Steady-State Thermochemical Model of a Wood-Burning Cook-Stove

Abstract

In naturally aspirated wood-burning stoves, the air-flow is driven by buoyancy forces which overcome the flow resistances inside the stove. This air flow, in turn, determines the wood-burning rate as well as the overall thermal and combustion efficiencies. The flow and associated heat/mass transfer and combustion phenomena are 3-dimensional and time dependent. In this paper, a simplified 4-zone well-stirred thermochemical model is developed by capturing steady-state effects of chemical reaction kinetics of char and volatile burning. The model predicts performance parameters such as thermal efficiency, composition of combustion products, and excess-air factors for an experimental stove. Effects of stove geometry, wood fuel characteristics, cooking vessel dimensions, and other ambient conditions are investigated.

Keywords:

• Thermo-chemical model
• Wood burning stoves

Notes

Note: Fuel Properties: ρ _wo  = 800 kg/m ³; D _wo  = 1.26 cm; A _wo  = 400 c m ²; x _vol  = 0.75; f = 0.15; Grate Dimensions: D _rod  = 2 cm; δ = 2 cm; Pan Temp T _pan  = 388 K; Ambient: T _∞ = 300 K;  = 0.

^a (Bhandari et al., 1988).

^b (Krishnaprasad and Bussman, 1986).

The authors are grateful to the reviewer for pointing out this new reference.

Sometimes, the Stefan-Tube Model is also used.

The choice of 50 in Eq. (7) is arbitrary. Sensitivity analysis for this value is presented in a later section.

Blackshear and Murthy (1965) report T _wo  − T _T  ≃ 220 C in Phase 1 and ∼320 C in Phase 2. Therefore, the assumption T _w0 − T _T  ≃ 150 C will be tested through sensitivity analysis in the Sensitivity Analysis section.

This latent heat is notional that mimics wood burning as volatile liquid fuel burning.

From zero-dimensional modeling, Δp = k V ²/2 (White, 1986) where k captures the effects of friction and momentum change.

These ratios are typically functions of wood surface temperature. In stoves, the range of average surface temperatures during different operating conditions is, however, small.

In Kausley and Pandit (2010), the reaction is taken as CO + (1/Φ) O ₂ → 2 (1 − 1/Φ) CO + (2/Φ − 1) C O ₂; thus allowing for formation of CO as well as C O ₂.

The heat of combustion ΔH _char for this reaction is 32.6 MJ/ kg when Graphite (Turns, 1996). But, for lighter and porous wood-char, it is taken as 14 MJ/kg.

This may appear anomalous. But, these fluxes are evaluated from average surface and zonal temperatures. As such, they only represent global balance and not local balance.

In stove literature, sometimes Emission Factor (EF) is quoted in g/kg of fuel. It can be deduced from the predicted values of species mass fractions at stove exit as

It may be noted that with wood diameter D _wo  = 1.26 cm and length 20 cm, for A _wo  = 400 c m ², the grate (D _gr  = 22 cm) will accommodate five pieces of wood. With increase in surface area, the number of wood pieces (or, the number of layers Nrow, see Eq. [15]) and, hence, resistance k _bed will proportionately increase.