Resistance to heat conduction

Each term in the denominator of Equation 4.11 is the reciprocal of a heat-transfer coefficient, and thus represents a resistance to heat transfer. The first term in the denominator represents the resistance to heat conduction across a scale formed on the inside surface of the tube, where the thickness and the thermal conductivity of the scale is rarely known. The thermal conductivity and the thickness of scale are not reported in the literature, but its reciprocal is designated by Rf i, the resistance to heat transfer caused by the tube-side scale, where... 

When a solid body is being heated by the hotter fluid surrounding it (such as a potato being baked in an oven), heat is first convected to the body and subsequently conducted within the body. The Biot number is the ratio of the internal resistance of a body to heat conduction (o its external resistance to heat conveetton. Therefore, a small Biot number represents small resistance to heat conduction, and thus small temperature gradients within the body. 

This is the heat flow between the isotherms d = and d = 2- It is inversely proportional to the resistance to heat conduction (cf. 1.2.2)... 

It is rather simple to calculate the resistance to heat conduction between a tube and an isothermal plane as shown in Fig. 2.18 b. With = l and k according to (2.94) we obtain from (2.96)... 

A simple calculation for the heating or cooling of a body of any shape is possible for the limiting case of small Biot numbers (Bi — 0). This condition is satisfied when the resistance to heat conduction in the body is much smaller then the heat transfer resistance at its surface, cf. section 2.1.5. At a fixed time, only small temperature differences appear inside the thermally conductive body, whilst... 

For turbulent flow of a fluid past a solid, it has long been known that, in the immediate neighborhood of the surface, there exists a relatively quiet zone of fluid, commonly called the Him. As one approaches the wall from the body of the flowing fluid, the flow tends to become less turbulent and develops into laminar flow immediately adjacent to the wall. The film consists of that portion of the flow which is essentially in laminar motion (the laminar sublayer) and through which heat is transferred by molecular conduction. The resistance of the laminar layer to heat flow will vaiy according to its thickness and can range from 95 percent of the total resistance for some fluids to about I percent for other fluids (liquid metals). The turbulent core and the buffer layer between the laminar sublayer and turbulent core each offer a resistance to beat transfer which is a function of the turbulence and the thermal properties of the flowing fluid. The relative temperature difference across each of the layers is dependent upon their resistance to heat flow. 

Many everyday heat flows, such as those through windows and walls, involve all three heat transfer mechanisms—conduction, convection, and radiation. In these situations, engineers often approximate the calculation of these heat flows using the concept of R values, or resistance to heat flow. The R value combines the effects of all three mechanisms into a single coefficient. 

Thermal insulation in use today generally affects the flow of heat by conduction, convection, or radiation. The extent to which a given type of insulation affects each mechanism varies. In many cases an insulation provides resistance to heat flow because it contains air, a relatively low thermal conductivity gas. Ill general, solids conduct heat the best, liquids are less conductive, and gases are relatively poor heat conductors. Heat can move across an evacuated space by radiation but not by convection or conduction. 

Bi very small, (say, <0.1). Here the main resistance to heat transfer lies within the fluid this occurs when the thermal conductivity of the particle in very high and/or when the particle is very small. Under these conditions, the temperature within the particle is uniform and a lumped capacity analysis may be performed. Thus, if a solid body of volume V and initial temperature Oo is suddenly immersed in a volume of fluid large enough for its temperature 0 to remain effectively constant, the rate of heat transfer from the body may be expressed as ... 

As the thickness of the lagging is increased, resistance to heat transfer by thermal conduction increases. Although the outside area from which heat is lost to the surroundings also increases, giving rise to the possibility of increased heat loss. It is perhaps easiest to think of the lagging as acting as a fin of very low thermal conductivity. For a cylindrical... 

Catalyst pellets often operate with internal temperatures that are substantially different from the bulk gas temperature. Large heats of reaction and the low thermal conductivities typical of catalyst supports make temperature gradients likely in all but the hnely ground powders used for intrinsic kinetic studies. There may also be a him resistance to heat transfer at the external surface of the catalyst. 

Additives are needed not only to make resins processable and to improve the properties of the moulded product during use. As the scope of plastics has increased, so has the range of additives for better mechanical properties, resistance to heat, light and weathering, flame retardancy, electrical conductivity, etc. The demands of packaging have produced additive systems to aid the efficient production of film, and have developed the general need for additives which are safe for use in packaging and other applications where there is direct contact with food or drink. 

On the other hand, it has been argued that the resistance to heat transfer is effectively within a thin gas film enveloping the catalyst particle [10]. Thus, for the whole practical range of heat transfer coefficients and thermal conductivities, the catalyst particle may be considered to be at a uniform temperature. Any temperature increases arising from the exothermic nature of a reaction would therefore be across the fluid film rather than in the pellet interior. 

The equations describing the concentration and temperature within the catalyst particles and the reactor are usually non-linear coupled ordinary differential equations and have to be solved numerically. However, it is unusual for experimental data to be of sufficient precision and extent to justify the application of such sophisticated reactor models. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the catalyst bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on reaction rate. A useful approach to the preliminary design of a non-isothermal fixed bed catalytic reactor is to assume that all the resistance to heat transfer is in a thin layer of gas near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption, a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the preliminary design of reactors. Provided the ratio of the catlayst particle radius to tube length is small, dispersion of mass in the longitudinal direction may also be neglected. Finally, if heat transfer between solid cmd gas phases is accounted for implicitly by the catalyst effectiveness factor, the mass and heat conservation equations for the reactor reduce to [eqn. (62)]... 

Physico-Chemical Properties. The industrial applications of chrysotile fibers were developed taking advantage of their particular combination of properties fibrous morphology, high tensile strength, resistance to heat and corrosion, low electrical conductivity, and high friction coefficient In many applications, the surface properties of the fibers also play an important role in such cases, a distinction between chrysotile and amphiboles can be... 

Non-isothermal and non-adiabatic conditions. A useful approach to the preliminary design of a non-isothermal fixed bed reactor is to assume that all the resistance to heat transfer is in a thin layer near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the approximate design of reactors. Neglecting diffusion and conduction in the direction of flow, the mass and energy balances for a single component of the reacting mixture are ... 

The practical heat-transfer coefficient is the sum of all the factors that contribute to reduce heat transfer, such as flow rate, cocurrent or countercurrent, type of metal, stagnant fluid film, and any fouling from scale, biofilm, or other deposits. The practical heat-transfer coefficient ((/practical) is, in reality, the thermal conductance of the heat exchanger. The higher the value, the more easily heat is transferred from the process fluid to the cooling water. Thermal conductance is the reciprocal of resistance (/ ), to heat flow ... 

Storage silo containing a solid the main resistance to heat transfer is located in the bulk of the product contained in the silo. The resistance of the wall and the external film are low compared to the conductive resistance of the solid. 

For natural convection, a correlation was established between the Nusselt criterion, which compares convective and conductive resistances to heat transfer and the Rayleigh criterion, which compares buoyancy forces with viscous friction ... 

As a fifth attempt, an increase of the heat transfer at the wall in the Thomas model is not practicable and would not be efficient, since the major part of the resistance to heat transfer is the conductivity in the product itself, as shown by the high value of the Biot criterion, 300, which is closer to Frank-Kamenetskii conditions than to Semenov conditions. 

In the emulsion phase/packet model, it is perceived that the resistance to heat transfer lies in a relatively thick emulsion layer adjacent to the heating surface. This approach employs an analogy between a fluidized bed and a liquid medium, which considers the emulsion phase/packets to be the continuous phase. Differences in the various emulsion phase models primarily depend on the way the packet is defined. The presence of the maxima in the h-U curve is attributed to the simultaneous effect of an increase in the frequency of packet replacement and an increase in the fraction of time for which the heat transfer surface is covered by bubbles/voids. This unsteady-state model reaches its limit when the particle thermal time constant is smaller than the particle contact time determined by the replacement rate for small particles. In this case, the heat transfer process can be approximated by a steady-state process. Mickley and Fairbanks (1955) treated the packet as a continuum phase and first recognized the significant role of particle heat transfer since the volumetric heat capacity of the particle is 1,000-fold that of the gas at atmospheric conditions. The transient heat conduction equations are solved for a packet of emulsion swept up to the wall by bubble-induced circulation. The model of Mickley and Fairbanks (1955) is introduced in the following discussion. 

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