Heat transfer calculations pdf

In principle, only a three- dimensional model can correctly describe the furnace process — in reality, all the equations used so far for describing the furnace process fail to obtain analytical solutions, and only the numerical methods can reach approximate solutions. Even for an approximate solution the amount of calculation is very large—slow or small-capacity computers are not up to the task. The experience method was previously most commonly applied to zero- dimensional models due to a lack of adequate understanding of the furnace process and related mechanisms.

Currently, the semiempirical method is grow- ing in popularity—this method is based on fundamental equations such as the thermal balance equation and radiative heat transfer equation, as well as certain coefficients or factors obtained through experimentation.

This method is primarily based on the energy conservation equation and the radiative heat transfer equation. The thermal balance equation is as follows:. The basic formula for calculating radiation heat transfer is the Stefan—Boltzmann law, which can be conducted in two different ways. Direct calculation of radiation heat the Hottel method as follows:. According to the projected radiation heat transfer the Gurvich method as follows:.

The above formulas are applicable to suspension-firing furnaces, as intro- duced in chapter: Heat Transfer in Fluidized Beds. During calculation in practice, Eq. Of course, this is only a phenomenological description.

In Fig. Assuming that the combustion is complete in a very short period of time, the heat transfer process has not yet started and the combustion products are at their highest pos- sible temperature.

See the following simple empirical formula:. This equation is not particularly convenient to calculate. The typical form of Eq. In Eq. This hypothesis is actu- ally in approximate form—the temperature field of the furnace has different degrees of heterogeneity, and there are heating surfaces at both ends of the flame, therefore, the above empirical equation and its inference can only be applied to qualitative analysis. In other words, it is not appropriate to apply it in quantitative engineering calculations except when validated by industrial tests.

Due to the complexity of the furnace process, the model for average flame temperature must be simplified. The results can only be applied to approximate qualitative analysis, but there is practical significance for this method itself— roughly simplifying a complex process into its most valuable components is very useful in engineering practice. Assume that fuel combusts completely instantaneously at the burner exit and reaches adiabatic combustion temperature Ta, and that heat transfer only occurs in the radial direction of the furnace axis; ignore heat transfer in the axial direc- tion one-dimensional model.

Then, from thermal balance:. Integrate Eq. According to the basic equation of heat transfer in furnaces in Eqs. Another method is also possible. Calculating average flame temperature Tg is a key issue when analyzing fur- nace heat transfer.

Different calculation formulas for Tg are adopted for different methods of calculating furnace heat transfer. All calculation formulas for Tg are empirical equations, including some correction factors.

Consider the two fol- lowing examples. Add a correc- tion factor for combustion conditions to yield the following Gurvich method equation:. Keep in mind several of the methods introduced above, including the theoretical founda- tion of radiative heat transfer, heat radiation of absorbed scattering media, radia- tive heat transfer of surfaces with transparent media, and radiative heat transfer from isothermal media to surfaces. The same basic assumptions uniform sur- face temperature and isothermal medium apply, though in practice, they are not accurate; in a real-world furnace, surface temperature including the water wall is not uniform—even the medium temperature in the furnace is nonuniform.

The following section examines the furnace process when the medium temperature is considered to be nonuniform, with special focus on radiative heat transfer. Heat transfer calculation equations and furnace emissivity were introduced in chapter: Heat Transfer in Fluidized Beds. This chapter introduces average flame temperature Tg, which allows us to obtain the rate of heat transfer. Here, we integrate this content and provide information regarding the acquisition and utilization of some useful empirical coefficients.

The Gurvich method, which is suitable for both suspension-firing and grate-firing furnaces, is introduced below. According to Eq. The following M values are impor- tant please also refer to Table D6. Flame center relative position Xm can be calculated by the following equation:. Average flame temperature is not included in Eq. Based on the radiative heat transfer equation, thermal balance equation, and Eq. Do note that this equation is completely empirical. Under the standard suggested by the former Soviet Union for boiler thermal cal- culation, Eq.

What was the foundation for this scope? From the thermal balance equation:. Bo 1 Tg4 5. Generally, M is not less than 0. The heat transfer in large-capacity boilers should be calculated a little dif- ferently. The Gurvich equation, Eq. The influence of temperature uniformity in the furnace was ignored during data analysis and modeling. When boiler volume is large, Eq. These data can be referred to easily during boiler design.

A few additional instructions are necessary for furnace heat transfer calcula- tion. There are two main goals when performing furnace heat transfer calcula- tions: 1 determining the transfer rate and the heat distribution in each heating surface of the boiler, and 2 solving and choosing the proper furnace outlet gas temperature prior to the slag screen to prevent slagging and tube burst from occurring in the convection heating surface downstream of the furnace exit.

Design and verification calculation Furnace heat transfer calculation is a part of the overall thermal calcula- tion of the boiler. VF is the enclosed volume in terms of the water wall center line or furnace wall when without a water wall. The horizontal plane passing through the half-height of the furnace hopper acts as the bottom boundary of VF for suspension-firing furnaces. AF is the area covering the vol- ume of VF; for grate-firing boilers the fire bed area is included in the total AF.

In China, engineers use the modified version of the Gurvich method to carry out furnace heat transfer calculation. Furnace heat transfer calculation involves the radiative heat transfer from the flame or high-temperature combustion products around the furnace wall. Assume that furnace surface as indicated in Fig.

The emissivity equals the radiative emissiv- ity from the flame to the furnace surface aF. Then, the heat transfer between the flame and furnace surface can be simplified into radiative heat transfer between two parallel infinite planes. According to the heat transfer principle, radiative heat transfer between the flame and furnace surface can be expressed as follows:.

The heat available to furnace Qt can be calculated using the following equation:. The temperature that fuel burns at under adiabatic conditions is the theoreti- cal combustion temperature, denoted by Ta, the value of which can be looked up on the gas enthalpy-temperature table according to the heat available to the furnace Qt.

From Eqs. Therefore, the basic equation for furnace heat balance can be determined based on Eqs. In actuality, flame temperature in the furnace varies along the furnace height. Different researchers have proposed many different calculation methods for av- erage flame temperature. The following equation is recommended for industrial boiler thermal calculation in China:.

Supposing that the ratio of flame temperature and theoretical combustion temperature is nondimensional, denoted by u:. According to experimental data, for a spreader stoker boiler, n is 0. Furnace surface temperature Tw denotes the surface temperature of the water wall tube external ash layer, and is expressed as follows:. Tt is the metal wall temperature of the water wall tube with unit K , which is usually the water saturation temperature at working pressure. See Eq. Coefficient m is used to consider the influence of the water wall deposition layer temperature Tw on furnace heat transfer.

Real-world heat transfer calculation in furnaces is very complicated. The basic steps for calculation using the above method are as follows. Calculate theoretical combustion temperature Ta. Heat Transfer Calculation in Furnaces Chapter 5 Calculate furnace system emissivity aF.

Calculate Boltzmann number Bo. Calculate heat transfer q Q. Here, we would like to emphasize the calculation of aF [see Eq. The above equation can remove the intermediate variable M.

TABLE 5. The enthalpy-temperature table related to the above conditions is shown in Table 5. Ig0 can be determined based on these known variables and their respective Cu. See the following stepwise process for thermal calculation in grate-firing furnaces:. The furnace includes a dense-phase zone also referred to as the bubbling bed and suspen- sion zone. Its structural characteristics involve heating surfaces with immersed tubes in the dense-phase zone Fig.

Heat transfer calculation for this type. Heat transfer calculation in the bubbling bed examines the heat transferred from the fluidized material to the immersed tubes. Design calculation and veri- fication calculation can be applied to this area differently according to different aims. Design calculation is performed according to coal information and boiler parameters to determine fluidization velocity, bed material height usually the height of the overflow port , and the air distributor area.

The immersed tube area is calculated according to the chosen bed material temperature, then the immersed tubes are arranged accordingly. Verification calculation is performed according to an already existing immersed heating surface area and its physi- cal design, as well as coal information and boiler parameters, to calculate bed material temperature.

The equations applied to the burn-out chamber of a grate-firing boiler can also be applied to heat transfer calculation in the suspension zone; the suspen- sion system emissivity can also be calculated according to the system emissivity of a grate-firing furnace. The heat transfer calculation for a BFB boiler back-end heating surface also adopts that of a grate-firing furnace. The BFB boiler is an outdated product that is rarely used in the current in- dustry.

Most commonly used are CFB boilers, so they are the focus of this book. Calculating heat trans- fer in a CFB, to this effect, is far more complex than calculating the same in a grate-firing furnace, BFB, or suspension-firing furnace, in which the material in the gas passes through the furnace only once.

Because CFB technology is now developing, there is as yet no commonly accepted CFB furnace heat transfer calculation method. Besides the basic principles and calculation methods of two-phase flow heat transfer introduced in chapter: Heat Transfer in Fluidized Beds , this section in- troduces a few basic processes and their relationships to heat transfer in CFB fur- naces.

In principle, the contents of this book can be combined with experimental and industrial data for any specific CFB boiler to calculate the heat transfer in CFB furnaces. There will be no detailed calculation method introduced here. In a CFB boiler, the furnace not only undergoes chemical reaction combus- tion and desulfurization , but also the heat exchanging of the gas-solid material with the working medium, as well as the gas-solid circulating in a closed loop.

The following are the basic characteristics of a CFB furnace. The furnace cross section heat release rate is the function of the rate of air flow through the furnace. Generally, for fossil fuels, furnace cross section heat release rate QF has the following approximate relation with superficial gas velocity U The sectional superficial gas velocity is limited somewhat concerning its ability to maintain fast fluidization in the furnace.

The excess air coefficient at the furnace exit of a typical CFB boiler is 1. CFB boiler designers must also consider other factors.

Fuel For design and operation of any boiler, including a CFB boiler, the influ- ence of fuel is crucial. The heating value, proximate analysis, and ultimate analysis data should be known during the preliminary design stage. The fuel heating value and boiler output and efficiency determine the input of the fuel. Proximate analysis of fuel affects the design of the cyclone separa- tor and back-end surfaces, and determines air distribution to some extent.

Better fuel reaction characteristics can improve combustion efficiency. Fuel particles that are large or hard to crush reduce combustion efficiency. The average particle size of the bed material determines the flow dynamic and heat transfer characteristics in the furnace. Further details regarding the influence of fuel properties on CFB boiler design and operation are listed in Table 5. Thermal balance Fuel combusts in the furnace of a CFB boiler.

Arrangements of the heating surface determine the heat distribution in the CFB boiler. As shown in Fig. Thermal balance of boilers can be calculated according to standard boiler thermal calculation methods, but for a CFB boiler that has desulfurization, the thermal effects of desulfurizer calcination and desulfurization reaction must be considered. Mass balance Solid material must be kept in balance during CFB boiler operation.

Solid material sent into the CFB boiler is mainly fuel and desulfurizer with added bed material for some furnaces. The CFB boiler has two ash outlets positioned at the back-end pass and at the furnace bottom, respectively.

Generally, a loop seal or external fluidized bed heat exchanger also discharges a portion of the ash; in addition, at a reversal chamber below the convection shaft some of the ash possibly leaves the system as well. Previous researchers have provided an example of mass balance [33]. There are four ash exits in the system: the furnace, external fluidized bed heat exchanger, convection shaft, and electrostatic precipitator.

The amount of ash and slag discharged from the system can be determined according to the material balance described above. The amount of circulated material is another very critical parameter in the CFB boiler concerning the design of the separator and loop seal, and should be examined in detail during material balance calculations.

According to fuel and the requirements of boiler performance, calculate the air requirement, combustion products, the gas enthalpy-temperature table, and thermal balance to establish the necessary foundation data for thermal calculation in the furnace. This step is largely in accordance with other types of furnaces. The major difference lies in the mass and heat balance caused by material circulation.

Calculate the furnace structural dimensions, including all heating surfaces in the furnace. Determine the furnace outlet gas temperature and conduct the heat transfer calculation.

Cal- culation should be divided into three parts at low loads of the boiler: sup- pose the outlet gas temperature at each zone, set the combustion fraction at each zone, calculate using trial and error, and verify whether the supposed gas temperature at each zone is within the allowable error using the thermal balance method.

At low loads, however, the material circulating rate in the furnace decreases so greatly that the CFB operates like a BFB, thus the dense-zone temperature is much higher than the temperature at the furnace exit. At this time, to obtain the bed temperature, zone calculations are needed and the heat transfer calculation in the dense-phase zone has to be performed separately.

Verify the thermal balance for all heating surfaces in the furnace. As opposed to the BFB boiler, the transition from the dense-phase zone to the dilute-phase zone is not clearly found in the CFB boiler, so their definitions vary.

Generally, the bed height at static state is in the range of 0. Thus, the bed height at the fluidized bed is between 1.

This value varies considerably according to the state of fluidization, so it is best to suggest the elevation of secondary air as a definition boundary. The dense-phase zone is from the air distributor to the lower secondary air, the transitional zone is from the lower secondary air to the upper secondary air, and the dilute-phase zone is from the upper secondary air to the furnace exit.

The calculation of this area is fairly simple, mainly due to the thermal resistance of the fire- resistant layer. The material concentration in this area is very high. In addition, the concentrations of material leaving the dense zone from its upper part and falling into the dense zone along the wall are all high. Calculating the fly ash concentration at the dense-phase zone outlet is a trial and error calculation, that is, the dense-phase outlet gas temperature must be known in order to calculate the heat transfer process.

For this reason, the follow- ing parameters are required to be assumed beforehand: the combustion fraction at dense-phase zone d, the ratio of the amount of falling material to rising mate- rial, and the temperatures of the rising and falling material, which are calculated as follows. The heat input into the dense-phase zone is Qdb:. The heat enthalpy carried by hot slag is:. Transform Eq. The left-hand side of Eq. According to experimental research, the ratio of falling ash and rising ash can be considered 0.

The ash carryover ratio is:. According to the above calculation, the material transfers most of the heat from fuel combustion at the dense-phase zone to the dilute-phase zone. The main pa- rameter that influences this enthalpy is the mass difference and temperature difference of the rising and falling material, as well as the fly ash amount Vfa.

If the exact amount and temperature difference of the rising and falling mate- rial can be accurately determined, ash concentration Cash can be calculated effectively. The above is a verification calculation—the given gas temperature at dense-phase outlet T1 is identified to calculate the material mass concentra- tion Cash.

The known material mass concentration Cash and other parameters can also be utilized to calculate the gas temperature at the dense-phase zone outlet. Calculating heat transfer in the back-end heating surface convection heating surface is also necessary.

These heating surfaces may be quite dis- parate in structure, arrangement, working medium, and gas properties, but their heat transfer process is similar, so heat transfer calculation can be conducted using the same method for all surfaces. The primary goal of convective heat transfer calculation is either to deter- mine the needed heating surface when the heat transfer rate is known, or to de- termine the rate of heat transfer when the heating surface is known.

The heating surface is usually tentatively planned prior to actual calculation. The larger the heat transfer coefficient, the stronger the heat transfer process. Per kg of fuel, the heat transfer equation is:. The heating surface area of the tubular air preheater is calculated according to the average surface area of the gas side and air side. In the thermal balance equation, the heat released by the gas equals the heat absorbed by water, steam, or air.

Heat from the gas to the working medium is:. Working medium absorbed heat can be calculated using the following equation:.

When a slag screen or boiler bank is positioned at the exit of the furnace, if the tube rows are equal to or more than 5, all the radiation heat at the furnace exit is considered absorbed by the tube bundles. If the tube rows are fewer, part of the heat passing through the bundles is absorbed then by the downstream heating surface.

The heat absorbed by air in the air preheater is:. The hot gas and heated working medium do not mix together at either side of the heating surface; heat moves from the hot gas through the tube wall to the working medium. To this effect, the heat transfer process is a com- bination of three separate processes: 1 heat release from hot gas to the outer tube surface, 2 heat conduction through the tube wall from the outer surface to the inner surface, and 3 heat release from the inner tube surface to the fluid.

We know that there are three basic modes of heat transfer: conduction, con- vection, and radiation. In actuality, the heat transfer process is usually a com- bination of these three modes, thus it is very complicated. See the following diagram of the general serial heat transfer process:. Radiation heat transfer can be expressed as follows:.

Conduction heat transfer can be expressed as follows:. See the following three equations for expressions of heat transfer in series through the boiler heating surface discussed above. Heat from hot gas to outer surface of tubes through convection and radiation:. Heat from inner surface of tubes to working medium through convection:. In the above three equations, h1 is the gas side convective heat transfer coef- ficient, h2 is the working medium side heat transfer coefficient, t1 and t2 are gas temperature and working medium temperature, respectively, and tos and tis are outer surface temperature and inner surface temperature of the tubes, respec- tively.

According to the energy conservation principle, during the steady-state pro- cess, the heat transferred in a serial process is equal:. Transform Eqs. In other words, the thermal resistance of all three processes can be expressed by linear superposition. Transform the thermal load mode of Eq.

For boilers, complete thermal calculation is part of the overall heat transfer calculation. In this section, a suspension-firing furnace serves as an example to introduce the thermal calculation of boilers and illustrate the dif- ferences between the grate-firing furnace, fluidized bed, and suspension-firing furnace.

The basic definitions of boiler heating surfaces are first introduced briefly to inform the thermal calculation process provided in the Appendix C. The basic requirement of the boiler proper The function of a boiler is to transfer the heat from fuel combustion to work- ing media through heating surfaces, and heat a low-temperature working medium to high temperatures heating water to steam, for example.

The boiler involves a series of processes including combustion, heat transfer, draft, water circulation, and steam—water separation. The design of a boiler proper is, in effect, the design of heating surfaces.

Thus, due to inherent complexity, strictly theoretical analysis is impossible. Basic equations of heat transfer in flame Fuels burn in the combustion chamber, releasing energy and forming the flame. The basic steady-state energy equation of heat transfer from the flame to the furnace walls is as follows:.

See the following:. The equation also differs from general transport equations due to the complex spatial inte- gral term QR, which is the primary difficulty of the solution. An ana- lytical solution is, by definition, impossible, so numerical methods are com- monly utilized, among which the heat flux method, domain method, and probability simulation method are most popular. Mathematical model of heat transfer in the furnace The heat flux method, domain method, and probability simulation method are all numerical methods of calculating the heat transfer rate of radiation in a furnace.

The models these methods are based on are incomplete, however, as they only describe the principles the temperature field must obey and require information to be given such as flow field, heat source distribution, and physical parameters. Continuity equation: law of conservation of mass. Energy equation: law of conservation of energy. Chemical balance equation: law of conservation and transformation of chemical species.

All these equations can be represented in a unified form as follows:. Each model may provide solutions for distributions of temperature, velocity, pressure, and chemical species concentration in the furnace, fully describing the characteristics of heat and mass transfer and chemical reactions. However, as mentioned above, the process of solving these equations is so complex that numerical methods are used instead to obtain an acceptable approximation. Simplified models based on data gath- ered through engineering experience empirical coefficients, in particular are usually adopted for technical applications.

Empirical methods also attribute uncertainty to one or several factors, including the heat transfer coefficient, thermal effective coefficient, and others. Calculation is always based on some basic theories, of course postulates, assumptions, laws, theorems, etc. Furnace heat transfer calculations are more empirical. The following section outlines a handful of useful calculations for classification based on spatial dimensions. There are zero-dimensional, one-dimensional, two-dimensional, and three- dimensional models available for application to furnace heating calculation.

In a zero-dimensional model, all physical quantities within the furnace are uniform and the results are averaged. This method is the one most often used for engi- neering design, and is the standard method for thermal calculation in China.

One-dimensional models are used to study changes in the physical quantities along the axis height of the furnace, where the physical quantity in the perpen- dicular plane is uniform.

This model has practical value for engineering projects such as large-capacity boilers. The two-dimensional model is mainly used for axisymmetric cylindrical furnaces, such as vertical cyclone furnaces. The three-dimensional model de- scribes the furnace process flow, temperature, chemical species fields, and so on , using three-dimensional coordinates x, y, z. In principle, only a three- dimensional model can correctly describe the furnace process — in reality, all the equations used so far for describing the furnace process fail to obtain analytical solutions, and only the numerical methods can reach approximate solutions.

Even for an approximate solution the amount of calculation is very large—slow or small-capacity computers are not up to the task. The experience method was previously most commonly applied to zero- dimensional models due to a lack of adequate understanding of the furnace process and related mechanisms.

Currently, the semiempirical method is grow- ing in popularity—this method is based on fundamental equations such as the thermal balance equation and radiative heat transfer equation, as well as certain coefficients or factors obtained through experimentation.

This method is primarily based on the energy conservation equation and the radiative heat transfer equation. The thermal balance equation is as follows:.

The basic formula for calculating radiation heat transfer is the Stefan—Boltzmann law, which can be conducted in two different ways. Direct calculation of radiation heat the Hottel method as follows:. According to the projected radiation heat transfer the Gurvich method as follows:. The above formulas are applicable to suspension-firing furnaces, as intro- duced in chapter: Heat Transfer in Fluidized Beds.

During calculation in practice, Eq. Of course, this is only a phenomenological description. In Fig. Assuming that the combustion is complete in a very short period of time, the heat transfer process has not yet started and the combustion products are at their highest pos- sible temperature.

See the following simple empirical formula:. This equation is not particularly convenient to calculate. The typical form of Eq. In Eq. This hypothesis is actu- ally in approximate form—the temperature field of the furnace has different degrees of heterogeneity, and there are heating surfaces at both ends of the flame, therefore, the above empirical equation and its inference can only be applied to qualitative analysis.

In other words, it is not appropriate to apply it in quantitative engineering calculations except when validated by industrial tests. Due to the complexity of the furnace process, the model for average flame temperature must be simplified. The results can only be applied to approximate qualitative analysis, but there is practical significance for this method itself— roughly simplifying a complex process into its most valuable components is very useful in engineering practice.

Assume that fuel combusts completely instantaneously at the burner exit and reaches adiabatic combustion temperature Ta, and that heat transfer only occurs in the radial direction of the furnace axis; ignore heat transfer in the axial direc- tion one-dimensional model.

Then, from thermal balance:. Integrate Eq. According to the basic equation of heat transfer in furnaces in Eqs. Another method is also possible.

Calculating average flame temperature Tg is a key issue when analyzing fur- nace heat transfer. Different calculation formulas for Tg are adopted for different methods of calculating furnace heat transfer.

All calculation formulas for Tg are empirical equations, including some correction factors. Consider the two fol- lowing examples. Add a correc- tion factor for combustion conditions to yield the following Gurvich method equation:. Keep in mind several of the methods introduced above, including the theoretical founda- tion of radiative heat transfer, heat radiation of absorbed scattering media, radia- tive heat transfer of surfaces with transparent media, and radiative heat transfer from isothermal media to surfaces.

The same basic assumptions uniform sur- face temperature and isothermal medium apply, though in practice, they are not accurate; in a real-world furnace, surface temperature including the water wall is not uniform—even the medium temperature in the furnace is nonuniform. The following section examines the furnace process when the medium temperature is considered to be nonuniform, with special focus on radiative heat transfer.

Heat transfer calculation equations and furnace emissivity were introduced in chapter: Heat Transfer in Fluidized Beds. This chapter introduces average flame temperature Tg, which allows us to obtain the rate of heat transfer. Here, we integrate this content and provide information regarding the acquisition and utilization of some useful empirical coefficients.

The Gurvich method, which is suitable for both suspension-firing and grate-firing furnaces, is introduced below. According to Eq. The following M values are impor- tant please also refer to Table D6. Flame center relative position Xm can be calculated by the following equation:. Average flame temperature is not included in Eq. Based on the radiative heat transfer equation, thermal balance equation, and Eq. Do note that this equation is completely empirical. Under the standard suggested by the former Soviet Union for boiler thermal cal- culation, Eq.

What was the foundation for this scope? From the thermal balance equation:. Bo 1 Tg4 5. Generally, M is not less than 0. The heat transfer in large-capacity boilers should be calculated a little dif- ferently. The Gurvich equation, Eq. The influence of temperature uniformity in the furnace was ignored during data analysis and modeling.

When boiler volume is large, Eq. These data can be referred to easily during boiler design. A few additional instructions are necessary for furnace heat transfer calcula- tion. There are two main goals when performing furnace heat transfer calcula- tions: 1 determining the transfer rate and the heat distribution in each heating surface of the boiler, and 2 solving and choosing the proper furnace outlet gas temperature prior to the slag screen to prevent slagging and tube burst from occurring in the convection heating surface downstream of the furnace exit.

Design and verification calculation Furnace heat transfer calculation is a part of the overall thermal calcula- tion of the boiler. VF is the enclosed volume in terms of the water wall center line or furnace wall when without a water wall. The horizontal plane passing through the half-height of the furnace hopper acts as the bottom boundary of VF for suspension-firing furnaces.

AF is the area covering the vol- ume of VF; for grate-firing boilers the fire bed area is included in the total AF. In China, engineers use the modified version of the Gurvich method to carry out furnace heat transfer calculation. Furnace heat transfer calculation involves the radiative heat transfer from the flame or high-temperature combustion products around the furnace wall. Assume that furnace surface as indicated in Fig. The emissivity equals the radiative emissiv- ity from the flame to the furnace surface aF.

Then, the heat transfer between the flame and furnace surface can be simplified into radiative heat transfer between two parallel infinite planes. According to the heat transfer principle, radiative heat transfer between the flame and furnace surface can be expressed as follows:.

The heat available to furnace Qt can be calculated using the following equation:. The temperature that fuel burns at under adiabatic conditions is the theoreti- cal combustion temperature, denoted by Ta, the value of which can be looked up on the gas enthalpy-temperature table according to the heat available to the furnace Qt.

From Eqs. Therefore, the basic equation for furnace heat balance can be determined based on Eqs. In actuality, flame temperature in the furnace varies along the furnace height. Different researchers have proposed many different calculation methods for av- erage flame temperature.

The following equation is recommended for industrial boiler thermal calculation in China:. Supposing that the ratio of flame temperature and theoretical combustion temperature is nondimensional, denoted by u:. According to experimental data, for a spreader stoker boiler, n is 0. Furnace surface temperature Tw denotes the surface temperature of the water wall tube external ash layer, and is expressed as follows:.

Tt is the metal wall temperature of the water wall tube with unit K , which is usually the water saturation temperature at working pressure. See Eq. Coefficient m is used to consider the influence of the water wall deposition layer temperature Tw on furnace heat transfer.

Real-world heat transfer calculation in furnaces is very complicated. The basic steps for calculation using the above method are as follows. Calculate theoretical combustion temperature Ta.

Heat Transfer Calculation in Furnaces Chapter 5 Calculate furnace system emissivity aF. Calculate Boltzmann number Bo.

Calculate heat transfer q Q. Here, we would like to emphasize the calculation of aF [see Eq. The above equation can remove the intermediate variable M. TABLE 5. The enthalpy-temperature table related to the above conditions is shown in Table 5. Ig0 can be determined based on these known variables and their respective Cu. See the following stepwise process for thermal calculation in grate-firing furnaces:. The furnace includes a dense-phase zone also referred to as the bubbling bed and suspen- sion zone.

Its structural characteristics involve heating surfaces with immersed tubes in the dense-phase zone Fig. Heat transfer calculation for this type. Heat transfer calculation in the bubbling bed examines the heat transferred from the fluidized material to the immersed tubes. Design calculation and veri- fication calculation can be applied to this area differently according to different aims.

Design calculation is performed according to coal information and boiler parameters to determine fluidization velocity, bed material height usually the height of the overflow port , and the air distributor area. The immersed tube area is calculated according to the chosen bed material temperature, then the immersed tubes are arranged accordingly.

Verification calculation is performed according to an already existing immersed heating surface area and its physi- cal design, as well as coal information and boiler parameters, to calculate bed material temperature. The equations applied to the burn-out chamber of a grate-firing boiler can also be applied to heat transfer calculation in the suspension zone; the suspen- sion system emissivity can also be calculated according to the system emissivity of a grate-firing furnace.

The heat transfer calculation for a BFB boiler back-end heating surface also adopts that of a grate-firing furnace. The BFB boiler is an outdated product that is rarely used in the current in- dustry.

Most commonly used are CFB boilers, so they are the focus of this book. Calculating heat trans- fer in a CFB, to this effect, is far more complex than calculating the same in a grate-firing furnace, BFB, or suspension-firing furnace, in which the material in the gas passes through the furnace only once. Because CFB technology is now developing, there is as yet no commonly accepted CFB furnace heat transfer calculation method.

Besides the basic principles and calculation methods of two-phase flow heat transfer introduced in chapter: Heat Transfer in Fluidized Beds , this section in- troduces a few basic processes and their relationships to heat transfer in CFB fur- naces. In principle, the contents of this book can be combined with experimental and industrial data for any specific CFB boiler to calculate the heat transfer in CFB furnaces.

There will be no detailed calculation method introduced here. In a CFB boiler, the furnace not only undergoes chemical reaction combus- tion and desulfurization , but also the heat exchanging of the gas-solid material with the working medium, as well as the gas-solid circulating in a closed loop. The following are the basic characteristics of a CFB furnace. The furnace cross section heat release rate is the function of the rate of air flow through the furnace.

Generally, for fossil fuels, furnace cross section heat release rate QF has the following approximate relation with superficial gas velocity U The sectional superficial gas velocity is limited somewhat concerning its ability to maintain fast fluidization in the furnace. The excess air coefficient at the furnace exit of a typical CFB boiler is 1.

CFB boiler designers must also consider other factors. Fuel For design and operation of any boiler, including a CFB boiler, the influ- ence of fuel is crucial.

The heating value, proximate analysis, and ultimate analysis data should be known during the preliminary design stage. The fuel heating value and boiler output and efficiency determine the input of the fuel. Proximate analysis of fuel affects the design of the cyclone separa- tor and back-end surfaces, and determines air distribution to some extent. Better fuel reaction characteristics can improve combustion efficiency. Fuel particles that are large or hard to crush reduce combustion efficiency.

The average particle size of the bed material determines the flow dynamic and heat transfer characteristics in the furnace. Further details regarding the influence of fuel properties on CFB boiler design and operation are listed in Table 5. Thermal balance Fuel combusts in the furnace of a CFB boiler. Arrangements of the heating surface determine the heat distribution in the CFB boiler.

As shown in Fig. Thermal balance of boilers can be calculated according to standard boiler thermal calculation methods, but for a CFB boiler that has desulfurization, the thermal effects of desulfurizer calcination and desulfurization reaction must be considered.

Mass balance Solid material must be kept in balance during CFB boiler operation. Solid material sent into the CFB boiler is mainly fuel and desulfurizer with added bed material for some furnaces. The CFB boiler has two ash outlets positioned at the back-end pass and at the furnace bottom, respectively. Generally, a loop seal or external fluidized bed heat exchanger also discharges a portion of the ash; in addition, at a reversal chamber below the convection shaft some of the ash possibly leaves the system as well.

Previous researchers have provided an example of mass balance [33]. There are four ash exits in the system: the furnace, external fluidized bed heat exchanger, convection shaft, and electrostatic precipitator.

The amount of ash and slag discharged from the system can be determined according to the material balance described above. The amount of circulated material is another very critical parameter in the CFB boiler concerning the design of the separator and loop seal, and should be examined in detail during material balance calculations.

According to fuel and the requirements of boiler performance, calculate the air requirement, combustion products, the gas enthalpy-temperature table, and thermal balance to establish the necessary foundation data for thermal calculation in the furnace. This step is largely in accordance with other types of furnaces.

The major difference lies in the mass and heat balance caused by material circulation. Calculate the furnace structural dimensions, including all heating surfaces in the furnace. Determine the furnace outlet gas temperature and conduct the heat transfer calculation. Cal- culation should be divided into three parts at low loads of the boiler: sup- pose the outlet gas temperature at each zone, set the combustion fraction at each zone, calculate using trial and error, and verify whether the supposed gas temperature at each zone is within the allowable error using the thermal balance method.

At low loads, however, the material circulating rate in the furnace decreases so greatly that the CFB operates like a BFB, thus the dense-zone temperature is much higher than the temperature at the furnace exit. At this time, to obtain the bed temperature, zone calculations are needed and the heat transfer calculation in the dense-phase zone has to be performed separately.

Verify the thermal balance for all heating surfaces in the furnace. As opposed to the BFB boiler, the transition from the dense-phase zone to the dilute-phase zone is not clearly found in the CFB boiler, so their definitions vary.

Generally, the bed height at static state is in the range of 0. Thus, the bed height at the fluidized bed is between 1. This value varies considerably according to the state of fluidization, so it is best to suggest the elevation of secondary air as a definition boundary. The dense-phase zone is from the air distributor to the lower secondary air, the transitional zone is from the lower secondary air to the upper secondary air, and the dilute-phase zone is from the upper secondary air to the furnace exit.

The calculation of this area is fairly simple, mainly due to the thermal resistance of the fire- resistant layer. The material concentration in this area is very high. In addition, the concentrations of material leaving the dense zone from its upper part and falling into the dense zone along the wall are all high. Calculating the fly ash concentration at the dense-phase zone outlet is a trial and error calculation, that is, the dense-phase outlet gas temperature must be known in order to calculate the heat transfer process.

For this reason, the follow- ing parameters are required to be assumed beforehand: the combustion fraction at dense-phase zone d, the ratio of the amount of falling material to rising mate- rial, and the temperatures of the rising and falling material, which are calculated as follows. The heat input into the dense-phase zone is Qdb:.

The heat enthalpy carried by hot slag is:. Transform Eq. The left-hand side of Eq. According to experimental research, the ratio of falling ash and rising ash can be considered 0. The ash carryover ratio is:. According to the above calculation, the material transfers most of the heat from fuel combustion at the dense-phase zone to the dilute-phase zone.

The main pa- rameter that influences this enthalpy is the mass difference and temperature difference of the rising and falling material, as well as the fly ash amount Vfa. If the exact amount and temperature difference of the rising and falling mate- rial can be accurately determined, ash concentration Cash can be calculated effectively. The above is a verification calculation—the given gas temperature at dense-phase outlet T1 is identified to calculate the material mass concentra- tion Cash.

The known material mass concentration Cash and other parameters can also be utilized to calculate the gas temperature at the dense-phase zone outlet. Calculating heat transfer in the back-end heating surface convection heating surface is also necessary. These heating surfaces may be quite dis- parate in structure, arrangement, working medium, and gas properties, but their heat transfer process is similar, so heat transfer calculation can be conducted using the same method for all surfaces.

The primary goal of convective heat transfer calculation is either to deter- mine the needed heating surface when the heat transfer rate is known, or to de- termine the rate of heat transfer when the heating surface is known. The heating surface is usually tentatively planned prior to actual calculation. The larger the heat transfer coefficient, the stronger the heat transfer process. Per kg of fuel, the heat transfer equation is:.

The heating surface area of the tubular air preheater is calculated according to the average surface area of the gas side and air side. In the thermal balance equation, the heat released by the gas equals the heat absorbed by water, steam, or air.