Intermediate heat carriers have been applied in engineering as enhanced heat transfer elements, but their theoretical analysis still needs to be improved. Therefore, an intermediate heat carrier is added to establish the quaternary model of the furnace gas under nongray radiation characteristics. Based on this model, an analytical expression of heat flux on the surface of the billet is derived. General rule of the impact of intermediate heat carrier on the thermal efficiency in the furnace can be properly derived by analytical calculation from a theoretical point of view. The results show that the longer the length of the intermediate heat carrier located at the top of the furnace, the greater the heat exchange capacity on the surface of the billet. Meanwhile, when the intermediate heat carrier is located in the center of the furnace top, the billet gets higher heat flux; the closer to both sides, the lower the heat flux. In addition, the influence that the surface emissivity of the intermediate heat carrier has on the heat transfer of the billet surface is related to the values of
In order to reduce carbon dioxide emissions from iron and steel enterprises and improve the thermal efficiency of heating furnace, increasing radiation from furnace wall is an effective method that needs more attention [
Due to the complexity of the radiation situation in the furnace, the previous research on the heating furnace with intermediate heat carriers was carried out through experiments, so its theoretical analysis still needs to be improved. As a result, there is no theoretical basis for the optimum structure, surface radiation characteristics, and installation position of the intermediate radiator, and no clear method can be found to regulate the temperature through the intermediate radiator. By theoretical calculation, the general rule of radiation heat transfer in the furnace can be obtained without consuming substantial experimental costs.
The development of industry needs to consume a lot of energy. For example, the energy for metal heating and glass melting mainly comes from the combustion of fossil fuels [
Energy-saving effect of the heating furnace can be effectively improved by enhancing the heat transfer in the furnace. Generally speaking, the radiation heat transfer system in the heating furnace can be considered as a ternary system [
In a ternary system, the furnace wall is designed to reflect (or reradiate) the energy radiated by furnace gas to material [
On the basis of the heating furnace with nongray radiation characteristics of furnace gas established by Yi et al. [
Due to the complexity of the heating process in the furnace, in order to obtain the analytical expression of the heat transfer process in the furnace with an intermediate heat carrier, the following simplifications should be made: The radiation heat transfer between the model sections was ignored, and it was considered that the radiation heat transfer occurs only inside each model section. The temperature distribution along the furnace width is assumed to be uniform in each model section. The impact of factors, such as oxidation burning loss, on heat transfer during the heating process is neglected. Both the furnace wall and billet is regarded as diffuse gray bodies, while the furnace gas has nongray characteristics. Because of the high temperature in the furnace, radiation is the main form of heat transfer in the furnace. In this study, the convective heat exchange between the furnace gas and the billet as well as that between the furnace gas and the furnace wall are neglected. For the coupled calculation of radiation and convective heat transfer, more details can be found in references [
On this basis, a one-zone quaternary radiation heat transfer model was established. Quaternary radiation heat transfer model is a simplified model of zonal method model, each zone of which is composed of furnace gas, intermediate heat carrier, heated billet, and furnace wall (furnace wall and furnace top). There is no radiation heat exchange in the length direction of furnace and the temperature is uniform along the width direction of furnace, so the section perpendicular to the length direction of furnace was taken for the analysis of radiation heat transfer, as shown in Figure
Section diagram of heating furnace with intermediate heat carrier. 1. Intermediate heat carrier. 2. Billet. 3. Furnace wall. 4. Furnace gas.
In this study, the temperature of billet and furnace gas was given, so that the energy equation of furnace gas can be disregarded; thus, the calculation [
The flue gas in the furnace was assumed to be isothermal with uniform density. Therefore, the zonal method was adopted, and heat flux variation [
Figure
Two-dimensional diagram of furnace with intermediate heat carrier.
According to the given size of the heating furnace, it can be obtained that
According to the geometric shape shown in Figure
According to the integrity of the angle factor, it can be obtained that
According to the relativity of the angle factor, it can be obtained that
Similarly, according to the relativity and integrity of the angular coefficient, it can be obtained that
By substituting the angular coefficient and the area of each part in the furnace into the calculation of the radiation exchange area [
The calculation of the direct exchange area is a main step in the zonal method. In this study, due to the uniform and equal surface temperature distribution of gas, furnace wall, and billet, the direct exchange area was calculated as follows.
When gas
When billet
When furnace wall
When the intermediate heat carrier
Next, the reflected heat flux density [
The calculation formulas of total exchange area
When the furnace environment is in a steady state, the energy equation of the inner surface of the furnace wall is as follows:
After arrangement, the fourth-power formula of furnace wall temperature can be obtained:
Because the added intermediate heat carrier was actually used as the expansion surface of the furnace wall, the temperature of the intermediate heat carrier can be set to be the same as that of the furnace wall:
By substituting it into the above equation, it can be obtained that
Similarly, the energy equation of the billet surface can be expressed as follows:
In this article, the expression of heat flux on the surface of billet was calculated and obtained under the condition of nongray furnace gas, and there was an intermediate heat carrier on the top of the furnace. When the nongray characteristic of the furnace gas is not taken into account, that is, the length of the intermediate heat carrier
This formula is the Τимофеев formula which is an important analytical formula for studying the thermal process of a furnace and also the basic formula for analytic calculation of furnace by scholars. Thus, the correctness of the formula derived from this study can also be proved from this perspective.
Next, by using computer programming calculation, the impact on heat flux in furnace with intermediate heat carrier can be discussed.
As mentioned above, the impact of intermediate heat carrier on theoretical analysis of surface heat exchange capacity of billet is unknown yet. Therefore, the length, position, and surface emissivity of the intermediate heat carrier are studied, and the impact of the intermediate heat carrier on the enhancement of heat transfer in the furnace is discussed in this article. The size of the furnace is set to
The variation of heat exchange capacity of billet with the length of intermediate heat carrier at different temperatures is studied, as shown in Figure
Variation curve of heat exchange capacity of billet with length of heat carrier at different temperatures. 1.
The furnace width direction is taken as abscissa (
Schematic diagram of heat carrier at different positions on furnace top. 1. Intermediate heat carrier. 2. Billet. 3. Furnace wall. 4. Furnace gas.
It can be seen from Figures
Variation curve of
When the emissivity of furnace gas and absorptivity of furnace wall were given at three different temperatures, the impact of emissivity variation of heat carrier at the center of furnace top on the heat exchange capacity
It can be seen from Figure
In case of
It can be seen from Figure
In case of
It can be seen from Figure
In case of
From the above three figures, it can be concluded that, in case of
In this article, an intermediate heat carrier with length of 0.5 m was added at the center of the furnace top. The value of
As can be seen from Figure
Comparison between the model in this article and that in literature when
The heat transfer from the wall to the billet is shown in Figure
As can be seen from Figures
Comparisons between the model in this article and that in literature for
It can be seen from Figure
It can be seen from Figures
In case of
It can be seen from Figure
In this study, a one-zone quaternary system model in the furnace with an intermediate heat carrier is established to derive the impact of length, position, and emissivity of the heat carrier on heat exchange capacity of the billet surface, and a conclusion by comparing with the literature data is summarized.
From the analysis, it can be seen that the longer the intermediate heat carrier located at the top of the furnace, the larger the heat exchange capacity on the billet surface. Thus, the length of the heat carrier can be increased as much as possible in the maximum allowable space of the furnace to obtain higher heat flux. The position of the intermediate heat carrier also affects the heat flux on the billet surface. When the heat carrier is located in the center of the furnace top, the billet gets higher heat flux, and the closer it is to the two sides, the lower the heat flux is. In the actual layout of the heat carrier on the furnace top, the heat carrier should be arranged in the center of the furnace top when possible. At the same time, in the case of
In summary, the addition of the intermediate heat carrier has a positive impact on the heat exchange capacity of the billet surface. However, in practical application, the impact of length, position, and emissivity of the heat carrier should be taken into account for better heat transfer enhancement effect in a furnace.
Slab
Furnace wall
Flue gas
Intermediate heat carrier
Area (m2)
Length of the intermediate radiator (m)
Furnace weight (m)
Furnace height (m)
Temperature (K)
Heat loss to the environment through
Heat flow of
Heat flow of
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from the wall and arrives at the slab; meanwhile, the gas is the only radiation source in the system (m2)
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Direct exchange area when energy radiates from
Angle factor of the
Angle factor of
Angle factor of
Angle factor of
Angle factor of
Emissivity
Absorptivity of
Absorptivity of
Absorptivity of
Absorptivity of gas when the radiation energies derive from
Total radiative exchange area of
Total radiative exchange area of
Total radiative exchange area of
Total radiative exchange area of
Total radiative exchange area of
Total radiative exchange area of
Total radiative exchange area of
Total radiative exchange area of
Total radiative exchange area of
Total radiative exchange area of
Total radiative exchange area of
total radiative exchange area of
Total radiative exchange area of
Reflected heat flux when the radiation energies radiate from
Reflected heat flux when the radiation energies radiate from the
Reflected heat flux when the radiation energies radiate from
Reflected heat flux when the radiation energies radiate from
Reflected heat flux when the radiation energies radiate from
Reflected heat flux when the radiation energies radiate from
Reflected heat flux when the radiation energies radiate from
reflected heat flux when the radiation energies radiate from
Reflected heat flux when the radiation energies radiate from
Reflected heat flux when the radiation energies radiate from
Reflected heat flux when the radiation energies radiate from
Reflected heat flux when the radiation energies radiate from
The data used to support the findings of this study are included within the article.
The authors declare that they have no conflicts of interest.
This paper was supported by the National Key R&D Plan of PR China (Project no. 2017YFB0304201) and the National Natural Science Foundation of PR China (project no. U1760115).