Radiative heating

Heat can be transferred to the sheet in several ways. The most common for thermo-forming is radiation from heater elements. The sheet is moved into or through an oven with radiant heating elements. In some thermoform/fiH/seal equipment, heating is by conduction. In this case, the sheet is pulled up against a heated plate, 

Black Body Radiation Spectrum as a Function of Temperature 

Plastic materials, even if they appear transparent in the visible spectrum, absorb energy in the infrared region. The amount of absorbance at any wavelength can be predicted from the IR spectrum of the material. Although the material may absorb over a broad range, each material has an optimum absorbance, a frequency at which it absorbs most strongly. 

In practice, the thermoformer oven temperature is set to match the theoretical best temperature for absorption of the particular polymer, and the heating time is determined by trial and error. Obviously, one should discuss the heating temperatures with the equipment manufacturer and the plastic supplier for recommendations. The heaters usually used in thermoformers are either calrod type or quartz lamps. Less frequently, other types of heaters are used. 

Plastic Material Ideal Wavelength. r Temperature Range, C 

Consider the amount of radiation arriving on the surface of the Earth at a distance of 1 AU or 1.5 x 1011 m. The total flux of the Sun is distributed evenly over a sphere of radius at the distance of the planet, d. From the luminosity calculation of the Sun, F, the solar flux at the surface of Earth, FEarth, is F/47t(1.5 x 1011)2 = 1370 Wm-2 from the least-square law of radiation discussed in Example 2.4 (Equation 2.4). Substituting this into Equation 7.6 with the estimate of the albedo listed in Table 7.2 gives a surface temperature for Earth of 256 K. 

The calculated surface temperature of the Earth can be compared with a mean surface temperature of 288 K. The difference in these temperatures is attributed to global warming mechanisms in the atmosphere. Similar calculations can be performed for any object at any distance from a star of known temperature. The calculations for the other objects in the solar system are presented for the other planets in Table 7.2. 

Body Radius (km) Surface pressure (bar) Albedo Effective temperature (K) Surface temperature (K) Surface g (m s-2) 

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Radiative heat tiansfei is negligible if the bed oi the heat-tiansfei surface is below 600°C. 

Third, design constraints are imposed by the requirement for controlled cooling rates for NO reduction. The 1.5—2 s residence time required increases furnace volume and surface area. The physical processes involved in NO control, including the kinetics of NO chemistry, radiative heat transfer and gas cooling rates, fluid dynamics and boundary layer effects in the boiler, and final combustion of fuel-rich MHD generator exhaust gases, must be considered. 

Whereas conductive and radiative heating are useful techniques for some appHcations, convective heating is by far the most common means of supplying the energy needed to evaporate the solvent, because convection is the only means of heating that also provides a means of transporting solvent vapor away from the surface of the coating. 

Specialized heat transfer nomenclature used for radiative heat transfer is defined in the subsection Heat Transmission hy Radiation. Nomenclature for mass transfer is defined in the subsection Mass Transfer. ... 

General References Much of the pertinent literature on radiative heat... 

Radiative Heat Transfer Heat-transfer equipment using the radiative mechanism for divided solids is constructed as a table which is stationary, as with trays, or moving, as with a belt, and/or agitated, as with a vibrated pan, to distribute and expose the burden in a plane parallel to (but not in contacl with) the plane of the radiant-heat sources. Presence of air is not necessary (see Sec. 12 for vacuum-shelf dryers and Sec. 22 for resubhmation). In fact, if air in the intervening space has a high humidity or CO9 content, it acts as an energy absorber, thereby depressing the performance. 

In rotary devices, reradiation from the exposed shelf surface to the solids bed is a major design consideration. A treatise on furnaces, including radiative heat-transfer effects, is given by Ellwood and Danatos [Chem. Eng., 73(8), 174 (1966)]. For discussion of radiation heat-transfer computational methods, heat fliixes obtainable, and emissivity values, see Schornshort and Viskanta (ASME Paper 68-H 7-32), Sherman (ASME Paper 56-A-III), and the fohowing subsection. 

Here R=r is the parameter for radiative heat transfer in K units, p is a heat of reaction term, in K/atm units tj is the fluid temperature in the j-th axial position e is the particle emissivity 1 is the celt dimension in m 6 is the clock time in minutes... 

Simulation by the improved Euler method has shown that a significant radiative heat transfer must be present before reaction zone migration can be demonstrated. 

Heat source with predefined total gain and the split between convective and radiative heat release... 

In the case of a given surface temperature, the amount of energy released is determined by the parameters for the convective and radiative heat exchange. As far as convection is concerned, these are the temperatures ol the heat source surface and room air, respectively, and the heat transfer coefficient. The radiative heat exchange is determined by the view factors and the temperatures of the surrounding surfaces. 

A fictive sky temperature, dependent on ambient temperature, emissivity, and cloudiness, is introduced to account for the long-wave radiative heat exchange between the building envelope and the sky. 

The room models implemented in the codes can be distinguished further by how detailed the models of the energy exchange processes are. Simple models use a combined convective-radiative heat exchange. More complex models use separate paths for these effects. Mixed forms also exist. The different models can also be distinguished by how the problem is solved. The energy balance for the zone is calculated in each time step of the simulation. 

Radiative heat exchange The heat exchange by radiation between the clothing surface, including uncovered skin, and the environment, in W m -. 

Radiative heat exchange, globe The heat exchange by radiation that takes place... 

Radiative heat transfer coefficient The heat-transfer coefficient wholly attributed to radiative heat transfer. 

The rate of combustion is set equal to the rate of heat applied to warm the entrained air plus the radiative heat losses ... 

Love, T. J. 1968. Radiative heat transfer. Cincinnati, OH C. E. Merrill. 

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 ... 

The geometric factor can be illustrated by considering the amount of sunlight (or radiative heat) received by Earth from the Sun. If you draw a huge sphere with a radius of 150 million km (93 million miles) around the sun that passes through Earth, the geometric factor for the Sun to Earth would he the ratio of the area on that sphere s surface blocked by Earth to the surface area of the sphere. Obviously, Earth receives only a tiny fraction of the total energy emitted from the Sun. 

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) ... 

These two points taken together illustrate that the temperature at the Earth s surface depends on bofh a radiative balance and all of the meteor-ologic processes that transport heat within the lower atmosphere and of course, all the oceanographic factors that transport heat in the ocean as well. So, at this juncture we must abandon the simple picture of a global-mean radiative heat... 

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