Heat transfers By conduction

An analogy exists between mass transfer by diffusion and heat transfer by conduction. Each involves coHisions between molecules and a gradient as the driving force which causes flow. Eor diffusion, this is a concentration gradient for conduction, the driving force is an energy gradient. Eourier s... 

Fourier s law is the fundamental differential equation for heat transfer by conduction ... 

To reduce heat transfer by conduction, an insulant should have a small ratio of solid volume to void. Additionally, a thin-wall matrix, a discontinuous matrix or a matrix of elements with minimum point contacts are all beneficial in reducing conducted heat flow. A reduction in the conduction across the voids can be achieved by the use of inert gases rather than still air. 

Conduction. In a solid, the flow of heat by conduction is the result of the transfer of vibrational energy from one molecule to another, and in fluids it occurs in addition as a result of the transfer of kinetic energy. Heat transfer by conduction may also arise from the movement of free electrons, a process which is particularly important with metals and accounts for their high thermal conductivities. 

HEAT TRANSFER BY CONDUCTION 9.3.1. Conduction through a plane wall... 

In the problems which have been considered so far, it has been assumed that the conditions at any point in the system remain constant with respect to time. The case of heat transfer by conduction in a medium in which the temperature is changing with time is now considered. This problem is of importance in the calculation of the temperature distribution in a body which is being heated or cooled. If, in an element of dimensions dr by dy by dr (Figure 9.9), the temperature at the point (x, y, z) is 9 and at the point (x + dx, y + dy, r. + dr) is (9 4- d6>), then assuming that the thermal conductivity k is constant and that no heat is generated in the medium, the rate of conduction of heat through the element is ... 

Analytical solutions of equation 9.44 in the form of infinite series are available for some simple regular shapes of particles, such as rectangular slabs, long cylinders and spheres, for conditions where there is heat transfer by conduction or convection to or from the surrounding fluid. These solutions tend to be quite complex, even for simple shapes. The heat transfer process may be characterised by the value of the Biot number Bi where ... 

In Section 9.3.4, consideration is given to the problem of heat transfer by conduction through a surrounding fluid to spherical particles or droplets. Relative motion between the fluid and particle or droplet causes an increase in heat transfer, much of which may be due to convection. Many investigators have correlated their data in the form ... 

Because the mechanisms governing mass transfer are similar to those involved in both heat transfer by conduction and convection and in momentum transfer (fluid flow), quantitative relations exist between the three processes, and these are discussed in Chapter 12. There is generally more published information available on heat transfer than on mass transfer, and these relationships often therefore provide a useful means of estimating mass transfer coefficients. 

Mass transfer from a single spherical drop to still air is controlled by molecular diffusion and. at low concentrations when bulk flow is negligible, the problem is analogous to that of heat transfer by conduction from a sphere, which is considered in Chapter 9, Section 9.3.4. Thus, for steady-state radial diffusion into a large expanse of stationary fluid in which the partial pressure falls off to zero over an infinite distance, the equation for mass transfer will take the same form as that for heat transfer (equation 9.26) ... 

The mechanism of conduction is most easily understood by the study of conduction through homogeneous isotropic solids, because in this case convection is not present. As a simple illustration of heat transfer by conduction, let a flat parallel-sided plate of a uniform solid material, whose flat faces are maintained at temperatures Tt and T2 respectively (Tj > T2) be considered (Figure 3.15). Heat would be transferred from the face at the higher temperature (Tj) to that at the lower temperature (T2). Let the rate of this transfer be dQjdt, and the area of the plate perpendicular to the direction of heat flow be S. If L is the plate thickness, then it is found that dQ/dt is proportional to (Tt - T2) S/L. In other words,... 

Figure 3.15 Heat transfer by conduction through a parallel-sided plate.

In the case of a porous solid, the rate of heat transfer by conduction can be expressed in the following manner ... 

Heat transfer by conduction between the water layers, gives a temperature change based on the temperatures at time step j — 1 ... 

Equation 9.1-15 equates the rate of heat transfer by conduction at the surface to the rate of heat transfer by conduction/convection across a thermal boundary layer exterior to the particle (corresponding to the gas film for mass transfer), expressed in terms of a film coefficient, h, and the difference in temperature between bulk gas at Tg and particle surface at Ts ... 

Boundary conditions are part of the mathematical description of a process. For the energy balance, the condition at the vessel wall is that the rate of heat transfer by conduction equals the rate of transfer to the heat transfer medium. Similarly the rate of mass transfer at the wall equals the rate of reaction on the wall if that is catalytic, or equals zero when the wall is inert and impermeable. Clearly, the temperature, composition and pressure of the inlet to the reactor are part of the problem specification. 

King, A. R. and Newitt, D. M. Trans. Inst. Chem. Eng. 33 (1955) 64. The mechanism of drying of solids. Part VII. Drying with heat transfer by conduction. 

Convection is not a singular heat transport vehicle as are conduction and radiation. Instead, convection increases conduction by constantly circulating warmer material away from hot surfaces and replacing it with colder material. This increases the effective temperature difference, which increases the rate of heat transfer by conduction. 

With respect to an individual food piece, the unit operation of freezing involves unsteady-state heat transfer in other words, the temperature of the food changes with time. In these circumstances heat transfer by conduction is described by Fourier s first law... 

For heat transfer by conduction through a thick-walled pipe of length I, it can be shown that... 

Heat Transfer by Conduction. In the theoretical analysis of steady state, heterogeneous combustion as encountered in the burning of a liquid droplet, a spherically symmetric model is employed with a finite cold boundary as a flame holder corresponding to the liquid vapor interface. To permit a detailed analysis of the combustion process the following assumptions are made in the definition of the mathematical model ... 

An important qualitative conclusion is that by increasing the diameter the heat transfer by conduction may be made arbitrarily small. In the absence of another mechanism of heat transfer, by increasing the diameter we may arbitrarily decrease the flame propagation velocity at the limit. 

If the evaporating and condensing surfaces were very close together, perhaps an inch or less, some diffusion transfer of water vapor would occur, without physical transport by circulating air. However, limited heat transfer by conduction from basin to cover could also occur. It is possible that the net effect would be a moderate increase in the water yield and a corresponding decrease in heat loss due to air circulation. But the practicality of close positioning of salt water surface and cover is questionable. 

Here we consider the case of a viscous or even solid reactive material contained in a vessel of known geometry. In this case, heat transfer takes place by pure conduction there is no flow within the reactive material. The situation is stable, when the heat losses by conduction compensate for the heat release in the material. Thus, the following questions must be answered Under which conditions may a thermal explosion (runaway) be triggered Under which conditions is the heat transfer by conduction sufficient to compensate for the heat release ... 

The governing heat transfer modes in gas-solid flow systems include gas-particle heat transfer, particle-particle heat transfer, and suspension-surface heat transfer by conduction, convection, and/or radiation. The basic heat and mass transfer modes of a single particle in a gas medium are introduced in Chapter 4. This chapter deals with the modeling approaches in describing the heat and mass transfer processes in gas-solid flows. In multiparticle systems, as in the fluidization systems with spherical or nearly spherical particles, the conductive heat transfer due to particle collisions is usually negligible. Hence, this chapter is mainly concerned with the heat and mass transfer from suspension to the wall, from suspension to an immersed surface, and from gas to solids for multiparticle systems. The heat and mass transfer mechanisms due to particle convection and gas convection are illustrated. In addition, heat transfer due to radiation is discussed. 

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