m³/s)

0.0025

0.003

Fig. 3. Effect of air flow rate on the ignition velocity at different moisture content [3].

air flow of 0.0028 m3/s measured using the anemometer at air inlet.

4.1.2. Suction created by hot flue gases inside the stove Suction created by hot flue gases and superficial air velocity is calculated by solving Eqs. (4)–(6) in iterations, with some initial value of superficial velocity. In the present case when 1 kg of wood particles (dp = 0.015 m cubes and qp = 812.4 kg/m3) are burnt in Harsha domestic stove (chamber dimensions: 0.2  0.2  0.105 m), with a fuel bed height of 0.1 m, suction (draught) developed is about 1.275 N/m2 and the corresponding superficial air

velocity is 0.1385 m/s. The superficial velocity calculated using this model (0.1385 m/s) matches reasonably with the superficial air velocity 0.15 m/s, measured with the anemometer, at the inlet port (Fig. 1b), assuming inlet air is uniformly distributed across the c/s of chamber and 35% (stove grate c/s area to entire chamber c/s area) of the sucked air is likely go through the bed. The superficial velocity calculated using this model of 0.1385 m/s, deviate somewhat from the superficial air velocity 0.0875 m/s, estimated from the effective maximum flame temperature model and with 162% of excess air. Fig. 2 shows the effect of bed height and flame temperature on suction (pressure gradient) developed by flue gases inside the stove. It is found that the suction developed inside the stove decreases with a decrease in the bed height, keeping other conditions same, such as amount of fuel and c/s area of the stove. Since the amount of fuel and stove c/s area are same, decrease in the bed height results into an increase in the bulk density and pressure drop across the fuel bed. As a result, suction developed inside the stove decrease. It can be also seen from the Fig. 2 that, with an increase in the flame temperature, suction developed inside the stove increases, at all the bed heights as expected.

4.1.3. Propagation of ignition front inside the stove As discussed in Section 2.3, ignition front velocity in the stove is calculated using Eq. (7). Fig. 3 shows the effect of air flow rate on the ignition front velocity with different wood moisture content. With an increase in the air flow rate, oxygen available increases which results into higher ignition velocity. When the air flow rate increase above the optimum value, excess air (nitrogen) takes away the heat from the flame in the upward direction and as a result ignition front velocity decreases. With an increase in the moisture content, heat required to evaporate the moisture from the fuel wood increases, thus the ignition front velocity (moving in the downward direction) and the fuel burn rate decreases for the same quantum of air suction. In the present case when 1 kg of wood particles (fuel bed density qs = 250 kg/m3 and bed height 0.1 m) with 10% moisture content are burnt in Harsha domestic stove (chamber dimensions: 0.2  0.2  0.105 m), maximum ignition front velocity obtained is about 0.038 mm/s. Air flow rate and fuel burn rate obtained at maximum ignition front velocity are 0.0014 m3/s and 0.38 g/s respectively. Air flow rate (0.0014 m3/s) at which maximum ignition front velocity is obtained matches exactly with the theoretical air requirement calculated from the effective maximum flame temperature model (0.0014 m3/s) and confirms the validity of this model. As the model developed by Saastamoinen et al. [3] is used in the current study by adjusting the parameters for a given system (packed bed of mango wood particles), though there is a change in ignition front velocity values, but the overall

Table 1 Effect of c/s area (L  B), fuel bed height and bulk density on the fuel burn rate.

(3)

Bed height (m) (4)

Fuel amount (kg) (5)

Bulk density, qb (kg/m3) (6) = (5)/((1)  (2)  (4))

Ignition front velocity (maximum) (mm/s) (7)

Burn rate (g/s) (8)

Power delivery rate (kW) (9)

0.105 0.105 0.105

0.1 0.1 0.1

0.25 1 4

250 250 250

0.0383 0.0383 0.0383

0.0957 0.383 1.532

1.68 6.7331 26.9326

Effect of fuel bed height 0.1 0.1 0.105 0.1 0.1 0.205 0.1 0.1 0.305

0.1 0.2 0.3

0.25 0.5 0.75

250 250 250

0.0383 0.0383 0.0383

0.0957 0.0957 0.0957

1.6824 1.6824 1.6824

Effect of bulk density 0.2 0.2 0.305 0.2 0.2 0.205

0.3 0.2

1 1

83.33 125

0.1148 0.0766

0.3847 0.383

6.7630 6.7331

L (m)

B (m)

H (m)

(1)

(2)

Effect of c/s area 0.1 0.1 0.2 0.2 0.4 0.4

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Governing Eqs. (30)–(36) in unsteady state heterogeneous mathematical model are solved by finite difference implicit scheme utilizing Tri-Diagonal Matrix Algorithm. Values of different parameters and computational conditions employed in this study are given in Tables B.2.1 and B.2.2 respectively (Appendix B). Detail computer code is written in Matlab version 7.0. Fig. 4a shows the temperature profiles in the bed (mango wood particles of 15 mm cubicle size) at locations of 60 mm and 10 mm above the grate, corresponding mass loss history of fuel bed is as shown in Fig. 4b. Model and the present experimental data show a good agreement in terms of peak temperatures and time required to attain the same, inspite of the actual variation in the individual particle sizes and the variation in the bulk density due to random packing of these particles in the packed fuel bed also justifying the initial assumption of treating fuel bed as a lumped parameter system. As the fuel bed is ignited at the top (bed height 100 mm), temperatures at location 60 mm from the base (grate) increases first, followed by the location which is 10 mm from the base, and starts decreasing when all the fuel is burnt. It can be observed that the calculated values correspond fairly well with the trends in the measured temperatures. Both, the experimental and model results indicate that, as soon as the temperature at a particular location inside the fuel bed reaches the ignition temperatures 650 K (377 °C), volatiles are released, combustion of these volatiles release further heat and the temperature at that location sharply increases. Model shows a good agreement with the experimental data over the entire burning period. Even when all the fuel is burnt, it takes time for the stove temperatures to reach ambient condition which is not considered in this model as it is not important during the cooking operation, but may be utilized to keep the cooked food hot. 4.2.1. Prediction of ignition flux The ignition front velocity can be derived from the experimental data (Fig. 4a) from the distance between the thermocouples and the time for the ignition front to travel between the two adjacent thermocouples (separated by a distance of 50 mm). Then, the ignition rate (kg/m2 s) can be obtained by the ignition front velocity multiplied by the initial bulk density of wood (250 kg/m3). In this text, the ignition front is assumed to be located where the thermocouple temperature reaches 650 K (ignition temperature for

Temperature (°C)

800 700 600 500 400 300 200 100 0

Expt (10 mm) Expt. (60 mm) Model (60 mm) Model (10 mm)

b

1.2

Fuel mass (kg)

0

0.8

500

1000

1500 Time (s)

2000

2500

Model Expt.

1

0.6 0.4 0.2 0 0

c

500

1000

1500

2000 2500 Time (s)

3000

3500

1.2 1 Fuel mass Power delivery

0.8 0.6 0.4 0.2 0 0

500

1000

1500

2000

2500

3000

3500

4000

16 14 12 10 8 6 4 2 0 4000

Power delivery (kW)

4.2. Unsteady state combustion

a 900

Fuel mass (kg)

profile and the trend indeed remains the same with their study with spruce wood particles. Table 1 shows the effect of c/s area of stove, fuel bed height and bulk density on the fuel burn rate. With increasing the c/s area, keeping other conditions same, such as the bulk fuel density and bed height by varying the amount of fuel, ignition front velocity is the same but the fuel burn rate increases. Though, the ignition front velocity is same, since the amount of fuel increases, increasing c/s area results into an increase in the overall fuel burn rate and the net energy delivery. By increasing the fuel bed height, keeping all other conditions same such as bulk density and c/s area by varying the amount of fuel, there is no effect on the ignition front velocity and the fuel burn rate, however the duration of combustion increases. With an increase in the bulk density, ignition velocity decreases, but there is little effect on the fuel burn rate, as the increased bed mass per unit volume compensates for the decrease in the ignition front velocity. Thus, critical parameters affecting the ignition front velocity are the fuel moisture content and the bulk density (decided by the fuel size and shape).

Time (s) Fig. 4. (a) Temperature history at different locations inside the fuel bed, (b) mass loss history in the fuel bed and (c) fuel mass loss history and instantaneous power delivery rate from Harsha domestic stove.

wood). Predicted ignition flux (0.022 kg/m2 s) matches fairly well with the experimental value of 0.023 kg/m2 s, and is equivalent to the actual burning rate obtained inside the stove. 4.2.2. Prediction of power delivery Power delivery from the stove can be estimated from the ignition mass flux as follows:

Power delivery ¼ ignition mass flux  c=s area  calorific value of fuel

ð37Þ

Power delivery calculated from the ignition mass flux obtained from the unsteady state mathematical model (15.5 kW, estimated from the model temp. profiles in Fig. 4a) matches well with the power delivery estimated from the ignition mass flux obtained during the experimentation (16.27 kW, estimated from the experimental temp. profiles in Fig. 4a). Fig. 4c shows the fuel mass loss history and instantaneous power delivery (estimated as the product of instantaneous fuel burn rate and calorific value of the fuel) from the Harsha domestic stove. At the start up, due to small temperature difference between the flue gases inside the stove and air outside the stove, air suction rate in the stove is low, which results into lower burn (combustion) rate and result into low power delivery. With the progression of time, increase in temperature inside the stove, increases the air suction rate which results into higher burn rate and high power delivery. At the end, excess air carries the heat from flame in the upward direction and reduces the flame propagation rate (ignition front velocity) in the downward direc-

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tion, resulting into lower ignition velocities and low power delivery (fuel burn rate). Ash formed during the wood combustion fills the space between the unburnt fuel particles reducing the voidage and increases the bulk density, which is also responsible for the low power delivery at the end. Since wood contains small amount of ash, and formed ash is not able to retain on the corrugated grate (plates inclined at 45°) of Harsha domestic stove, contribution of ash in lowering the power delivery rate is almost negligible. Average power delivery of the stove is 5.6 kW. Maximum instantaneous power delivery obtained is about 14.1 kW giving a turndown ratio of about 3.

Appendix A Ignition. front velocity Ignition front velocity is the speed with which thermal wave of 650 K (equivalent ignition temperature for wood) is propagating in the fuel bed, and can be given by following equation. Ignition front velocity ¼

Distance betn two locations Time required by thermal wave of 650 K to travel the distance

ðA1Þ 4.2.3. Model limitations In the present model, solid fuel combustion inside the stove is assumed in the form of a packed bed of solid fuel and air quantity equivalent to that of suction created by hot flue gases is flowing from grate to packed bed in the upward direction, but in reality air is entering in the stove from grate as well as the perforated side walls. Air entering from the sidewall results into higher burn rates at the wall compared to the centre of fuel bed, but in the present model uniform burn rate over the entire c/s has been assumed. When ignition front moves from location of 60–10 mm from the bottom, air entering from side holes at 60 mm is cooling the flame to some extent as shown in Fig. 4a. The model is not able to predict this behavior, as the air quantity entering through the side walls, has not been accounted for in the present model.

Time required for ignition front to reach at the centre of individual particle and at the bottom of bed is given in Table A1. Since the ratio of time required for ignition front to propagate at the centre of individual particle to time required to propagate at the bottom of bed is very small (0.075), particles can be considered as thermally thin and eliminate the need for separate solution for temperature profiles inside the particles. Appendix B B.1. Calculations of effective maximum flame temperature Theoretical air required for burning 1 kg of wood (elemental composition C = 52.9%; H2 = 6.3%, N2 = 0.1%, O2 = 39.7% and Ash 1% [16]) can be calculated as

Theoretical O2 requirement for complete combustion 5. Conclusions In this paper, different steady states as well as unsteady state models have been developed for solid fuel combustion for the Harsha domestic stove. When wood is burnt completely, adiabatic flame temperature predicted is 1622 °C with stoichiometric quantity of air and when 162% of excess air is being sucked in, the actual flame temperature drops to 860 °C. Suction created by flue gases inside the stove, increases with an increase in the flame temperature but decreases with a decrease in bed height, if fuel amount and the stove dimensions remain the same. In the Harsha domestic stove homogeneous and heterogeneous combustion occurs simultaneously, compared to sequential homogeneous and heterogeneous combustion in packed bed wood combustion with air fed only from the bottom. Models used earlier for the prediction of ignition front velocity (volatile release rate) in a tall packed bed wood combustion are modified and used to predict propagation of combustion front (overall fuel burn rate) in Harsha domestic stove, which is further used to calculate fuel burn and the power delivery rate. The model predicts the effect of the principal factors, such as the flow rate of air, moisture content, and the density of fuel on the ignition front velocity and the fuel burn rate. A one-dimensional mathematical model for the transient heterogeneous combustion has been developed for wood combustion in a domestic stove. The processes included in the model comprise: moisture evaporation, wood pyrolysis, homogeneous combustion of volatiles followed by the heterogeneous reaction (combustion) of char. The model provides fuel mass loss rate, temperature profiles at different locations inside the stove and ignition flux which is equivalent to the burning rate. The steady state model for the calculation of air suction created inside the stove can be combined further with unsteady state mathematical model to get the clearer picture of velocity profiles and temperature profiles, along the vertical height of the fuel bed.

¼ O2 required for complete combustion of C to CO2 þ O2 required for complete combustion of H to H2 O

ðB:1:1Þ

 O2 present in the solid fuel Moles of individual element and oxygen required for complete combustion is given in Tables B.1.1 and B.1.2. Theoretical air requirement = 0.218 kg mol (4.875 m3) = 1.354  103 m3/s (assuming 1 kg wood burn in 1 h). The total heat liberated by complete combustion of wood (Qc) can be calculated as

Q c ¼ Mass of wood  Net calorific value of fuelðNCVÞ

ðB:1:2Þ

Table A1 Calculation of time required for ignition front to reach at the centre of individual particle and at the bottom of packed bed. Ignition front velocity (m/s) Time to reach centre of individual particle (s) Time to reach bottom of bed (s) Ratio of time required for ignition front to propagate at the centre of individual particle to time required to propagate at the bottom of bed

0.000038 197.37 2631.58 0.075

Table B.1.1. Theoretical oxygen (O2) requirement for complete combustion. Constituent

kg

MW

kg mol

Theoretical O2 requirement

Carbon Hydrogen Nitrogen Oxygen Ash Total

0.529 0.063 0.001 0.397 0.01 1.0

12 2 28 32 – –

0.044 0.031 3.15  105 0.014 – –

0.044 0.015 – 0.014 0.0 0.045

Theoretical O2 requirement for complete combustion = 0.045 kg mol.

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cp ¼ a þ bT þ cT 2 þ dT

Table B.1.2. Heat capacity equation constants for gas species [17]. Compound

a

b  103

c  106

d  109

CO2 H2O N2 O2 CO CH4

21.3655 32.4921 29.5909 26.0257 29.0277 19.2464

64.2841 0.0796 5.141 11.7551 2.1865 52.1135

41.056 13.2107 13.1829 2.3426 11.6437 11.973

9.7999 4.5474 4.968 0.05623 4.7065 11.3173

Table B.2.1. Thermophysical properties of gas and solid [9]. Thermal conductivity of gas (W/m K) Dynamic viscosity (pa s) Specific heat capacity for gas (J/mol K) Thermal conductivity for air (W/m K) Specific heat capacity for wood (J/mol K)

kg = 4.8  104 Tg0.717 lg = 1.98  105(Tg/300)2/3 cp,g(Tg) = (0.99 + 1.22  104Tg  5.68  103Tg2)  103 kair(Tg) = 5.66  105Tg + 1.1  102 cp,s = 977.75ln(Ts)  4144.4

3

ðB:1:4Þ

where cp represents the specific heat of individual species (J/ kg mol K or J/kg K), a, b, c, and d are the coefficients of equation for specific heat (Table B.1.2), and T is the temperature (K). Change in flame temperature, when third order polynomial expressions is used to correlate Qc (Heat liberated by complete combustion) in Eq. (2), it was found that an accuracy of 1% is obtained hence third order polynomial expression has been used in further calculation. Higher order contributes less than 1% improvements. Solving, Eqs. (2) and (B.1.4) in iterations, gives the effective maximum flame temperature as 1895 K (1622 °C). B.2. Thermophysical properties of gas and solid and computational conditions employed in the unsteady state model The results of unsteady state heterogeneous combustion mathematical model using the thermochemical properties in Table B.2.1 and computational conditions in Table B.2.2 are given in Fig. 4a and 4b. References

Table B.2.2. Computational conditions. Bed height (m) Bed width (m) Cubicle particle dimension, dp (m) Particle density, qp (kg/m3) Bulk density of the bed, qs (kg/m3) Bed voidage () Inlet air flow rate (kg/m2 s) Space step (mm) Time step (s)

0.1 0.2 0.015 812.14 250 0.69 0.1 0.67 1  103

Net calorific value (NCV) of wood is calculates as follows:

NCV ¼ Gross calorific valueðGCVÞ  Latent heat loss in moisture vaporization

ðB:1:3Þ

GCV of wood is considered as 18,810 kJ [16] and latent heat of moisture vaporization at 25 °C is 2441 kJ/kg. NCV = 17425.95 kJ Total heat liberated by complete combustion of wood Qc = 1  NCV = 17425.95 kJ A steady state energy balance equation for combustion of fuel (wood) can be given by Eq. (2). Specific heat of individual gas species in Eq. (2) is a function of temperature and can be given by following equation:

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