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## Flues and Chimneys

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**Flues and Chimneys**朱信 Hsin Chu Professor Dept. of Environmental Engineering National Cheng Kung University**1. Functions of the Flue System**• The function of the flue in combustion equipment can be summarized quite simply: it is for the safe and effective disposal of the products of combustion. • This focuses on two considerations, namely bringing the products of combustion to the outlet of the flue at the required conditions (such as temperature and velocity), and ensuring that the location of this outlet is such that the environmental impact of the discharge is controlled.**There are two ways in which the dispersal of the combustion**products can be effected. • If the fuel has a very low sulfur content (such as natural gas) then it is often possible to dilute the products of combustion with ambient air and to discharge the diluted mixture at a low level.**This may be desirable economically as it avoids the need to**construct a high-level discharge, or it might be aesthetically appealing if the presence of a chimney, either outside the building or appearing at the rooftop, is thought to be undesirable. • The majority of flue systems discharge the combustion products at a high level via a flue or chimney.**Contemporary chimneys are generally of circular**cross-section and are of metal fabrication. • An important consideration in chimney design not discussed here is the wind loads imposed on the structure, which can be carried by the fabric of the chimney itself or by external bracing such as fins or wires.**In addition to the steady-state loads on a chimney,**vibrations can be induced by the regular shedding of vortices from the cylindrical surface (the same mechanism which causes telephone wires to hum). • The spiral “strakes” which are often attached to the upper part of a chimney are there to reduce this effect.**The force for moving the flue gas within the system can come**from the buoyancy of the hot gas within the flue, from external fan power or from a combination of both. • In addition to maintaining the correct flow rate of gas through the flue it is essential to maintain the temperature of the gas within the flue system above the water vapor dew point, or the acid dew point if a high sulfur content fuel is being burned.**In terms of mechanisms, we are interested in the heat**transfer and fluid flow performance of the flue, recognizing that both these considerations must be integrated in the engineering design of the flue system.**2. Chimney Heat Transfer**2.1 Heat Transfer Mechanism • The rate of heat transfer affects the temperatures in the system, which in turn determine the safety margin in respect of possible corrosion problems, and also the pressure difference due to buoyancy forces, known as the chimney draught.**The most common situation is where the temperature,**composition and flow rate of the gas entering the flue are known, and the objective is to find the temperature of the gas as it is discharged from the flue.**The approach adopted here is to consider the flue in**classical heat exchanger terms. • This approach involves two stages: evaluating an overall thermal conductance (U-value) followed by an analysis of the performance of the flue, taking into account the flows of the system fluids (flue gas and ambient air).**2.2 U-value of a Chimney**• Consider the cross-section sketch of a chimney wall shown in Fig. 11.1 (next slide).There are three sequential stages in the steady-state heat transfer process:(1) Convective heat transfer from the hot flue gas to the inside surface of the chimney.**(2) Heat transfer between the inside and outside surfaces**of the chimney. If the chimney is of solid construction, the mechanism for this will be conduction. If there is an air gap present, then a combined mode of heat transfer (conduction/convection together with radiation) will be operating.**(3) Convective heat transfer from the outside surface of**the chimney to the ambient air. Under still air conditions this will be by natural convection, but in general the action of wind will induce forced convection from the chimney.**These processes can be represented thus: Q = hiAi(tg-tsi) Q**= hfAf(tsi-tso) (1) Q = hoAo(tso-to)where Q is the heat flux (W) h is the heat transfer coefficient (W/m2/K) A is the area (m2) t is the temperature (℃)Subscripts: f: fabric g: gas i: inside o: outside s: skin**In equation (1) the heat transfer across the fabric has been**expressed in terms of a fabric heat transfer coefficient, hf, and a cross-sectional area, Af, over which this operates. • The contributory terms to (hfAf) depend on the construction of the chimney, as will be shown later.**The above equations can be summarized giving: (2)**• The rate of heat transfer is conventionally represented in the form: Q = UoAo (tg-to) (3)where Uo represents the overall heat transfer coefficient for the exchanger and Ao represents the area which is associated with it.**Any of the three area Ai, Af or Ao could be used for this**purpose, but here the outside surface area of the chimney (the largest of the three) has been used. • An expression for the overall U-value of the chimney is obtained by dividing equation (2) by equation (3): (4)**If the chimney is of circular cross-section and does not**have an appreciable taper, the areas in the above expression are given by:where L is the length (height) of the chimney.**If the thickness of the insulation/fabric is small compared**with the radius, then equation (4) simplifies to that of one-dimensional heat transfer with all the areas being equal. • The expression for the U-value is then: (5)where k is the thermal conductivity of the gas.**Above expression is generally sufficiently accurate for most**practical purposes. • For convenience, we can replace (ro- ri) with x, the thickness of the fabric layer.**The thermal resistance of the fabric layer is then:**• For a composite construction of n layers, the total thermal resistance is found by adding up the individual layer resistances:**A common configuration for chimneys of less than 15 m height**is to have an outer skin of aluminum alloy, with a low-emissivity surface, combined with a steel inner lining with an air gap of around 6 mm between the two metals. • The heat transfer across an air gap is affected by the emissivity of the surfaces and the width of the gap.**In general, the thermal resistance of an air gap increases**with its width, but the value remains substantially constant at separations greater than 20 mm. • The following values can be taken:Low emissivity surface High emissivity6 mm 0.18 0.120 mm+ 0.35 0.18the units being K/m2/W.**To evaluate equation (5), values are needed for the inside**and outside surface coefficients of heat transfer, together with the thermal resistance of the chimney fabric and a means of estimating its effective heat transfer area.**Inside Surface Coefficient**• The flow of gas in the chimney may well be driven by buoyancy forces, but these are generated by the difference in density between the hot flue gas and the ambient air. • Under these circumstances the contribution to the buoyancy force provided by the difference in temperature between the flue gas and the inside surface of the chimney will be very small, and heat transfer from the gas to the chimney inside surface will take place by forced convection.**The flue gas flow regime (whether the flow is laminar,**transitional or turbulent) is indicated by the value of Reynolds number:Re = vdi/νwhere ν is the kinematic viscosity of the flue gas.**For a circular cross-section the characteristic dimension d**is given by the diameter of the chimney. • To get some perspective on this situation we can take a range of diameters between 0.25 m and 2 m, and consider the applicable range of flue gas velocity (v) to be between 6 m/s and 20 m/s.**The kinematic viscosity of a gas varies with temperature,**and, although values for individual gases are readily available, it is not possible to calculate accurately the viscosity of a mixture from the values and volume fractions of its constituents. • The estimated kinematic viscosity of a flue gas resulting from the combustion of a natural gas with 20% excess air is compared with the values for air in Table 11.1 (next slide).**At a temperature of t ℃ the kinematic viscosity of air is**approximated by:ν= (0.1335 + 0.925×10-3 t)10-4 m2/s (7) giving a value at 200℃ of 0.000032 m2/s.**The Reynolds number for a flue gas velocity of 9 m/s in a**chimney of 750 mm diameter is thus:which is well into the turbulent regime.**The emissivity of the flue gas is low, hence the predominant**mode of heat transfer is forced convection. A relationship for forced convection from a turbulent gas flow inside a cylindrical tube is : Nu = 0.023 Re0.8 Pr0.4 (6)where the Nusselt number, Nu, is given by:and the prandtl number, Pr, by**Most gases have a value of Pr of about 0.74, and this value**is substantially independent of temperature, hence equation (6) simplifies to; Nu = 0.02 Re0.8and the coefficient of heat transfer is obtained knowing the diameter of the tube, d, and the thermal conductivity of the gas, k.**Once again, a value for k for the gas mixture could be**estimated from a knowledge of the individual gas properties and the mixture composition. • Here it is also an acceptable approximation to use values for air. • The thermal conductivity of air can be obtained from: kair = 0.02442 + 0.6992×10-4 t W/m/Kwhere t is the temperature in ℃. At 200℃ this gives a value of 0.0384 W/m/K.**Example 1:Estimate the internal coefficient of heat transfer**in a 500 mm diameter chimney. The flue gas velocity is 10 m/s and the gas temperature 250℃. • Solution:Start by working out the gas kinematic viscosity and thermal conductivity:ν=(0.1335+0.925×10-3×250) ×10-4=3.64×10-5 m2/s**k=0.02442+0.6992×10-4×250=0.0419 W/m/K**• The Nusselt number, Nu, isNu=0.02×(1.37×105)0.8=257**The coefficient of heat transfer:**• An approximate value of hi can be obtained more quickly from Fig. 11.2 (next slide), where values of hi × di (internal film coefficient × chimney diameter) are plotted as a function of v × di (flue gas velocity × chimney diameter) for flue gas temperatures ranging from 100 to 300℃.**For the above example v × di=10×0.5=5 m2/s, giving a value**of hi × di from the graph at 250℃ of 10.8 W/m/K, resulting in an estimated value of:**Outside Surface Coefficient**• The heat transfer processes taking place on the outside surface of the chimney are rather more complex than is the case for the inside surface coefficient. • Radiation heat transfer does have a part to play-the surface of the chimney will exchange heat by radiation to the surrounding environment, and the convective heat loss will be affected by the prevailing wind speed.**In calm conditions, the convective heat transfer from the**outside surface of the chimney will be by natural convection. • As the wind velocity increases, forced convection will become the dominant mechanism.**A chimney exposed to the wind approximates to a cylinder**with its axis at right-angles to the direction of the flow. • The relevant heat transfer relationship, valid for Reynolds numbers between 103 and 105 is:**Assuming a constant value for Prandtl number for air of**0.74, this expression simplifies to: (8) • In this case the Reynolds and Nusselt numbers refer to the outside diameter, do, of the chimney.The outside convective heat transfer coefficient is then given by:**For the case of forced convection the temperature of the air**has only a small effect on the value of ho, and Fig. 11.3 (next slide) shows the variation of hc,o with windspeed for a range of chimney outside diameters.**Example 2:Estimate the outside convective heat transfer**coefficient for a 750 mm diameter chimney exposed to a wind of 10 m/s.Assume the air temperature to be 5℃. • Solution:At 5℃ the kinematic viscosity of air from equation (7) is:ν = (0.1335+0.925×10-3×5)10-4 = 0.0000138 m2/s**The Reynolds number is then:**• Nu =0.024(5.43×105)0.6 (from equation (8)) =662.4**The thermal conductivity of air at 5℃ is:k =**0.02442+(0.6992×10-4×5) = 0.0248 W/m/K • giving an outside convective film coefficient of

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