Heat transfer mechanism

The main heat transfer processes that are come across in plastics processing are conduction, convection and viscous heating, with radiation only playing a role in thermoforming. Most products are much thinner than they are wide, so only one-dimensional heat flow (Fig. 5.2) will be considered. The heat flow direction is along the x axis, perpendicular to the surface of the product there are planar isotherms perpendicular to the x axis. The heat flow Q is considered across an area A of the isothermal surface. 

Isotherms for steady one-dimensional heat flow through a plastic, due to a heat flow Q onto the surface area A, from either radiation, convection or conduction from a metal. 

The thermal conductivity k of a material is defined by steady-state conduction. The heat flux Q (W) is parallel to the negative temperature gradient 

For polymers k is of the order of 0.2Wm K This is much smaller than the 50Wm K for steel, due to the lack of free conduction electrons, and the weak forces between polymer chains. Steady-state conduction occurs through the foam-insulated wall of a domestic refrigerator the temperature at any point in the foam remains constant, however  

Transient conduction conditions occur in polymer processing. Appendix A derives Eq. (A.14) for one-dimensional transient heat flow, which contains the thermal diffusivity a. This is the combination k/pCp of the thermal conductivity k, density p and specific heat Cp. For most polymer melts a is approximately equal to O.lmm s (Fig. 5.3). For the melting of low-density polyethylene in an extruder, typical conditions are a barrel temperature of To = 220 °C, an initial polymer temperature Tp = 20 °C, and a melting process complete at T = 120 °C. Consequently, using Eq. (C.19), after a contact time t, the melt front is at a distance from the barrel given by 

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DropletHea.tup, A relation for the time required for droplet heatup, T can be derived based on the assumption that forced convection is the primary heat-transfer mechanism, and that the Ran2-MarshaH equation for heat transfer to submerged spheres holds (34). The result is... 

Other types of cokemaking technology include both batch and continuous processes, and processes that use electrical induction as the heat-transfer mechanism. Processes under development are further described in Reference 16. 

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 ... 

Because heat-transfer equipment for solids is generally an adaptation of a primarily material-handhng device, the area of heat transfer is often small in relation to the overall size of the equipment. Also pecuhar to sohds heat transfer is that the At varies for the different heat-transfer mechanisms. With a knowledge of these mechanisms, the At term generally is readily estimated from temperature hmita-tions imposed by the burden characteristics and/or the construc tion. 

Drying temperatures may range up to 1000 K, the limiting temperature for most common structure metals. At the higher temperatures, radiation becomes an important heat-transfer mechanism. 

Design Methods for Direct-Heat Rotary Dryers Direct drying in a direct-heat rotary dryer is best expressed as a heat-transfer mechanism as follows ... 

Radiative heat transfer is perhaps the most difficult of the heat transfer mechanisms to understand because so many factors influence this heat transfer mode. Radiative heat transfer does not require a medium through which the heat is transferred, unlike both conduction and convection. The most apparent example of radiative heat transfer is the solar energy we receive from the Sun. The sunlight comes to Earth across 150,000,000 km (93,000,000 miles) through the vacuum of space. FIcat transfer by radiation is also not a linear function of temperature, as are both conduction and convection. Radiative energy emission is proportional to the fourth power of the absolute temperature of a body, and radiative heat transfer occurs in proportion to the difference between the fourth power of the absolute temperatures of the two surfaces. In equation form, q/A is defined as ... 

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. 

Radiant heat transfer had historically been the biggest heat transfer mechanism for windows. Low-e materials were developed and have historically been used to control for heat transfer. An example of the popularity of using metals to reflect heat to control for radiant heat transfer is the thermos bottle. Applying that new technology to windows, and getting materials that normally would affect transparency of the product to remain visually neutral, was a huge advance to the industry. 

The temperature distribution in the flow direction for a fixed flow rate differs for different devices. This suggests that the heat transfer mechanism in these devices is not identical. The non-uniform (of about 20%) heat flux leads to conditions at which the wall temperature increases sharply. Idealizing the heat flux as uniform can result in a significant error in prediction of the temperature distribution. 

Two-phase heat transfer in micro-channel heat sink was associated with different mechanisms for low, medium, and high-quality flows. Bubble flow and nucleate boiling occur only at low qualities (Xe < 0.05) corresponding to very low heat fluxes. High fluxes produce medium-quality (Xe = 0.05—0.55) or high-quality (Xe = 0.55—1.0) flows depending on the flow rate, where heat transfer is dominated by annular film evaporation. Due to the large differences in heat transfer mechan-... 

Kandlikar SG (2004) Heat transfer mechanisms during flow boiling in micro-channels. ASME J Heat Transfer 126 8-16... 

Although the above idealized case cannot represent nucleate boiling, the highly effective heat transfer mechanism due to evaporation over even a portion of the heat transfer surface at any one time is evident. 

Figure 2.23 Instantaneous representation of nucleate boiling surface showing distribution of heat transfer mechanisms (a) plan view (b) profile view. (From Hsu and Graham, 1976. Copyright 1976 by Hemisphere Publishing Corp., New York. Reprinted with permission.)...

The heat transfer mechanism of a vapor-liquid mixture in which the critical heat flux has been exceeded can be classified as partial or stable film boiling. The differ-... 

As was shown before, the Leidenfrost temperature is the second transformation of heat transfer mechanisms. Empirical correlations have been established by film boiling data obtained from water at high pressure levels. For a wide range of steam-water mixture velocities, the correlation for hFB reported by Bishop et al. (1965), as shown in Eq. (4-37), is recommended for use in design. 

Chyu, M. C., 1989, Formation and Heat Transfer Mechanism of Vapor Mass during Nucleate Boiling, in Thermal, Non-equilibrium in Two-Phase Flow, pp. 157-181, ENEA, Rome. (2)... 

The vial heat transfer coefficient is the sum of heat transfer coefficients for three parallel heat transfer mechanisms (1) direct conduction between glass and shelf surface at the few points of actual physical contact, Kc (2) radiation heat exchange, Kr, which has contributions from the shelf above the vial array to the top of the vials, Krt, and from the shelf upon which the vial is resting, Krb and (3) conduction via gas-surface collisions between the gas and the two surfaces, shelf and vial bottom, Kg ... 

Figure 33 Comparison of heat transfer mechanisms for glass vials on a polished stainless steel shelf. Pressure is in millitorr. The vial identification numbers are manufacturers designations. (From Ref. 1.)...

In the vaporization process, the formation of a continuous vapor phase causes a transition from bubble to annular flow. This flow-pattern transition is accompanied by a gradual change in the heat-transfer mechanism. Both... 

Transition Zone III is of utmost importance, since the formation of dry spots is accompanied by a dramatic change in the heat transfer mechanism. In such units as gas-fired boilers, the dry spots may cause the tube wall temperature to approach the temperature of the heating gas. However, before the tube wall temperature reaches a steady-state value, the tensile strength of the tube wall is reduced, and rupture may occur. This phenomenon, called burn-out, may also occur at any point along the tube wall if the wall heat flux qmt is large enough so that a vapor film forms between the tube wall and the liquid surface. 

The analysis of tubular contactors for heat transfer with phase changes in fluid-fluid systems was shown to be heavily dependent on a proper understanding of two-phase hydrodynamics. It was shown that three basic flow patterns exist within a tube, each with a different heat-transfer mechanism. The formulation of the proper mass and energy models pinpointed three key... 

Three main flow patterns exist at various points within the tube bubble, annular, and dispersed flow. In Section I, the importance of knowing the flow pattern and the difficulties involved in predicting the proper flow pattern for a given system were described for isothermal processes. Nonisother-mal systems may have the added complication that the same flow pattern does not exist over the entire tube length. The point of transition from one flow pattern to another must be known if the pressure drop, the holdups, and the interfacial area are to be predicted. In nonisothermal systems, the heat-transfer mechanism is dependent on the flow pattern. Further research on predicting flow patterns in isothermal systems needs to be undertaken... 

For the total vaporization process, it is generally assumed that four basic heat-transfer regions exist within the tube, each representing a distinct heat-transfer mechanism with the transition from one region to another being gradual ... 

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