Heat transfer, conductive

Heat transfer takes place by three mechanisms conduction, convection, and radiation. In conductive heat transfer, the heat flows from regions of high temperature to regions of low temperature. The transfer takes place due to motion at the molecular level. Matter must be present in order for conduction to occur. The material itself does not need to be in motion for conduction to take place in fact, many times the conducting medium will be stationary. In a solid material, the only mode of heat transfer is conduction [16]. In convection, heat transfer is due to the bulk motion of the fluid. Convective heat transfer only occurs in fluids. In radiation, heat or radiant energy is transferred in the form of electromagnetic waves. 

The most important relationship in conductive heat transfer is Fourier s law for conduction in the x direction  

Fourier s law states that the heat will flow from high to low temperatures. The heat flow is proportional to the thermal conductivity, the temperature gradient, and the cross-sectional area normal to heat flow. Thus, in order to calculate the heat flow, one has to know the thermal conductivity of the material and the temperature distribution within the material. The temperature distribution has to be determined by solving the energy equation (Eq. 5.5) as discussed in Section 5.1.3. 

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The heat-transfer coefficient of most interest is that between the bed and a wall or tube. This heat-transfer coefficient, is made up of three components. To obtain the overall dense bed-to-boiling water heat-transfer coefficient, the additional resistances of the tube wall and inside-tube-waH-to-boiling-water must be added. Generally, the conductive heat transfer from particles to the surface, the convective heat transfer... 

Fundamental models correctly predict that for Group A particles, the conductive heat transfer is much greater than the convective heat transfer. For Group B and D particles, the gas convective heat transfer predominates as the particle surface area decreases. Figure 11 demonstrates how heat transfer varies with pressure and velocity for the different types of particles (23). As superficial velocity increases, there is a sudden jump in the heat-transfer coefficient as gas velocity exceeds and the bed becomes fluidized. 

The most widely used and best known resistance furnaces are iadirect-heat resistance furnaces or electric resistor furnaces. They are categorized by a combination of four factors batch or continuous protective atmosphere or air atmosphere method of heat transfer and operating temperature. The primary method of heat transfer ia an electric furnace is usually a function of the operating temperature range. The three methods of heat transfer are radiation, convection, and conduction. Radiation and convection apply to all of the furnaces described. Conductive heat transfer is limited to special types of furnaces. 

Contact Drying. Contact drying occurs when wet material contacts a warm surface in an indirect-heat dryer (15—18). A sphere resting on a flat heated surface is a simple model. The heat-transfer mechanisms across the gap between the surface and the sphere are conduction and radiation. Conduction heat transfer is calculated, approximately, by recognizing that the effective conductivity of a gas approaches 0, as the gap width approaches 0. The gas is no longer a continuum and the rarified gas effect is accounted for in a formula that also defines the conduction heat-transfer coefficient ... 

Figure 5 shows conduction heat transfer as a function of the projected radius of a 6-mm diameter sphere. Assuming an accommodation coefficient of 0.8, h 0) = 3370 W/(m -K) the average coefficient for the entire sphere is 72 W/(m -K). This variation in heat transfer over the spherical surface causes extreme non-uniformities in local vaporization rates and if contact time is too long, wet spherical surface near the contact point dries. The temperature profile penetrates the sphere and it becomes a continuum to which Fourier s law of nonsteady-state conduction appfies. 

Fig. 5. Profile of conduction heat transfer across the gap between a sphere and a flat plate vs projected radius, R = 3 mm, of the sphere at 40°C and 2.1...

Between 1 s and 1 min specific contact time, conduction heat-transfer performance decreases theoretically as the 0.29 power of contact time. This is consistent with empirical data from several forms of indirect-heat dryers which show performance variation as the 0.4 power of rotational speed (21). In agitator-stirred and rotating indirect-heat dryers, specific contact time can be related to rotational speed provided that speed does not affect the physical properties of the material. To describe the mixing efficiency of various devices, the concept of a mixing parameter is employed. An ideal mixer has a parameter of 1. 

TABLE 11-9 Thermal Properties of Various Materials as Affecting Conductive Heat Transfer... 

A large Biot Number means that conduction controls the energy transfer to/from the plastic and large temperature gradients will exist in the plastic. A small Biot Number means that convection is the dominant factor. The above analysis was for conduction heat transfer (B, - oo). When the plastic moulding is taken out of the mould we need to check the value of B,. In this case... 

Convection is the heat transfer in the fluid from or to a surface (Fig. 11.28) or within the fluid itself. Convective heat transport from a solid is combined with a conductive heat transfer in the solid itself. We distinguish between free and forced convection. If the fluid flow is generated internally by density differences (buoyancy forces), the heat transfer is termed free convection. Typical examples are the cold down-draft along a cold wall or the thermal plume upward along a warm vertical surface. Forced convection takes place when fluid movement is produced by applied pressure differences due to external means such as a pump. A typical example is the flow in a duct or a pipe. 

A fire tube contains a flame burning inside a piece of pipe which is in turn surrounded by the process fluid. In this situation, there is radiant and convective heat transfer from the flame to the inside surface of the fire tube, conductive heat transfer through the wall thickness of the tube, and convective heat transfer from the outside surface of that tube to the oil being treated. It would be difficult in such a simation to solve for the heat transfer in terms of an overall heat transfer coefficient. Rather, what is most often done is to size the fire tube by using a heat flux rate. The heat flux rate represents the amount of heat that can be transferred from the fire tube to the process per unit area of outside surface of the fire tube. Common heat flux rates are given in Table 2-11. 

Wlien a temperature difference exists in or across a body, an energy transfer occurs from the high-tem-perature region to the low-temperature region. This heat transfer, q, which can occur in gases, liquids, and solids, depends on a change m temperature, AT, over a distance. Ax (i.e., AT/z)ix) and a positive constant, k, which is called the thermal conductivity of the material. In equation form, the rate of conductive heat transfer per unit area is written as... 

A window consisting of a single piece of clear glass can also he treated with R-value analysis. As with the wall, there is convective and radiative heat transfer at the two surfaces and conductive heat transfer through the glass. The resistance of the window is due to the two surface resistances and to the conductive resistance of the glass, For typical window glass, R = 0.003 (W/ni -°C)" (0.02 (Btu/h-ft -°F) ) so the total resistance of the window is = (0.12 + 0.003 + 0.04) (W/m -- C) ... 

A = total exchanger bare tube heat transfer, ft or, net external surface area of tubes exposed to fluid heat transfer, ft or, area available for heat transfer, ft (for conduction heat transfer, A is a cross-sectional area, taken normally in the direction of heat flow, ft2). 

The subject of this chapter is single-phase heat transfer in micro-channels. Several aspects of the problem are considered in the frame of a continuum model, corresponding to small Knudsen number. A number of special problems of the theory of heat transfer in micro-channels, such as the effect of viscous energy dissipation, axial heat conduction, heat transfer characteristics of gaseous flows in microchannels, and electro-osmotic heat transfer in micro-channels, are also discussed in this chapter. 

One particular characteristic of conduction heat transfer in micro-channel heat sinks is the strong three-dimensional character of the phenomenon. The smaller the hydraulic diameter, the more important the coupling between wall and bulk fluid temperatures, because the heat transfer coefficient becomes high. Even though the thermal wall boundary conditions at the inlet and outlet of the solid wall are adiabatic, for small Reynolds numbers the heat flux can become strongly non-uniform most of the flux is transferred to the fluid at the entrance of the micro-channel. Maranzana et al. (2004) analyzed this type of problem and proposed the model of channel flow heat transfer between parallel plates. The geometry shown in Fig. 4.15 corresponds to a flow between parallel plates, the uniform heat flux is imposed on the upper face of block 1 the lower face of block 0 and the side faces of both blocks... 

Figure 3. Finite element simulation of plane Couette flow with thermal dissipation and conductive heat transfer. (f) — fixed temperature condition (c) — convective boundary condition.

In conductive heat transfer, the transfer is always in the direction of decreasing temperature and is proportional to the magnitude of the temperature gradient the constant of proportionality being the thermal conductivity of the system. 

Conduction Heat transfer between higher and lower temperature substances or objects as a result of direct contact between the substances or objects. 

The boiling Nusselt number (NuJ, or Nusselt number for bubbles, is defined as the ratio of the boiling heat transfer rate to the conduction heat transfer rate through the liquid film,... 

Yoder showed that radiation heat transfer and axial conduction heat transfer in the tube wall have a negligible effect on predicting wall temperatures. The following equations were used by Yoder and Rohsenow (1980) as well as previous investigators such as Bennett et al. (1967b), Hynek (1969), and Groeneveld (1972). 

Chen, J. C., Chen, K. L., Analysis of Simultaneous Radiative and Conductive Heat Transfer in Fluidized Beds, Chem. Eng. Commun., 9 255-271 (1981)... 

For the analysis, a steady-state fire was assumed. A series of equations was thus used to calculate various temperatures and/or heat release rates per unit surface, based on assigned input values. This series of equations involves four convective heat transfer and two conductive heat transfer processes. These are ... 

Amount of Heat, Heat Conductivity, Heat Transfer and Cooling Velocity... 

Conduction band minima, in compound semiconductors, 22 148-151 Conduction (heart) block, 5 86 Conduction dryers, coatings, 7 29 Conduction freezing, 42 83—84 Conduction furnaces, 42 295—296 Conduction heat transfer, 9 105-106 43 242-245... 

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