Heat Transfer Involving Solids

Predict the order of increasing boiling points for the following HjS HjO CH4 Hj KBr. 

T 1 ze the polarity and size of each substance to determine the kinds of intermolecular 

The melting point (freezing point) of a substance is the temperature at which its solid and liquid phases coexist in equilibrium. 

The melting point of a solid is the same as the freezing point of its liquid. It is the temperature at which the rate of melting of a solid is the same as the rate of freezing of its liquid under a given applied pressure. 

The normal melting point of a substance is its melting point at one atmosphere pressure. Changes in pressure have very small effects on melting points, but they have large effects on boiling points. 

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Melting Point 13-11 Heat Transfer Involving Solids 13-12 Sublimation and the Vapor Pressure of Solids... 

Film conductances are also often defined for the impedance to thermal conduction when two solid conductors are placed in mechanical contact. A significant contact resistance is often observed when, on a microscopic scale, heat transfer involves an air-gap between the materials. Under such conditions, phonon propagation must be replaced by the kinetic interaction amongst gaseous atoms and then back to phonon heat transfer in the next solid. Fibrous and foam insulation axe effective thermal insulators because of the numerous contact resistances involved in the transfer of heat. 

Heat transfer involving a change of phase is classified as convective heat transfer even though when the solid phase is involved, the overall process involves combined and interrelated convection and conduction. Heat transfer during boiling, condensation, and solidification (freezing) all, thus, involve convective heat transfer. 

Many of the important cases of heat transfer involve the flow of heat from one fluid through a solid retaining wall into another fluid. This heat must flow through several resistances in series. The net rate of heat transfer can be related to the total temperature-difference driving force by employing an overall coefficient of heat transfer [/ thus, for steady-state conditions,... 

Mathematical modeling of mass or heat transfer in solids involves Pick s law of mass transfer or Fourier s law of heat conduction. Engineers are interested in the steady state distribution of heat or concentration across the slab or the material in which the experiment is performed. This steady state process involves solving second order ordinary differential equations subject to boundary conditions at two ends. Whenever the problem requires the specification of boundary conditions at two points, it is often called a two point boundary value problem. Both linear and nonlinear boundary value problems will be discussed in this chapter. We will present analytical solutions for linear boundary value problems and numerical solutions for nonlinear boundary value problems. 

Steady state mass or heat transfer in solids and current distribution in electrochemical systems involve solving elliptic partial differential equations. The method of lines has not been used for elliptic partial differential equations to our knowledge. Schiesser and Silebi (1997)[1] added a time derivative to the steady state elliptic partial differential equation and applied finite differences in both x and y directions and then arrived at the steady state solution by waiting for the process to reach steady state. [2] When finite differences are applied only in the x direction, we arrive at a system of second order ordinary differential equations in y. Unfortunately, this is a coupled system of boundary value problems in y (boundary conditions defined at y = 0 and y = 1) and, hence, initial value problem solvers cannot be used to solve these boundary value problems directly. In this chapter, we introduce two methods to solve this system of boundary value problems. Both linear and nonlinear elliptic partial differential equations will be discussed in this chapter. We will present semianalytical solutions for linear elliptic partial differential equations and numerical solutions for nonlinear elliptic partial differential equations based on method of lines. 

In many cases of heat transfer involving either a liquid or a gas, convection is an important factor. In the majority of heat-transfer cases met in industrial practice, heat is being transferred from one fluid through a solid wall to another fluid. Assume a hot fluid at a temperature ti flowing past one side of a metal wall and a cold fluid at t flowing past the other side to which a scale of thickness x, adheres. In such a case, the conditions obtaining at a given section are illustrated dia-... 

Heat is involved in most real-life processes. This permits heat—into or out of a system—to serve as a universal detector. In many cases, the heat into or out of a system can be measured nondestruc-tively. Heat transfer occurs in three ways conduction, convection, and radiation. Conduction occurs between solid materials when placed in contact with each other. Convection occurs when a hot material and a cold material are separated by a fluid (gas or liquid). Radiative heat transfer involves the emission and consequent absorption of electromagnetic radiation between a hot and cold material. 

Different types of heat transfer processes are called modes. The main modes of heat transfer are convection, radiation, and conduction. For a temperature gradient that exists between a surface and a moving fluid, one should use the term convection. The radiation mode of heat transfer is driven by electromagnetic waves emitted from all surfaces of finite temperature, so there is a net heat transfer by radiation between two surfaces at different temperatures. When a temperature gradient exists in a stationary medium, heat fiows under the law of conduction heat transfer. In the case of solid materials, such as polymers, conduction is the dominant mechanism for heat transfer, involving mainly lattice vibrations and, in few cases, the transfer of kinetic thermal energy from one electron to another. 

In an unsteady-state energy balance the same principle applies. The accumulation of energy within a process where all the energy forms are considered including kinetic, potential, heat flow rates, enthalpies, and stirrer works may result in an increase in the thermal energy and a rise in temperature. Unsteady-state heat transfer involves the transfer of heat under conditions where the temperature changes with time. For the simple case of one-dimensional conduction in a solid slab, the accumulation of heat is a product of the mass and specific heat of the material and the increase in temperature where ... 

Because the Chilton-Colburn analogy turned out to be successful experimentally, we sometimes forget the frailty of its original basis. It was justified by available data for both fluid flow and heat transfer at solid walls. It was much more of a guess for mass transfer, where the important cases involved transfer across the fluid—fluid interfaces common to absorption and extraction. The mass transfer correlation at fluid oUd walls was based on just five data points. Clearly, Chilton and Colburn made an inspired guess. 

The definition of the heat-transfer coefficient is arbitrary, depending on whether bulk-fluid temperature, centerline temperature, or some other reference temperature is used for ti or t-. Equation (5-24) is an expression of Newtons law of cooling and incorporates all the complexities involved in the solution of Eq. (5-23). The temperature gradients in both the fluid and the adjacent solid at the fluid-solid interface may also be related to the heat-transfer coefficient ... 

Processes in which solids play a rate-determining role have as their principal kinetic factors the existence of chemical potential gradients, and diffusive mass and heat transfer in materials with rigid structures. The atomic structures of the phases involved in any process and their thermodynamic stabilities have important effects on drese properties, since they result from tire distribution of electrons and ions during tire process. In metallic phases it is the diffusive and thermal capacities of the ion cores which are prevalent, the electrons determining the thermal conduction, whereas it is the ionic charge and the valencies of tire species involved in iron-metallic systems which are important in the diffusive and the electronic behaviour of these solids, especially in the case of variable valency ions, while the ions determine the rate of heat conduction. 

An important mixing operation involves bringing different molecular species together to obtain a chemical reaction. The components may be miscible liquids, immiscible liquids, solid particles and a liquid, a gas and a liquid, a gas and solid particles, or two gases. In some cases, temperature differences exist between an equipment surface and the bulk fluid, or between the suspended particles and the continuous phase fluid. The same mechanisms that enhance mass transfer by reducing the film thickness are used to promote heat transfer by increasing the temperature gradient in the film. These mechanisms are bulk flow, eddy diffusion, and molecular diffusion. The performance of equipment in which heat transfer occurs is expressed in terms of forced convective heat transfer coefficients. 

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