Non-isothermal Medium Research Articles

Simulation of Free Radical Bulk/Solution Homopolymerization Using Mono- and Bi-functional Initiators

Monofunctional and bifunctional peroxides are extensively utilized in the production of polystyrene. However, their decomposition kinetics is still an important area to investigate. A computer package developed previously by Gao and Penlidis (1996), which was based on mono-fimctionally initiated polymerization, is extended in this study to cover homopolymerization of styrene using bifunctional initiators. A database of a wide variety of bifimctional peroxides used in polystyrene production is developed along with a database for twelve new monofimctional initiators. The package handles several different scenarios of styrene polymerization, whether it is in bulk / solution or isothermal / non-isothermal medium. The model is tested with a wide range of conversion and average molecular weight data either from the literature or available from industry. Simulation results agree with the data trends, which makes the simulator a very powerful tool in aid of initiator selection and evaluation. At the end of the paper, results on homopolymerizations of acrylates and methacrylates are also discussed.

Modeling Varying-Heat-Transfer-Area Batch Processe

Analytical equations are developed for heating and cooling of liquid batches, where the volume changes with time. Both reacting and nonreacting batches, as well as isothermal and nonisothermal exchange media, are considered. The operations of evaporation and exothermic chemical reaction are discussed as typical examples of batch heating and batch cooling. Previous effort at modeling varying-heat-transfer-area batch processes involved the use of a chart, and the calculations required graphical/numerical integration in the case of a nonisothermal exchange medium; here, analytical solutions are presented for the lime dependence of the batch volume and the heat transfer rate. Furthermore, the previously made assumption of the arithmetic mean for the temperature driving force is shown to be unnecessary, as the log-mean temperature difference leads to a simple, appropriate analysis.

Acoustic stabilization of the wavefront of a laser beam in a nonuniform gaseous medium

The action of an acoustic field on a nonisothermal gaseous medium for the purpose of improving the optical characteristics of the medium is studied. Restoration of optical uniformity of the gas and stabilization of the wavefront of a laser beam were modelled in experiments with acoustic flows.

Thermal fluctuation field in an inhomogeneous nonisothermal medium

Thermal fluctuation field in an inhomogeneous nonisothermal medium

Radiant heat transfer in a closed system of semiopaque bodies separated by an emitting and absorbing gas medium

A radiant heat-transfer problem is solved for a closed emitting system bounded by a nonisothermal semiopaque shell with the absorption and emission of a nonisothermal gas medium taken into account.

Determination of the coefficient of thermal efficiency of heating surfaces, bounding a flat layer of nonisothermal dissipative medium

A method is proposed for calculating the coefficient of thermal efficiency of flat nonisothermal dissipative media taking into account the radiative characteristics of the bounding surfaces.

Heat exchange with different schemes for introducing the heat-exchange agent into a furnace

The effect of the scheme for introducing the heat-exchange agent into a furnace for heat exchange in a selective nonisothermal gaseous medium is investigated taking into account the heat loss due to convection depending on the emissivity of the metal and the furnace lining.

Determination of the thermal efficiency factor of surfaces bounding a plane layer of a nonisothermal nondissipative medium

A method to compute the thermal efficiency factor is proposed for a plane layer of nonisothermal and nondissipative medium with radiating and reflecting boundaries, and an analysis is given of its dependence on the optical thickness of the layer and the form of the temperature profile.

The transport of resonance radiation in a nonisothermal medium—the effect of a varying Doppler width

A method is presented for treating the transport of resonance radiation under the influence of a varying Doppler width resulting from temperature changes. The method is applied to transport of resonance photons in the earth's thermosphere for media of modest and large optical depths. The drop in temperature below the exosphere can lead to almost a factor of two reduction in the nadir viewing intensity observed, e.g., from satellites. The effect is weaker, however, for zenith viewing intensities, especially in the isothermal region.

Numerical results for the thermal scattering functions

A recent formulation in radiative transfer defined the thermal scattering functions that characterize radiative transfer from a general, plane-parallel, finite medium driven solely by an internal distribution of thermal sources. Exiting diffuse intensities are expressed as space convolutions of the thermal scattering functions with any thermal source distribution. A parametric study is presented to obtain the basic structure of these scattering functions. The independent variables of these azimuthally independent functions are the direction consine μ and source location t, while the parameters are the single scattering albedo ω, total optical depth t 0, and the asymmetry factor g in the Henyey-Greenstein phase function. The basic functional trends are discussed using various parametric plots, and selected tabular results are given to allow numerical checks. The computational method is invariant imbedding. As a particular application, these functions are used in the following companion paper to obtain exiting intensities from inhomogeneous and nonisothermal media.

Multi-dimensional radiative transfer in non-isothermal cylindrical media with non-isothermal bounding walls

A systematic approach for the exact calculation of multi-dimensional radiative heat flux in a cylindrical emitting-absorbing non-isothermal medium with non-isothermal bounding walls is described. Closed form exact solutions are obtained for radiative transfer inside (finite and infinite) cylinders and concentric cylinders with prescribed three-dimensional temperature distribution. For the special case of one-dimensional cylindrically symmetric situation, the exact solution obtained in the present work is shown to be equivalent to the exact solution obtained in a previous study, although the solution presented here is much more elegant in approach and simpler in form. Numerical results are also presented for the case of isothermal media bounded by piecewise isothermal walls.

On the validity of a generalized Kirchhoff's law for a nonisothermal scattering and absorptive medium

The relationship of directional hemispherical reflectivity to emissivity is investigated for a nonisothermal medium with isotropic coherent scattering and absorption. Departures from a generalized Kirchhoff's Law occur due to the long range nature of the scattering process. Such departures occur in lunar thermal emission at microwave but not at infrared frequencies.

Theoretical Analysis of Radiative Heat Transfer in a Scattering Medium

The problem of radiative heat transfer in a nonisothermal medium is considered. The analysis is carried out for plane parallel plates separated by an anisotropically scattering atmosphere. A usable solution is obtained by iteration of the set of equations that result from approximation of the radiative transport equation.

Radiative Heat Transfer Between Parallel Plates Separated by a Nonisothermal Medium With Anisotropic Scattering

The problem of radiative heat transfer in a nonisothermal medium is considered. The analysis is carried out for a plane parallel atmosphere separated by a cloud of particles which scatters radiant energy in an anisotropic fashion. Linear and isothermal temperature profiles are compared for enclosures with partially reflecting diffuse boundaries. The solutions are obtained by representing the integral term of the radiative transport equation by a quadrature. The resulting set of nonhomogeneous differential equations are solved utilizing the method of idempotents.

Stationary Temperature Distribution in an Electrically Heated Conductor

The thermodynamic theory of irreversible processes as developed by Onsager, de Groot, and Callen is used to derive in a straightforward way the partial differential equation for the stationary temperature distribution in an electrically heated, chemically inhomogeneous conductor. It is shown that the form of this differential equation given in 1900 by Diesselhorst (for homogeneous media) in terms of the electrical potential gradient ∇·κ∇T+στ∇T·∇φ+σ(∇φ)2=0, is incorrect. Diesselhorst's equation reads ∇φ in which κ is the thermal conductivity (for zero electrical current), T the temperature, σ the isothermal electrical conductivity, and τ the Thomson coefficient. The correct form of the equation, for the special case of a chemically homogeneous conductor, is ∇·κ∇T+(1/σ)J2−τJ·∇T=0, where J is the electrical current density. The correct form can be obtained from Diesselhorst's equation by substitution of the ``isothermal Ohm's law'' J=−σ∇φ, which, however, is not valid in a nonisothermal medium. The apparent difficulty is resolved by the method of Onsager-de Groot-Callen, and it is shown that the correct differential equation expressed in terms of electrical potential is much more complicated than the form given by Diesselhorst.