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Heat and Mass Transfer

1.1 Introduction

Commercial grade raw material calcination in a rotary kiln is common to make an economical product. The end product feeding regions are divided into several segments to achieve calcined outcomes like dolomite, spinel, mag-chrome, bauxite, etc. Ineffective heat distribution and mass-transfer during rotation result in an immature and uncalcined product that eventually reduces the properties of the refractories. While considering the nonuniform heat distribution in a kiln, there is always a chance to form a premature uncalcined product with a moisture-absorbing tendency; dolomite is an excellent example. Similarly, incomplete spinel conversion from a mixture of MgO and Al2O3 in synthetic raw materials eventually enhances the volume expansion in spinel-based refractory, as well as the improper calcination of natural bauxite facilitates forming a porous mass that absorbs more water during the castable casting results in premature failure.

Organic binder essentially develops a polymeric network and binding refractory grains, but a gradual formation of ceramic bonding requires a predefined temperature in the firing. Tunnel or batch kilns are used in the refractory industry to achieve prerequisite temperatures for high-performance working lining, backup lining, and continuous casting refractories. A highly efficient kiln may provide uniform heat distribution all along the sides from top to bottom, sidewall burner zone to opposite side wall burner zone, car to car, and brick stack to stack; otherwise, some bricks are overfired or underfired. Low temperature is responsible for higher porosity, low bulk density, and cold crushing strength. In contrast, overfired may produce unexpected expansion/shrinkage behavior and low eutectic phases in the presence of impurities.

Precast and Refractory lining preheating in the steel industry shop floor is essential before processing molten steel. Process efficiency depends on the refractory material properties like density, thermal conductivity, and specific heat. However, the foremost thing is the employed process temperature and how it is transferred effectively throughout the system. Continuous argon gas purging through a porous plug facilitates homogenous molten steel composition and temperature throughout the vessel. This multiphase heat transfer behavior differs from heat transfer in a single-phase solid or gaseous environment. Moreover, there is enough scope for heat loss from steel vessels (BOF, LF, Tundish) either through the open space or refractory lining. Different refractory quality experience a temperature gradient due to differences in thermal conductivity from working to safety lining in a vessel.

Raw material calcination, shaped refractory firing, refractory preheating, maintaining uniform temperature in the entire mass of molten steel, and temperature loss through working lining to the outer vessel shell are critical issues and worthy of analyzing the perspective of heat and mass-transfer phenomena. A schematic representation of such a relation is given in Figure 1.1. The inset solid to liquid to gas conversion depends on the temperature that usually enhances kinetic energy and diffusion of atoms. Thus, heat and mass-transfer fundamentals are considered a starting discussion to explore the properties and analysis for the designing refractory for the steel sector.

Figure 1.1 A schematic representation of heat and mass-transfer in refractory processing, production, and application sectors. The atomic arrangement defines solid, liquid, and gas states and possible separation under heat.

1.2 Energy Conservation

Industry measures the temperature profile in a kiln or furnace, but heat distribution is technically responsible for device efficiency. The temperature is different from the heat. The heat transfer is distinctly different from thermodynamics. Temperature (T, °C) measures the quantity of energy influenced by the molecules of a material or system and predicts both the degrees of hotness and direction of heat transfer. Heat (Q, Joule) measures thermal energy transfer from a hotter body to a colder one. Thus, heat transfer describes how much heat, transfer rate, and resultant temperature distribution are inside the body. However, thermodynamics is concerned with the equilibrium state of matter, the amount of heat transferred (dQ), the amount of work done (dW), and the final form of the system. In practice, heat transfer is complementary and an extension of thermodynamics.

a) Control Volume (Open system)

The first law of thermodynamics defines the conservation of total energy and can only change if it crosses the boundaries. A region of fixed mass known as the closed system allows the transfer of heat through boundaries and work done on or by the system, resulting in the total energy changes of the system, as illustrated in Equation (1.1) and Figure 1.2a.

Figure 1.2 (a) Closed system with a time interval (?t), (b) control volume instantly.

Where total energy change stored in the system is ?Esystem, net heat transferred to the system is Q, and new work done by the system is W. In the same chronology, control volume (or open system) region has many possible mass entries. Herein, the "many" terminology refers to the possibility of the energy it carries with it when entering and leaving the mass in the control volume, known as energy advection, which facilitates energy across the boundaries of a control volume. Thus, energy can enter and leave the control volume due to heat transfer from the boundaries, work done on or by the control volume, and energy advection. The total energy combines internal energy and mechanical energy (cumulative potential and kinetic energy). Internal energy can be further subdivided by thermal energy and other forms of internal energy, such as chemical and nuclear energy. Thermal and mechanical forms of energy are a prime concern in heat transfer. The sum of these energies is not conserved because of the possibility of conversion between other forms of energy and thermal energy. However, the stored energy rate must be balanced during inflow and outflow energy in the control volume. Thus, the change in mechanical and thermal energy stored (?Estored) over the time interval ?t and generation of thermal energy (Eg) in the control volume is:

The incidence rate of stored energy (Èstored) increment in the controlled volume is represented in Figure 1.2b and calculated by Equation (1.3):

Total mechanical energy represents the sum of KE (kinetic energy = mv2, where m is the mass and v is the velocity, respectively); PE (potential energy = mgh, where g and h are the gravitational acceleration and vertical distance, respectively); and U (internal energy). However, the internal energy (U) consists of:

• A sensible component comprised of rotational, translational, and vibrational motion of the molecules/atoms of the matter;
• Component of latent indicates the intermolecular forces influencing the changes in phase between vapor, liquid, and solid states;
• Accounts of chemical components for stored energy in the chemical bonds in atoms; and
• The accounts of nuclear components for the binding forces in the nucleus.

In a heat transfer study, sensible (Usen) and latent (Ulat) are the most important internal energy components and together are known as thermal energy (Ut); thus, Ut = Usen + Ulat. Sensible and latent energy is responsible for temperature (although it depends on pressure) and phase change, respectively. For example, in the control volume region, if the material changes from solid to liquid represents melting, and liquid to vapor indicates vaporization, boiling, and evaporation, the latent energy increases. Conversely, condensation (vapor to solid) or solidification and freezing (liquid to solid) decreases the latent energy. Thus, stored energy (Estored) is, Estored = KE + PE + Usen + Ulat. The KE and PE are often small, and if there is no phase change, both mechanical energy and Ulat can be neglected, and thus, Estored = Usen; if no temperature change, Estored = Ulat.

The inflow and outflow incidence in the control volume region is initiated from a surface; thus, it is a surface phenomenon. The process exclusively on the control surface is ordinarily proportional to the surface area. Therefore, the concepts of inflow and outflow of energy terms include the transfer of heat associated with solid medium (conduction), liquid presence (convection), vacuum (radiation), and work interactions that occur at the boundaries of the system. If mass enter or leave the control volume boundary, both the inflow and outflow advected mechanical and thermal energy in the control volume. For instance, if entering mass-flow rate ?, then the control volume is the product of ? (ut + ½v2 + gh), where ut represents the thermal energy per unit mass, and (½v2 + gh) is the mechanical energy per unit mass.

b) Surface Energy Balance

Energy conservation at the surface is an important aspect. As shown in Figure 1.3, the control surfaces are assumed on either side of the bold physical boundary where no mass or volume is enclosed. Herein, Equation...