Introduction

The deforestation and the shortage of wood have becoming a problem in Nigeria. The hike of the hydrocarbon fuel and the intent discoveries of the possibility of extinction of the crude oil make the renewable energy to be accepted. One of the renewable energy resources is biomass. It can be divided into biomass plantation, forest residues agricultural residues.The resources reported produced 33 percent of energy consumed in developing countries and carbon dioxide generated during combustion will compensate photosynthesis. Thus nearly zero net gain carbon dioxide can be obtained especially for biomass plantations (Eriksson and Prior, 1990). Agricultural residues account for the largest biomass available worldwide. Biomass is free, indigenous and environmentally friendly. It can be used as fuel, examples are sawdust, coconut shell ground nut shell etc. Although, the majority of the residues are not widely accepted to be used as direct fuel compare to other fuel. Biomass has been viewed not as the single replacement for oil, but as one element in a wider portfolio of renewable sources of energy (Ashworth, 2002). The production of energy from biomass involves a range of technologies that include solid combustion, gasification, and fermentation. These technologies produce liquid and gas fuels from a diverse of biological resources— traditional crops (sugarcane, maize, oilseeds), crop residues and waste (maize Stover, wheat straw, rice hulls, cotton waste), energy-dedicated crops (grasses and trees), the organic component of urban waste. The outcomes are biomass products that provide multiple energy services such as cooking fuels, heat, electricity, and transportation fuels. It is this very diversity that provides potential of a win-win development path for the environment, social and economic development, and energy security (European Union, 2006).

Design and Calculation

In designing of a Briquette stove, certain materials serve as guidelines in achieving desirable results. Such materials are usually of known standards either readily available in markets or found from previously conducted research results. Examples of such materials are the fuel type, size and shape, material for construction of stove, the pot type and size and type of insulation. The components designed for were combustion chamber, the body of the stove, the grate, the fuel loading tray, the pot supporting frame, the firebox or starter box and the handle.

Pot sizes of the stove should range between 20cm and 50cm and 30cm pot size would be a standard family sized pot. (Winiarski ). The apparent density of briquettes made from nearly all materials ranges between 0.18g/cm3 and 0.3g/cm3 for intermediate pressure (5MPa – 100MPa). (Bossel, 1984).

A special feature in the briquette is the presence of holes uniformly spaced in a star pattern running throughout the height of the briquette. The numbers of hole ranges between four and nineteen in steps of three. The diameter also varies based on the number of holes selected.

These holes not only allow briquette to dry evenly, but they also result in an even burning process by allowing flames and gasses to escape evenly from the briquette. The size of the holes (diameter) depends on the amount of air required for complete combustion of the fuel; the rate at which the air passes through the briquette during reaction is controlled by the size of the hole.

A briquette having 10 holes (diameter of 12mm each) is selected for the stove.

Combustion Chamber

For a cylindrical chamber, the range of the side space around the briquette inside the chamber should be between ¼ inch (0.625cm) and ½ inch (1.25cm) minimum and maximum respectively.(Krishna, 2000).

Diameter = 13cm (assuming side space if 1cm).

Area of a cylinder is given by:

Area = πr2 (cm2)

Where π is a constant (3.142) and r is the radius of the cylinder.

Area = π (d/2) 2 = 3.142 × (13/2)2 (cm2) = 132.73cm2

Taking the chamber height about two times taller than its diameter to create a short chimney above the briquette which cleans up smoke and reduce emission (Winiarski,1997). A taller combustion chamber, more than three times the diameter will clean up more smoke, but a shorter chamber bellow two times diameter will bring hotter gases to the pot. ( Asian Institute of technology,2002).then, height of the chamber when diameter 13cm is given as (13 × 2) cm = 26cm.Therefore, the dimensions of the combustion chamber are diameter (13cm), height (26cm) and Area ( 132.73cm2)

Volume = πr2h, where h = height, r = radius, Volume = 3451cm3

Design of Air Vent

For complete combustion of the fuel, 7.24kg of air is required.

Density of air is about 1.2kg/m3. The volume of air required is given by:

Density (kg/m3) = Mass of Air (kg)/Volume of Air (m3)

Therefore, the volume of air (m3) required is volume (m3) = Mass (kg) / Density (kg/m3) = 6.033m3 for 1kg of fuel.

Let a standard boiling time for two liters water in a family sized pot of 30cm to be between five minutes and ten minutes at a fire power of about 5kW.(Ballard-Tremeer and Smith, 1987 ). Considering the briquette density (0.3g/cm3),Volume = πr2h , where r = radius of briquette, h = height of briquette and is a constant.

External diameter of briquette is 12cm (radius = 6cm) (π × 62 × 7.5) cm3 = 848.23cm3

Internal diameter of 10 holes if 1.2cm each= (10 × π × 0.62 × 7.5)cm3 = 84.82cm3

Volume of briquette = Volume of external – Volume of internal = 848.23cm3 – 84.82cm3 = 763.41cm3

Mass of briquette = Density of briquette × Volume of briquettes ,M = 0.23kg

5kW fire power boils water for 5minutes- 10minutes then,1.75kg of fuel (16MJ/kg) produces 5.5kW of power and 1.75kg burns for 1 hour. Therefore, a fuel of 0.23kg would burn for; ([1/1.75] × 3600(sec) × 0.23) sec = 473.14sec

Volume of air required = 6.033m3

Rate of flow of air (Q) = volume / time = 1.28 × 10-2 m3/s

Rate of flow of air (Q) = velocity of air × area of vent.

At standard atmospheric pressure and temperature, the velocity of air per unit area is about 1.5m/s (www.wikipedia.com “velocity of air per unit area”).

Area of vent = 85.03cm2

The space within the stove through which hot air flows and the opening into the stove should be of the same size to maintain constant cross sectional area and keep good draft throughout the stove. Size of space within the stove is given by;

S = volume of 10 holes in briquette + volume of space around the briquette. ( Winiarski,1997 )

Volume of 10 holes in the briquette is 84.82cm2

Space around the briquette is 1cm,

Volume of space around the briquette is (π × [1/2]2 × 7.5)cm3 = 5.89cm3

Therefore size of space (S) within the stove is 84.82 + 5.89 = 90.71cm3

To maintain constant cross sectional area, an air vent if about 90cm2 areas is suitable.

Air Vent Dimension

Area = 90cm2, Assume a rectangular vent, the opening leads directly to the base of the combustion chamber. The combustion chamber is placed above the opening to ensure hot air which is initially burnt comes into the chamber. For the vent opening to fit perfectly within the opening of the chamber, the length of the opening should be less than the diameter of the chamber.

Therefore, length of rectangular vent is assumed 11cm

Width = Area / length = 90cm2 / 11cm = 8.2cm

Design of Grate

The briquette sits in a grate present at the bottom of the combustion chamber. The grate is characterized with uniform holes of about 2cm2 areas to ensure flow of air into the chamber and easy dropping of ash into the ash plate to avoid clogging. Large holes would allow briquette to fall off when not completely burnt and too small holes will prevent enough air from getting into the chamber to complete combustion.

Design grate for maximum weight of briquette;

Assume a maximum mass of 1kg,

Force on grate = 1kg × 9.81 m/s = 9.81N

Assume weight is uniformly absorbed by 2 members of the grate of 130mm each (equal to the diameter of the chamber).

Maximum bending moment on the 2 bars is given by; M = WL2 / 12 (Timoshenko, 1968).

Where M = maximum bending moment, W= force on grate, L= length of bar.

Force on grate = 9.81N, therefore force on each bar is 9.81/2 = 4.9N

So, M = 4.9N × (130mm)2 / 12 = 6900.83Nmm2

The bars are subjected to bending stress (δb) due to the force on it.

(Tensile Stress) Maximum allowable stress δmax = 0.53Ys for tensile stress

Where Ys = Yield strength of material and 0.53 = tensile constant.

Using mild steel of yield strength (Ys) = 200N/mm2

δmax = 0.53 × 200N/mm2 = 106N/mm2

The section modulus (z) which is the ratio of the moment of inertia of the cross section about the neutral axis (l) to the distance from the neutral axis to the extreme, is given by

z = m / δmax

Where m= maximum bending moment, δmax = maximum stress.

z = 6900.102Nmm2 / 106N/mm2 = 65.102mm4

Using a circular bar, (z) = d3 / 32 Where d is the diameter of the bar.

65.102 = πd3 / 32,

d = ∛((65.102 ×32)/π) = 8.72mm

The diameter of each bar is 8.72mm, a standard size of 10mm is used. The two bars are crossed to form a right angle at their center. Smaller bars of about 5mm are then joined to the two bars at intervals of 2cm parallel to both bars. A grate of 4cm2 is formed.

Design of Body of Stove

The size of the outer body of the stove is determined by the size of the pot and the gap between the pot and the shield. The stove body extends up to form a shield around the pot.

Diameter of stove body = diameter of pot + gap between the pot and shield.

Pot diameter (family sized) = 30cm

There are three gaps associated with the stove design; gap between the bottom of the pot and the top edge of the combustion chamber, gap at the edge of the pot and gap at the side of the pot.

These gaps are necessary to improve the thermal efficiency of the stove.

Gap at edge of chamber is given by;

Gc = Ac / Cc

Where Gc = gap, Ac = area of combustion chamber, Cc = circumference of chamber.

Ac = 132.73cm2, Cc = 2πRc, Where Rc = radius of chamber.

Cc = 2 × π × 6.5cm = 40.841cm

Therefore, Gc = (132.72cm2) / (40.841cm) = 3.25cm.

Gap at edge of pot Gp = Ac/Cp, Where Cp = circumference of pot

Therefore, Cp = 2πRp, Where Rp= radius of pot

Cp = 2 × π × (30/2) = 94.25cm, Therefore Gp = (132.73cm2)/(94.25cm) = 1.41cm

Gap at side of the pot is the same as gap at edge of pot = 1.41cm

Diameter of stove body = 30 + 1.41 = 31.41cm

Height of stove body = height of air vent + height of chamber + height of gap + height of pot = 49.4cm about 50cm high.

Design of Fuel Loading Tray

The tray is inclined at an angle that allows the fuel to slide into the combustion chamber. The coefficient of friction between the wood and metal is between 0.4 and 0.6 (Timoshenko and Young, 1968). Designing for three briquettes of 0.3kg mass each, Weight if tray = 3× 0.3 × 9.81 = 8.83N

F = mg × cos e – N = mg × cos e –mg × sin θ

µ (coefficient of friction) = F/N = tan θ

Assuming µ = 0.6, tan θ = 0.6, tan-1 0.6 = 30.10

At angle of 310, the fuel starts to slide. Using an angle of 350 gives a quick slide of the fuel. Therefore θ = 350

F = mg × cos35 – mg × sin35, mg = W = 8.83N

F = 8.83cos35 – 8.83sin35 = 7.23 – 5.06 = 2.17N, A frictional force of 2.17N is overcomes before fuel slides.

Load Bearing Capacity of the Tray

Assume a tray length of 40cm (three briquette diameter and a little clearance). Assume a briquette force of 1kg on it, W = 9.81N, Maximum bending moment, M = WL2/12

M = 9.81 × 402/12 = 1308Nmm2, Maximum allowable stress, δmax = 0.53Ys

Ys (yield strength) for mild steel = 200Nmm-2. δmax = 0.53 × 200 = 106Nmm-2

Section Modulus (Z) = M/δmax = 1308/106 = 12.34mm4

Using a rectangular bar of 40cm length and 13cm width, Z = Lh2/6, h = √((6×Z)/L) = 0.043mm

This shows that the tray requires a relative flat bar of about 1mm thick to 2mm thick or lesser.

Design of Supporting Frame

The supporting frame consists of the pot rest and top sit of the pot. A mass of 30cm cast iron cooking pot full of water and beans is taken as bout 10kg. Force exerted = 10 × 9.81 = 98.1N

Using 3 pot rests located at the edge of the combustion chamber with a length of 3.2cm (the size of the gap between the pot and the combustion chamber) and treating the rest as column

Each rest is to withstand a force of 98.1/3 = 32.7N, Maximum bending moment, M = WL2/12 = 7290.4Nmm2

Maximum allowable stress δmax = 0.48Ys for compressible force. Assume mild steel of Ys = 200N/mm2

Therefore, δmax = 0.48 × 200N/mm2 = 96N/mm2Section modulus = M/δ = 2790.4/96 = 29.07mm4

For circular section, Z = (πd3/32), Therefore, d = ∛((32×29.07)/π) =6.7m.

3bars of diameter of about 10mm are used.

The top sit has a diameter of the combustion chamber = 130mm. the force 98.1N is uniformly distributed on the seat. Force acting on a unit length of the seat is given by 98.1/130mm = 0.75N.

Maximum bending moment per unit length the arc, M = WL/8 = (0.75 × 130)/8 = 12.26N/mm2

Maximum stress δmax = 0.53Ys for tensile stress using a mild steel of Ys = 200N/mm2

δ = 0.53 × 200 = 106N/mm2

For a flat sheet with rectangular section, Z = (bh2)/δ

h = √((6×Z)/b) = √((6×(12.26/106))/130) = 0.073mm ≈ 0.1mm.

Therefore, a sheet of 0.1mm on the smallest sized mild steel sheet is sufficient for the top sit.

Design of Starter Box

A starter box is required to ignite the fuel from below. The starter box is removable and fix in perfectly into the space provided for the air vent and channels the air directly to the combustion chamber. An opening is cut at the top end of the box which aligns with the base opening of the chamber. The box serves as the starter box where some wood is lighted and inserted to light the briquette. Also, it serves as the channel for the air flowing into the stove. During combustion, ash is produced which drops into this box and emptied from this box.

Dimensions of the box are Length of opening (11cm) and height of box (8.2cm)

The box is slide into the opening and a stopper at the farthest end of the combustion chamber stops it. The length of the box is therefore 13cm+9.2cm+7cm = 29.2cm long

13cm is the diameter of the chamber of the chamber, 9.2cm is the gap between the outer wall of the chamber and the inner wall of the stove body, 7cm is the clearance that extends outside the stove. An air valve is provided to cover the opening at the entrance of the firebox. The valve helps to control the amount of air in case of wind.

A circle of diameter 11cm is cut at the top end of the box to align with the base opening of the combustion chamber to ensure passage of air into the chamber.

Load Bearing Capacity of Stove

The stove is subjected to load from the pot which is transmitted through the supporting frame, and distributed to the combustion chamber and the body of the pot.

Assuming a maximum load of 20kg, sharing this load on the combustion chamber and the body of the stove at 10kg each, The force each is 10kg × 9.81 = 98.1N

For the combustion chamber of diameter 13cm, a maximum allowable stress of δmax = 0.48Ys due to compressive force using mild steel of Ys = 200N/mm2, δmax = 0.48 × 200 = 96N/mm2

δmax is also defined as F/A where F is the force acting on the member and A is the cross sectional area.

Therefore, A = F/δmax = 98.1/96 = 1.022mm2,The chamber is a cylinder of circumference, πd= 408.41mm

If the cylinder is stretched out to form a rectangle of length equal to the circumference and a thickness not known,

A = L × B = circumference × thickness, therefore thickness = 0.0025mm

A mild steel of thickness less than 0.1 would comfortably bear the load placed on it.

For stove body, using the same mild steel of Ys = 200N/mm2

Force on stove =98.1N,δmax = 96N/mm2

A = F/δmax = 1.022mm2, Circumference of body = πd = 3.14 × 314.1mm = 986.77mm

Area = circumference × thickness, thickness = 1.022mm2/986.77 = 0.0010mm

Also, a mild steel of thickness less than 0.1mm would be sufficient for the design of the stove body.

The combustion chamber in the stove on four circular solid bars of height = 8.5cm, each bar experiences a force of 98.1N/4 = 24.525N.Maximum bending moment (M) of the bar due to compression is given by, M = WL2/12 = 14766.09Nmm2, Maximum allowable stress = 0.48Ys,Assume a mild steel of Ys = 200N/mm2

δmax = 0.48 ×200 = 96N/mm2

Section modulus = moment/maximum stress = 14766.09Nmm2/96N/mm2,Z = 153.81mm

For a solid cylinder, Z = πd3/32,d = ∛((32×Z)/π) = 11.61mm

Each bar carrying the chamber is designed with a diameter of about 12mm to 15mm.

Design of Carrying Handle

For ease of transportation, a handle is required. The handle is attached to the body of the stove, long enough to cover the height of the pot and still leaves some space. Assuming the handle is attached to the stove some few mm below the edge of the combustion chamber (50mm).The length of the column of the handle is designed by,50mm+32mm+120mm = 202mm ≈ 202 + some space above the pot.

An approximate height 35cm is used for the handle. The beam of the handle to which the column is attached is a bit wider than the stove, about 34cm in length. A total weight of the stove (20kg × 9.81) is exerted on the beam.

Load on beam = 20kg × 9.81 = 196.2N, Length of beam = 34cm = 340mm

For a beam fixed at both end, Maximum bending moment, M = WL/8 = 8338.50Nmm2

Maximum allowable stress from tensile force δmax = 0.53Ys using mild steel of 200N/mm2

δmax= 0.53 × 200N/mm2 = 106N/mm2

Section modulus = moment / stress limit = 8338.50Nmm2 / 106N/mm2

Z = 78.67mm3

Section modulus for a circular solid = (πd3)/32, d = ∛((32×Z)/π) = 9.29mm

A circular solid bar (mild steel) of about 10mm in diameter is used as the handle beam. Two handle columns of 35cm (350mm) long each share the load equally. Load on each column = (20kg/2) × 9.81 = 98.1N

Maximum bending moment M on column (fixed at an end) = WL/4 = 8583.75Nmm

Maximum allowable stress δmax = 0.53Ys,Ys of mild steel = 200N/mm2

δmax = 0.53 × 200 = 106N/mm2

Section modulus Z = M/δmax = 8583.75/106 = 80.98mm3

Z = πd3/32 for circular solid bar

d = ∛((32×Z)/π) = 9.38mm. The column of the handle is about 10mm diameter and 350mm in length.

Assembly of the Components

The combustion chamber was on four bars of about 15 mm diameter and a height of 85mm each and the bars on the base of the stove body. The stove body was on a base which serves as the base of the whole stove arrangement. An opening cut at the base of the stove body equal to the dimension of air vent. The firebox inserted through this opening and passes through the four bars carrying the combustion chamber. It stopped by a tin sheet at the farthest end of the chamber.

The combustion chamber curved in at the base by 1cm to serve as a sit for the grate. An opening that fitted a briquette perfectly cut both on the body of the stove and the combustion chamber just above the grate to serve as fuel opening. The loading tray joined to the body of the stove at this point. The pot supporting frame joined to the top of the combustion chamber and the corresponding point on the body of the stove. The handle attached to the body of the stove. The full assembled and component parts drawing are shown in figure 1 All necessary welding joints were properly welded and the stove ready to use.

The deforestation and the shortage of wood have becoming a problem in Nigeria. The hike of the hydrocarbon fuel and the intent discoveries of the possibility of extinction of the crude oil make the renewable energy to be accepted. One of the renewable energy resources is biomass. It can be divided into biomass plantation, forest residues agricultural residues.The resources reported produced 33 percent of energy consumed in developing countries and carbon dioxide generated during combustion will compensate photosynthesis. Thus nearly zero net gain carbon dioxide can be obtained especially for biomass plantations (Eriksson and Prior, 1990). Agricultural residues account for the largest biomass available worldwide. Biomass is free, indigenous and environmentally friendly. It can be used as fuel, examples are sawdust, coconut shell ground nut shell etc. Although, the majority of the residues are not widely accepted to be used as direct fuel compare to other fuel. Biomass has been viewed not as the single replacement for oil, but as one element in a wider portfolio of renewable sources of energy (Ashworth, 2002). The production of energy from biomass involves a range of technologies that include solid combustion, gasification, and fermentation. These technologies produce liquid and gas fuels from a diverse of biological resources— traditional crops (sugarcane, maize, oilseeds), crop residues and waste (maize Stover, wheat straw, rice hulls, cotton waste), energy-dedicated crops (grasses and trees), the organic component of urban waste. The outcomes are biomass products that provide multiple energy services such as cooking fuels, heat, electricity, and transportation fuels. It is this very diversity that provides potential of a win-win development path for the environment, social and economic development, and energy security (European Union, 2006).

Design and Calculation

In designing of a Briquette stove, certain materials serve as guidelines in achieving desirable results. Such materials are usually of known standards either readily available in markets or found from previously conducted research results. Examples of such materials are the fuel type, size and shape, material for construction of stove, the pot type and size and type of insulation. The components designed for were combustion chamber, the body of the stove, the grate, the fuel loading tray, the pot supporting frame, the firebox or starter box and the handle.

Pot sizes of the stove should range between 20cm and 50cm and 30cm pot size would be a standard family sized pot. (Winiarski ). The apparent density of briquettes made from nearly all materials ranges between 0.18g/cm3 and 0.3g/cm3 for intermediate pressure (5MPa – 100MPa). (Bossel, 1984).

A special feature in the briquette is the presence of holes uniformly spaced in a star pattern running throughout the height of the briquette. The numbers of hole ranges between four and nineteen in steps of three. The diameter also varies based on the number of holes selected.

These holes not only allow briquette to dry evenly, but they also result in an even burning process by allowing flames and gasses to escape evenly from the briquette. The size of the holes (diameter) depends on the amount of air required for complete combustion of the fuel; the rate at which the air passes through the briquette during reaction is controlled by the size of the hole.

A briquette having 10 holes (diameter of 12mm each) is selected for the stove.

Combustion Chamber

For a cylindrical chamber, the range of the side space around the briquette inside the chamber should be between ¼ inch (0.625cm) and ½ inch (1.25cm) minimum and maximum respectively.(Krishna, 2000).

Diameter = 13cm (assuming side space if 1cm).

Area of a cylinder is given by:

Area = πr2 (cm2)

Where π is a constant (3.142) and r is the radius of the cylinder.

Area = π (d/2) 2 = 3.142 × (13/2)2 (cm2) = 132.73cm2

Taking the chamber height about two times taller than its diameter to create a short chimney above the briquette which cleans up smoke and reduce emission (Winiarski,1997). A taller combustion chamber, more than three times the diameter will clean up more smoke, but a shorter chamber bellow two times diameter will bring hotter gases to the pot. ( Asian Institute of technology,2002).then, height of the chamber when diameter 13cm is given as (13 × 2) cm = 26cm.Therefore, the dimensions of the combustion chamber are diameter (13cm), height (26cm) and Area ( 132.73cm2)

Volume = πr2h, where h = height, r = radius, Volume = 3451cm3

Design of Air Vent

For complete combustion of the fuel, 7.24kg of air is required.

Density of air is about 1.2kg/m3. The volume of air required is given by:

Density (kg/m3) = Mass of Air (kg)/Volume of Air (m3)

Therefore, the volume of air (m3) required is volume (m3) = Mass (kg) / Density (kg/m3) = 6.033m3 for 1kg of fuel.

Let a standard boiling time for two liters water in a family sized pot of 30cm to be between five minutes and ten minutes at a fire power of about 5kW.(Ballard-Tremeer and Smith, 1987 ). Considering the briquette density (0.3g/cm3),Volume = πr2h , where r = radius of briquette, h = height of briquette and is a constant.

External diameter of briquette is 12cm (radius = 6cm) (π × 62 × 7.5) cm3 = 848.23cm3

Internal diameter of 10 holes if 1.2cm each= (10 × π × 0.62 × 7.5)cm3 = 84.82cm3

Volume of briquette = Volume of external – Volume of internal = 848.23cm3 – 84.82cm3 = 763.41cm3

Mass of briquette = Density of briquette × Volume of briquettes ,M = 0.23kg

5kW fire power boils water for 5minutes- 10minutes then,1.75kg of fuel (16MJ/kg) produces 5.5kW of power and 1.75kg burns for 1 hour. Therefore, a fuel of 0.23kg would burn for; ([1/1.75] × 3600(sec) × 0.23) sec = 473.14sec

Volume of air required = 6.033m3

Rate of flow of air (Q) = volume / time = 1.28 × 10-2 m3/s

Rate of flow of air (Q) = velocity of air × area of vent.

At standard atmospheric pressure and temperature, the velocity of air per unit area is about 1.5m/s (www.wikipedia.com “velocity of air per unit area”).

Area of vent = 85.03cm2

The space within the stove through which hot air flows and the opening into the stove should be of the same size to maintain constant cross sectional area and keep good draft throughout the stove. Size of space within the stove is given by;

S = volume of 10 holes in briquette + volume of space around the briquette. ( Winiarski,1997 )

Volume of 10 holes in the briquette is 84.82cm2

Space around the briquette is 1cm,

Volume of space around the briquette is (π × [1/2]2 × 7.5)cm3 = 5.89cm3

Therefore size of space (S) within the stove is 84.82 + 5.89 = 90.71cm3

To maintain constant cross sectional area, an air vent if about 90cm2 areas is suitable.

Air Vent Dimension

Area = 90cm2, Assume a rectangular vent, the opening leads directly to the base of the combustion chamber. The combustion chamber is placed above the opening to ensure hot air which is initially burnt comes into the chamber. For the vent opening to fit perfectly within the opening of the chamber, the length of the opening should be less than the diameter of the chamber.

Therefore, length of rectangular vent is assumed 11cm

Width = Area / length = 90cm2 / 11cm = 8.2cm

Design of Grate

The briquette sits in a grate present at the bottom of the combustion chamber. The grate is characterized with uniform holes of about 2cm2 areas to ensure flow of air into the chamber and easy dropping of ash into the ash plate to avoid clogging. Large holes would allow briquette to fall off when not completely burnt and too small holes will prevent enough air from getting into the chamber to complete combustion.

Design grate for maximum weight of briquette;

Assume a maximum mass of 1kg,

Force on grate = 1kg × 9.81 m/s = 9.81N

Assume weight is uniformly absorbed by 2 members of the grate of 130mm each (equal to the diameter of the chamber).

Maximum bending moment on the 2 bars is given by; M = WL2 / 12 (Timoshenko, 1968).

Where M = maximum bending moment, W= force on grate, L= length of bar.

Force on grate = 9.81N, therefore force on each bar is 9.81/2 = 4.9N

So, M = 4.9N × (130mm)2 / 12 = 6900.83Nmm2

The bars are subjected to bending stress (δb) due to the force on it.

(Tensile Stress) Maximum allowable stress δmax = 0.53Ys for tensile stress

Where Ys = Yield strength of material and 0.53 = tensile constant.

Using mild steel of yield strength (Ys) = 200N/mm2

δmax = 0.53 × 200N/mm2 = 106N/mm2

The section modulus (z) which is the ratio of the moment of inertia of the cross section about the neutral axis (l) to the distance from the neutral axis to the extreme, is given by

z = m / δmax

Where m= maximum bending moment, δmax = maximum stress.

z = 6900.102Nmm2 / 106N/mm2 = 65.102mm4

Using a circular bar, (z) = d3 / 32 Where d is the diameter of the bar.

65.102 = πd3 / 32,

d = ∛((65.102 ×32)/π) = 8.72mm

The diameter of each bar is 8.72mm, a standard size of 10mm is used. The two bars are crossed to form a right angle at their center. Smaller bars of about 5mm are then joined to the two bars at intervals of 2cm parallel to both bars. A grate of 4cm2 is formed.

Design of Body of Stove

The size of the outer body of the stove is determined by the size of the pot and the gap between the pot and the shield. The stove body extends up to form a shield around the pot.

Diameter of stove body = diameter of pot + gap between the pot and shield.

Pot diameter (family sized) = 30cm

There are three gaps associated with the stove design; gap between the bottom of the pot and the top edge of the combustion chamber, gap at the edge of the pot and gap at the side of the pot.

These gaps are necessary to improve the thermal efficiency of the stove.

Gap at edge of chamber is given by;

Gc = Ac / Cc

Where Gc = gap, Ac = area of combustion chamber, Cc = circumference of chamber.

Ac = 132.73cm2, Cc = 2πRc, Where Rc = radius of chamber.

Cc = 2 × π × 6.5cm = 40.841cm

Therefore, Gc = (132.72cm2) / (40.841cm) = 3.25cm.

Gap at edge of pot Gp = Ac/Cp, Where Cp = circumference of pot

Therefore, Cp = 2πRp, Where Rp= radius of pot

Cp = 2 × π × (30/2) = 94.25cm, Therefore Gp = (132.73cm2)/(94.25cm) = 1.41cm

Gap at side of the pot is the same as gap at edge of pot = 1.41cm

Diameter of stove body = 30 + 1.41 = 31.41cm

Height of stove body = height of air vent + height of chamber + height of gap + height of pot = 49.4cm about 50cm high.

Design of Fuel Loading Tray

The tray is inclined at an angle that allows the fuel to slide into the combustion chamber. The coefficient of friction between the wood and metal is between 0.4 and 0.6 (Timoshenko and Young, 1968). Designing for three briquettes of 0.3kg mass each, Weight if tray = 3× 0.3 × 9.81 = 8.83N

F = mg × cos e – N = mg × cos e –mg × sin θ

µ (coefficient of friction) = F/N = tan θ

Assuming µ = 0.6, tan θ = 0.6, tan-1 0.6 = 30.10

At angle of 310, the fuel starts to slide. Using an angle of 350 gives a quick slide of the fuel. Therefore θ = 350

F = mg × cos35 – mg × sin35, mg = W = 8.83N

F = 8.83cos35 – 8.83sin35 = 7.23 – 5.06 = 2.17N, A frictional force of 2.17N is overcomes before fuel slides.

Load Bearing Capacity of the Tray

Assume a tray length of 40cm (three briquette diameter and a little clearance). Assume a briquette force of 1kg on it, W = 9.81N, Maximum bending moment, M = WL2/12

M = 9.81 × 402/12 = 1308Nmm2, Maximum allowable stress, δmax = 0.53Ys

Ys (yield strength) for mild steel = 200Nmm-2. δmax = 0.53 × 200 = 106Nmm-2

Section Modulus (Z) = M/δmax = 1308/106 = 12.34mm4

Using a rectangular bar of 40cm length and 13cm width, Z = Lh2/6, h = √((6×Z)/L) = 0.043mm

This shows that the tray requires a relative flat bar of about 1mm thick to 2mm thick or lesser.

Design of Supporting Frame

The supporting frame consists of the pot rest and top sit of the pot. A mass of 30cm cast iron cooking pot full of water and beans is taken as bout 10kg. Force exerted = 10 × 9.81 = 98.1N

Using 3 pot rests located at the edge of the combustion chamber with a length of 3.2cm (the size of the gap between the pot and the combustion chamber) and treating the rest as column

Each rest is to withstand a force of 98.1/3 = 32.7N, Maximum bending moment, M = WL2/12 = 7290.4Nmm2

Maximum allowable stress δmax = 0.48Ys for compressible force. Assume mild steel of Ys = 200N/mm2

Therefore, δmax = 0.48 × 200N/mm2 = 96N/mm2Section modulus = M/δ = 2790.4/96 = 29.07mm4

For circular section, Z = (πd3/32), Therefore, d = ∛((32×29.07)/π) =6.7m.

3bars of diameter of about 10mm are used.

The top sit has a diameter of the combustion chamber = 130mm. the force 98.1N is uniformly distributed on the seat. Force acting on a unit length of the seat is given by 98.1/130mm = 0.75N.

Maximum bending moment per unit length the arc, M = WL/8 = (0.75 × 130)/8 = 12.26N/mm2

Maximum stress δmax = 0.53Ys for tensile stress using a mild steel of Ys = 200N/mm2

δ = 0.53 × 200 = 106N/mm2

For a flat sheet with rectangular section, Z = (bh2)/δ

h = √((6×Z)/b) = √((6×(12.26/106))/130) = 0.073mm ≈ 0.1mm.

Therefore, a sheet of 0.1mm on the smallest sized mild steel sheet is sufficient for the top sit.

Design of Starter Box

A starter box is required to ignite the fuel from below. The starter box is removable and fix in perfectly into the space provided for the air vent and channels the air directly to the combustion chamber. An opening is cut at the top end of the box which aligns with the base opening of the chamber. The box serves as the starter box where some wood is lighted and inserted to light the briquette. Also, it serves as the channel for the air flowing into the stove. During combustion, ash is produced which drops into this box and emptied from this box.

Dimensions of the box are Length of opening (11cm) and height of box (8.2cm)

The box is slide into the opening and a stopper at the farthest end of the combustion chamber stops it. The length of the box is therefore 13cm+9.2cm+7cm = 29.2cm long

13cm is the diameter of the chamber of the chamber, 9.2cm is the gap between the outer wall of the chamber and the inner wall of the stove body, 7cm is the clearance that extends outside the stove. An air valve is provided to cover the opening at the entrance of the firebox. The valve helps to control the amount of air in case of wind.

A circle of diameter 11cm is cut at the top end of the box to align with the base opening of the combustion chamber to ensure passage of air into the chamber.

Load Bearing Capacity of Stove

The stove is subjected to load from the pot which is transmitted through the supporting frame, and distributed to the combustion chamber and the body of the pot.

Assuming a maximum load of 20kg, sharing this load on the combustion chamber and the body of the stove at 10kg each, The force each is 10kg × 9.81 = 98.1N

For the combustion chamber of diameter 13cm, a maximum allowable stress of δmax = 0.48Ys due to compressive force using mild steel of Ys = 200N/mm2, δmax = 0.48 × 200 = 96N/mm2

δmax is also defined as F/A where F is the force acting on the member and A is the cross sectional area.

Therefore, A = F/δmax = 98.1/96 = 1.022mm2,The chamber is a cylinder of circumference, πd= 408.41mm

If the cylinder is stretched out to form a rectangle of length equal to the circumference and a thickness not known,

A = L × B = circumference × thickness, therefore thickness = 0.0025mm

A mild steel of thickness less than 0.1 would comfortably bear the load placed on it.

For stove body, using the same mild steel of Ys = 200N/mm2

Force on stove =98.1N,δmax = 96N/mm2

A = F/δmax = 1.022mm2, Circumference of body = πd = 3.14 × 314.1mm = 986.77mm

Area = circumference × thickness, thickness = 1.022mm2/986.77 = 0.0010mm

Also, a mild steel of thickness less than 0.1mm would be sufficient for the design of the stove body.

The combustion chamber in the stove on four circular solid bars of height = 8.5cm, each bar experiences a force of 98.1N/4 = 24.525N.Maximum bending moment (M) of the bar due to compression is given by, M = WL2/12 = 14766.09Nmm2, Maximum allowable stress = 0.48Ys,Assume a mild steel of Ys = 200N/mm2

δmax = 0.48 ×200 = 96N/mm2

Section modulus = moment/maximum stress = 14766.09Nmm2/96N/mm2,Z = 153.81mm

For a solid cylinder, Z = πd3/32,d = ∛((32×Z)/π) = 11.61mm

Each bar carrying the chamber is designed with a diameter of about 12mm to 15mm.

Design of Carrying Handle

For ease of transportation, a handle is required. The handle is attached to the body of the stove, long enough to cover the height of the pot and still leaves some space. Assuming the handle is attached to the stove some few mm below the edge of the combustion chamber (50mm).The length of the column of the handle is designed by,50mm+32mm+120mm = 202mm ≈ 202 + some space above the pot.

An approximate height 35cm is used for the handle. The beam of the handle to which the column is attached is a bit wider than the stove, about 34cm in length. A total weight of the stove (20kg × 9.81) is exerted on the beam.

Load on beam = 20kg × 9.81 = 196.2N, Length of beam = 34cm = 340mm

For a beam fixed at both end, Maximum bending moment, M = WL/8 = 8338.50Nmm2

Maximum allowable stress from tensile force δmax = 0.53Ys using mild steel of 200N/mm2

δmax= 0.53 × 200N/mm2 = 106N/mm2

Section modulus = moment / stress limit = 8338.50Nmm2 / 106N/mm2

Z = 78.67mm3

Section modulus for a circular solid = (πd3)/32, d = ∛((32×Z)/π) = 9.29mm

A circular solid bar (mild steel) of about 10mm in diameter is used as the handle beam. Two handle columns of 35cm (350mm) long each share the load equally. Load on each column = (20kg/2) × 9.81 = 98.1N

Maximum bending moment M on column (fixed at an end) = WL/4 = 8583.75Nmm

Maximum allowable stress δmax = 0.53Ys,Ys of mild steel = 200N/mm2

δmax = 0.53 × 200 = 106N/mm2

Section modulus Z = M/δmax = 8583.75/106 = 80.98mm3

Z = πd3/32 for circular solid bar

d = ∛((32×Z)/π) = 9.38mm. The column of the handle is about 10mm diameter and 350mm in length.

Assembly of the Components

The combustion chamber was on four bars of about 15 mm diameter and a height of 85mm each and the bars on the base of the stove body. The stove body was on a base which serves as the base of the whole stove arrangement. An opening cut at the base of the stove body equal to the dimension of air vent. The firebox inserted through this opening and passes through the four bars carrying the combustion chamber. It stopped by a tin sheet at the farthest end of the chamber.

The combustion chamber curved in at the base by 1cm to serve as a sit for the grate. An opening that fitted a briquette perfectly cut both on the body of the stove and the combustion chamber just above the grate to serve as fuel opening. The loading tray joined to the body of the stove at this point. The pot supporting frame joined to the top of the combustion chamber and the corresponding point on the body of the stove. The handle attached to the body of the stove. The full assembled and component parts drawing are shown in figure 1 All necessary welding joints were properly welded and the stove ready to use.