**FLUID FLOW AND HEAT TRANSFER **

**IN A **

**SINGLE-PAN WOOD STOVE **

RAJESH GUPTA

Department of Mechanical Engineering, Maulana Azad National Institute of Technology, Bhopal Bhopal, Madhya Pradesh - 462007 India

Dr. N.D. MITTAL

Department of Applied Mechanics, Maulana.Azad National Institute of Technology, Bhopal Bhopal, Madhya Pradesh - 462007 India

**Abstract : **

This paper presents simulation of buoyancy induced flow in an analogue of a single pan wood stove. In the present analysis, flow through fuel bed is modeled as flow through porous medium and heat release in the bulk fluid due to combustion is represented by uniform generation of heat. The heat transfer and fluid flow model is then used to conduct a parametric study of the effects of various geometric and operating parameters namely spacing between the stove and pan, inlet radius, height, diffuser radius, outer radius, porosity of fuel bed and power. The results are discussed with relevance to stove design and performance. In general, the influence of these parameters is observed to be more pronounced on heat transfer to pan and secondary mass flow rate than on primary flow rate. However, the effect of fuel bed porosity on both primary and secondary flow rates as well as heat transfer is significant.

**Keywords: **woodstove, buoyancy induced flow, heat transfer and fluid flow modeling.

**Nomenclature **

Da Darcy number

Gr Grashof number

Pr Prandtl number

Qgen Volumetric heat generation

Vr Radial velocity

Vz Axial velocity

Greek Symbols

Non-dimensional temperature

Porosity of fuel bed

Permeability of fuel bed

Dynamic viscosity

Kinematic viscosity

Density

Subscripts & Superscripts

^ Non-dimensional quantity

Vol. 2(9), 2010, 4312-4324

**1.** **INTRODUCTION **

The research on biomass stove has covered a lot of ground ever since wood burning stove group (WSG) [[1]] was established in late 1980s. The sole objective of WSG was to promote research and development in the field of cook stove to obtain better thermal efficiency and lower emissions. In early days, the cook stove research was primarily focused on qualitative understanding of thermal and physical processes in a cook stove. A number of investigations were devoted to analyze flames and their interactions with the parent stove geometry. Clearly, the objective was to optimize stove geometry so that the performance of the stove could be improved. The outcome of numerous such studies helped building a data base regarding various issues related to design, development, performance and construction of cook stoves. Some of the significant findings were about the optimum gap between the stove and the pan, optimum diameter to height ratio for combustion chamber, role of primary and secondary air inlets, chimney, grate and material of construction etc. A detailed review of investigations can be found in Kohli and Ravi [[2]]. Mukunda et.al [[3]] and Bhandari et.al.[[4]] developed single pan woodstoves which were designed to achieve better combustion. These design modifications essentially included improvement of flow passages to achieve enhanced momentum, permitting preheating of air for heat recovery. They reported thermal efficiencies up to 40 % against respective power ratings of their stoves. Date[[5]] presented an imple, analytical, steady state model for the single pan wood stove. The model was used to predict effects of geometric and operating parameters such as power, pan diameter, wood size and swirl. The prediction of the model compared well with the experimental results of Bhandari et. al. [[4]] except in case of power. It is reported that grate height, primary port and feed port diameter had very little effect on the efficiency as compared to the stove-vessel gap par At this stage, it was realized that there was a need to seek a fresh approach towards the cook stove research. It was perhaps time to avoid excessive experimentation for a wide range of geometric parameters in order to arrive at some meaningful conclusion regarding design and performance of cook stove in general regardless of type of stove or type of fuel being used. Therefore, search for a simple but an adequate model, which can correlate geometric parameters with the system performance parameters namely thermal efficiency, power etc., was in order. The computational fluid dynamics (CFD) models which were known to be proven scientific tool and widely used to replace time consuming and expensive experimental work was proposed by Kohli [[15]]. The CFD simulation of cook stove would subsequently provide necessary input such as mass flow rates, heat transfer to pan, thermal efficiency to the model to be developed eventually. This model would be much like the other models that had already been developed by contemporary researchers based on a simple mathematical relationship between the various performance parameters of stoves. The proposed model was applied to investigate buoyancy-induced flow in a single pan sawdust stove.

The model consisted of equations of continuity, momentum and energy and were solved numerically. In this model, pyrolysis and combustion were not included and actual combustion was modeled as a uniform heat release throughout the domain through a heat source in the energy equation. The effects of those parameters that define the stove geometry on mass flow rate and heat dissipation to vessel were analyzed. Further, flow visualization was employed to study flow patterns in the gap between stove and vessel. The flow patterns were found sensitive to the gap with regard to the flow separation in the diffuser region.

The present investigation is an attempt to extend the CFD simulation to explore wood stove where fluid flow, heat transfer, pyrolysis and combustion are taking place simultaneously in the fuel bed unlike the sawdust stove. A single pan wood stove called Janta Stove [[6]] developed by Central Glass and Ceramic Research Institute of India (CGCRI) is chosen for the analysis. The salient feature of this stove is its diffuser shaped combustion chamber made of ceramic. It is provided with primary and secondary air inlets separately to feed the air required for combustion. The primary air is fed through the three air inlets of equal area located on the outer metallic shell below the grate. Similarly, ten secondary air inlets are provided at the outer shell at slightly higher elevation than the primary air inlets. Air entering the stove through secondary air inlets, then, makes its way to the combustion chamber after passing through a large number of capillary like passages provided in the ceramic body to preheat the air before entering the combustion chamber.

### 2.

**MATHEMATICAL FORMULATION**

feed port are also replaced by a peripheral slot around the stove body having the same area as that of all the secondary air ports along with area of the fuel feed port put together. It is expected that this minor alteration of stove geometry would not alter the flow characteristics rustically and that the comparison of the predictions of our analysis with respect to the experimental behavior of original stove would still be valid. The two-dimensional, axisymmetric model of the stove is shown in Figure 1.

Ceramic Liner Grate

Secondary Air

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Figure 1. Axi-symmetric Analogue of a wood stove

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3 r2r0 r1

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### H Secondary air slot

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p### Grate

Figure 2. Computational domain

Vol. 2(9), 2010, 4312-4324
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_{gen}Table 1: Definitions of various non-dimensional parameters

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The variation of specific heat in terms of temperature is expressed by a cubic polynomial of Gebhart et. al. [[10]] as: 9987 . 0 ˆ 0691 . 0 ˆ 3408 . 0 ˆ 1291 . 0

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**BOUNDARY CONDITIONS **
**At the inlet: **

At inlet the stagnation pressure is taken equal to the ambient pressure at the same elevation. Then, neglecting the viscous losses due to acceleration of the fluid from surroundings to the stove inlet, Bernoulli equation can be used to express the static fluid pressure in terms of velocity. Further, the fluid is assumed to enter the stove axially, thus, radial velocity at the inlet is taken to be zero. Then, continuity equation dictates that the normal gradient of axial mass flux should also be zero. The temperature at the stove inlet can be assumed to the ambient temperature,

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Vol. 2(9), 2010, 4312-4324

**At the axis of symmetry: **

Due to assumed axisymmetry of the flow, computations may be carried out for only half of the domain as shown by hatched lines in figure 2. Symmetry, then, dictates that the radial velocity as well as the normal gradients of axial mass flux and temperature is zero on the axis:

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**At the stove exit: **

The exhaust gases leaving the combustion chamber can be treated as a jet entering a still medium i.e. static pressure is equal to the local ambient pressure. Also, assuming that the flow leaves the exit radially, consequently, axial velocity is zero. Thus, boundary conditions at the exit can be written as;

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**At the solid wall: **

Both the right boundaries as well as the top disc are considered as solid walls. The right boundary of the
computational domain consists of the solid wall enclosing the inlet section, the ceramic wall liner enclosing the
combustion chamber and the bottom disc. On these boundaries, for velocities no slip boundary condition would
apply and for temperature the convective boundary condition is imposed. The bottom of the pan also known as top
disc is maintained at a constant temperature of 1000_{C. }

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The Nusselt number Nu0 is defined in table 1. The heat transfer coefficient h0 is assumed to be constant at entire
wall boundary and its value is taken as 10w/m2_{. }

**At the secondary air inlets: **

The air can be assumed to enter the stove normal to the boundary through secondary port i.e. axial velocity is zero. The stagnation pressure is taken equal to the local ambient pressure at that elevation. Then, static pressure at secondary port is related to velocity by the Bernoulli's equation. The temperature at the secondary inlet is taken as the ambient temperature,

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*is the axial height of the secondary air inlet.*

_{s}**3.** **SOLUTION METHODOLOGY **

only while finer mesh is used in the secondary air inlet and diffuser bend regions. The number of grid points chosen in radial and axial directions depended upon the dimensions of radius of axial and radial diffuser, stove height etc. Typically, a grid of size 100X118 is used for the baseline case (table 2). At outer wall, ratio of minimum to maximum grid size is 0.009.

The resulting system of equation was solved by line by line TDMA (Tri-Diagonal-Matrix-Algorithm) solver iteratively. The iterations were stopped when root mean square (r.m.s.) value of residual in the continuity equation reduced by four to five orders of magnitude. Solutions were checked for grid independence using increasingly finer meshes until change in the mass flow rate and total heat transfer to pan was reduced below 5%. The computer code was validated for open tube case against the results of Kageyama and Izumi [[14]] and also for the sawdust stove against the results of Kohli [[15]]. For open tube and sawdust stove cases, the results were found to be within 5% and 10% agreement respectively.

**4.** **RESULTS AND DISCUSSION **

The parameters which influence the performance of a cook stove can be listed mainly in two groups, namely, geometric and thermal parameters. Typically, the geometric parameters consist of size of inlet/outlet ports and the dimensions of combustion chamber while the operating parameters include power, type of fuel, fuel bed porosity etc. In the present analysis, the effects of stove inlet radius, outlet radius, height of stove, diffuser radius, spacing between the stove and the pan, input power and the fuel bed porosity on the performance of the chosen stove have been computed. Further, stove performance is also evaluated based on heat transfer rate to the pan and since it provides an indication of the availability of heat for cooking purpose. The dimensional input parameters used for generating the data are given in table 2.

Table 2: Various cases included for parametric study

Case id ri r0 r2 r3 H1 H2 ∆Hs s P

(in kW) Baseline

case 65 80 110 140 150 80 25 15 0.65 1.0

rdf080 65 80 80 140 150 80 25 15 0.65 1.0

rdf130 65 80 130 140 150 80 25 15 0.65 1.0

Ht200 65 80 98.75 140 150 50 25 15 0.65 1.0

Ht300 65 80 136.25 140 150 150 25 15 0.65 1.0

Sp10 65 80 110 140 150 80 25 10 0.65 1.0

Sp20 65 80 110 140 150 80 25 20 0.65 1.0

rex120 65 80 110 120 150 80 25 15 0.65 1.0

rex195 65 80 110 195 150 80 25 15 0.65 1.0

phi050 65 80 110 140 150 80 25 15 0.50 1.0

phi080 65 80 110 140 150 80 25 15 0.80 1.0

Ip500 65 80 110 140 150 80 25 15 0.65 0.5

Ip1200 65 80 110 140 150 80 25 15 0.65 1.2

**Effect of geometric parameters on flow variables: **

Vol. 2(9), 2010, 4312-4324

a reduction in heat transfer to pan

*Q*

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*with increase in diffuser radius. Variations of various parameters such as axial velocity and temperatures leading to corresponding variations in mass flow rate and*

_{pan}*Q*

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*may well be understood by variation of resistance to flow due to variation in diffuser radius. An increase in diffuser radius results in decrease in flow resistance, hence, more secondary air is drawn into the system. Therefore, total mass flow rate is increasing significantly even though the primary air flow shows very little variation. But an increase in mass flow is cumulative effect of density as well as average velocity. Greater resistance to flow at smaller diffuser radius also means higher gas temperatures i.e. lower densities. Thus, increase in mass flow rate may have been caused due to predominance of higher gas velocities over the lower gas densities.*

_{pan}Figures 3(b) and 4(b) show the effect of diffuser height on the axial velocity and temperature profiles respectively. The velocity profiles show two peaks of almost equal magnitude while with increasing height, peak magnitudes of velocity profiles increase significantly. For lower height, the peak in the central zone is suppressed and only a slight variation of velocity is observed over much of the diffuser cross-section. In general, the temperature remains nearly constant over much of the diffuser cross section for a given height but temperature at any point on the cross-section decrease with reduction in stove height. Figure 5(b) show increase in both primary and secondary flow rates, however, increase in secondary mass flow rate is significant as compare to the increase observed for primary flow rate. Figure 5(b) also shows a reduction in heat transfer to pan which is result of reduction of temperatures with increase in stove height. Any variation in flow rate may be resulted from the net effect of density and velocity, therefore, an increase flow rate appears to have caused due to predominance of increase in velocity over the reduction in density.

The effect of spacing on the axial velocity and temperatures is shown in the figures 3(c) and 4(c). For larger spacing, velocity is higher over the entire cross-section of the diffuser. It is also seen that the peak in the central region is significantly greater as compare to the peak in the near wall region. For lower spacing, the profile has only one peak while the velocity elsewhere remains mostly uniform. The behavior of temperature profiles is similar what has been seen for variation in diffuser radius and height. For limiting values of spacing, s = 5 and 25 mm, the temperature are found to be lower than the temperatures for the spacing s = 10 to 15 mm. The spacing between stove and pan controls the resistance to outflow in the radial diffuser. Higher spacing would lead to lower resistance to outflow. Consequently, the pressure above the fuel bed decreases. Hence, flow rates of both secondary and primary air would increase. However, increase in secondary air is more pronounced as shown in figure 5(c). Increase in flow rates is typically caused by increase in density as well as velocity. Hence, lower temperatures are seen for increasing spacing. Figure 5(c) also shows the effect of spacing on

*Q*

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*. It is observed that the total heat transferred to pan is maximum for an optimum value of spacing which lies between s = 10 to 15 mm. As far as total heat transfer to pan is concerned, an increase in spacing leads to two mutually conflicting effects i.e. increase of mass flow rate and reduction in the bulk fluid temperature. The relative magnitude of these two effects determines the net increase or decrease in*

_{pan}*Q*

###

. At spacing lower than the optimum value of spacing, reduction in mass flow rate results in lower heat transfer coefficient, hence, reduction in the total heat transfer while for the spacing higher than the optimum spacing, reduction in bulk fluid temperature causes decrease in heat transfer.The radial diffuser radius affects the axial velocity almost evenly over most of the diffuser cross-section as observed in figure 3(d). With increase in outer radius, velocity is found to decrease at any point over the axial diffuser exit. An increase in outer radius causes an increase in viscous resistance in the radial diffuser region resulting in lower fluid velocities. Consequently, the total mass flow rate decreases as predicted in figure 5(d). Further, figure 5(d) depicts an increase in

*Q*

###

*which may be attributed due to increase in heat transfer area even though the gas temperature showed little variation.*

_{pan}resistance, consequently, higher primary flow rate and lower secondary air flow rate. The mass flow rate and

*Q*

###

_{pan}both are found to increase with increasing porosity as depicted in figure 5(e). The increase of temperatures with increasing porosity can be explained with the reduction in secondary flow rate instead of the total mass flow. Although the flow pattern for marginal values of porosity remains similar to that of baseline case, an interesting flow pattern is observed to have developed when the fuel bed porosity was very high i.e. a situation as if there were no fuel bed. Increase in heat transfer may be caused by the increase in heat transfer coefficient due to significant increase in primary air flow rate.

From figure 3(f), it is found that the behavior of axial velocity profile due to variation in input power is somewhat peculiar; the fluid velocities at the axis of symmetry are higher for lower power inputs while at the wall velocities are higher for higher power inputs. On the other hand for lower power input, axial Velocity at axis of symmetry is higher and lower at the wall. The axial velocity profiles were found to be affected uniformly by the variation of power input in case of sawdust stove of Kohli [[7]]. Figure 4(f) shows the effect of power input to the stove on the gas temperatures. The shape of the three temperature profiles is similar, however, higher temperatures are observed for higher power input. Higher temperatures due to increase in power causes corresponding reduction in density. With increase in power whether the mass flow rate of air will increase or decrease will depend upon how the power is divided between fuel bed and axial diffuser. Figure 5(f) indicates reduction in mass flow rates and increase of

*Q*

###

*with respect to increase in power input. The reduction in mass flow rate may be attributed due to predominance of density over the velocity while heat transfer to pan may have increased due to reduction in mass flow rate and increase in gas temperatures.*

_{pan}**5.** **Conclusions **

In the present study, influence of various geometric and operating parameters related to single pan wood burning stove have been analyzed in the context of stove performance by conducting a numerical simulation of buoyancy induced flow in the chosen stove geometry. The results of the analysis are summarized as follows:

1. Increase in stove height, spacing between stove and the vessel and axial diffuser radius shows slight variation in the mass flow rate of primary air while secondary mass flow increases sharply. With increase in radial diffuser radius, secondary mass flow rate decreases whereas primary flow remains mostly unaffected.

2. Increasing the axial diffuser radius from 80 mm to 120 mm shows increase in total mass flow rate nearly by 100%.

3. Increasing the height from 200mm to 300mm shows an increase in total mass flow rate by approximately 200%.

4. Increasing the spacing from 5mm to 25mm shows an increase in total mass flow rate by nearly 300%. 5. Fuel bed porosity exhibited significant influence on both primary as well as secondary flows. With increase

in porosity, primary flow rate increases sharply while secondary mass flow decreases.

6. Heat transfer to pan is found maximum for an optimal value of spacing lies between 10mm to 15 mm, however, it reduces for spacing lower and higher than the optimal spacing.

7. Heat transfer to pan increases with increases in axial as well as radial diffuser radius, stove height and fuel bed porosity. But, with further increase in porosity heat transfer begins to decrease.

8. It is observed that the inclusion of diffuser like shape in the combustion chamber tends to increase the mass flow rate through the stove and total heat transfer to the vessel significantly.

**References **

[1] Wood Burning Stove Group, Eindhoven and Apeldoorn, the Netherlands.

[2] Kohli S., Ravi M.R. (1996): Biomass stoves : A Review, SESI Journal,**6**, pp. 101-145.

[3] Mukunda H.S., Dasappa S., Swati B., Shrinivasa U.(1993): Studies on stove for powdery biomass, International Journal of Energy
Research, **17**, pp. 281-291.

[4] Bhandari S, Gopi S, Date A.W.(1988): Investigation of CTARA wood burning stove: Part I. experimental investigation. Sadhana; **13**,
pp. 271-293.

[5] Date A.W.(1988): Investigation of CTARA wood burning stove: Part - II analytical investigation. Sadhana **13**, pp. 295-317.

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[7] Kohli S.(1992): Buoyancy induced flow and heat transfer in biomass stoves, Ph.D thesis, Indian Institute of Science, Bangalore. [8] Bejan Adrian Nield D.A., Bejan Adrian (1992): Convection in porous media, springer-verlag, New York, pp. 5-12.

[9] White F.M. (1974): Viscous fluid flow, McGraw Hill, New York, pp. 28-33.

[10] Gebhart B, Jaluria Y, Mahajan RL, Sammakia, B.(1988): Buoyancy induced flows and Transport, Hemisphere, New York, pp. 934-936.

[11] Patankar S.V. (1980): Numerical heat transfer and fluid flow, Hemisphere Publishing Corporation, New York.

[12] Ray S., Date A.W. (2000): A calculation procedure for solution of incompressible Navier Stokes equations on curvilinear
non-staggered grids, Numerical Heat Transfer, Part B, **38**, pp. 93-131.

[13] Minkowycz W.J., Sparrow E.M., Schneider G.E., Pletcher R.H. (1988): Handbook of numerical heat transfer, John Wiley & Sons, Inc., New York, pp. 905-947.

[14] Kageyama M., Izumi R. (1970): Natural heat convection in a vertical circular tube, Bull. JSME **13**, pp. 382-394.

[15] Kohli S.(1993): Heat transfer to a horizontal disc using a buoyancy induced jet, International Journal of Heat Mass Transfer, **36**(16),

(a) (b)

(a) (b)

(c) (d)

(e) (f)

Figure 3: Effect of various parameters defining the stove geometry on axial velocity (a) axial diffuser exit radius, (b) stove height, (c) spacing between vessel and stove, (d) radial diffuser exit radius, (e) porosity of fuel bed, (f) power.

Vol. 2(9), 2010, 4312-4324

### (a) (b)

### (c) (d)

### (e) (f)

### (a) (b)

### (c) (d)

### (e) (f)

Figure 5: Effect of various parameters defining the stove geometry on non-dimensional mass flow rate

*m*

###

###

and heat transfer to pan*Q*

###

_{pan}