On the differential approximation in radiative transfer

Zusammenfassung Die Anwendbarkeit des Differentialnäherungswertes bei der Berechnung der Wärmeübertragung durch Strahlung wird für verschiedene geometrische Konfigurationen geprüft. Es wird gezeigt, dass mit Ausnahme der eindimensionalen flachen Schicht der Differentialnäherungswert nur beschränkt verwendbar ist.

---

---

This work was sponsored by the US Air Force, Office of Aerospace Research Aerospace Research Laboratories, under Contract AF 33(615)-3104. The author is indebted to Prof.L. S. Wang for several stimulating discussions.     

Positively homogeneous functions in atmospheric radiative transfer theory

Positively homogeneous functions are applied to describe absorption and scattering processes within the framework of atmospheric radiative transfer theory. Solid angle integrations are understood as surface integrations over arbitrary solid angle surfaces which are defined beyond the common picture of atmospheric radiative transfer.     

Variance of a standard vector Monte Carlo estimate in the theory of polarized radiative transfer

The spectral radius ρ of the matrix integral operator defining the covariance matrix of a standard vector Monte Carlo estimate in the polarized radiative transfer problem is examined. The theory of positive operators is used to analytically calculate ρ = ρ₀ for transfer through an infinite homogeneous medium. For a bounded medium, it is shown that ρ is approximately equal to ρ₀ times the spectral radius of the operator corresponding to radiative transfer without polarization. This is shown numerically by estimating the iterations of the corresponding resolvent and approximately analytically by using a perturbation of a special functional.     

On the algebraic theory of scattering

Within the context of the algebraic theory for simple quantum mechanical potential scattering, we establish existence and completeness of generalized wave operators for a large class of long-range potential scattering problems. Our approach utilizes a priori knowledge of the spectral properties of the scattering Hamiltonian and an algebraic theorem on the uniqueness of a particular Euclidean group representation.     

On the invariance principle of scattering theory

The invariance principle of scattering theory is proved under certain rate-of-convergence conditions. As a consequence we obtain an invariance principle in the case of potential scattering with potentials V(x) satisfying (1+|x|)^δV(x)∈l₂(R³) for some δ > 0.     

Optimal paths for minimizing entransy dissipation during heat transfer processes with generalized radiative heat transfer law

A common of finite-time heat transfer processes between high- and low-temperature sides with generalized radiative heat transfer law [q ∝ Δ(Tⁿ)] is studied in this paper. In general, the minimization of entropy generation in heat transfer processes is taken as the optimization objective. A new physical quantity, entransy, has been identified as a basis for optimizing heat transfer processes in terms of the analogy between heat and electrical conduction recently. Heat transfer analyses show that the entransy of an object describes its heat transfer ability, as the electrical energy in a capacitor describes its charge transfer ability. Entransy dissipation occurs during heat transfer processes, as a measure of the heat transfer irreversibility with the dissipation related thermal resistance. Under the condition of fixed heat load, the optimal configurations of hot and cold fluid temperatures for minimizing entransy dissipation are derived by using optimal control theory. The condition corresponding to the minimum entransy dissipation strategy with Newtonian heat transfer law (n = 1) is that corresponding to a constant heat flux rate, while the condition corresponding to the minimum entransy dissipation strategy with the linear phenomenological heat transfer law (n = −1) is that corresponding to a constant ratio of hot to cold fluid temperatures. Numerical examples for special cases with Newtonian, linear phenomenological and radiative heat transfer law (n = 4) are provided, and the obtained results are also compared with the conventional strategies of constant heat flux rate and constant hot fluid (reservoir) temperature operations and optimal strategies for minimizing entropy generation. Moreover, the effects of heat load changes on the optimal hot and fluid temperature configurations are also analyzed.     

On the role of radiative heat transfer in air gaps in vertical continuous casting

A recent asymptotic thermomechanical model for the formation and evolution of air gaps in vertical continuous casting in round moulds is used as the basis for understanding the importance of radiative heat transfer between the mould wall and the solidified shell. Asymptotic analysis is used to systematically reduce the model to a moving boundary problem with a boundary condition in integro-differential form. In addition, a dimensionless parameter is found which determines whether radiation is significant or not for prescribed process operating conditions. Sample computations are carried out using parameters relevant to the continuous casting of copper, and the results are used to interpret earlier findings in the literature on the interaction between air-gap width and thermal radiation.     

Time-dependent radiative transfer in a semi-infinite medium with a reflecting boundary

An exact solution for the intensity due to a pulse radiation on the free surface of a semiinfinite medium with a known surface reflectivity is obtained via the multiple collision method. The time-dependent scalar intensity at the free surface is evaluated for several reflectivities and albedos using the corresponding steady state solution.

---

Zusammenfassung Die exakte Lösung für die von einem Strahlungspuls erzeugte Intensität auf der freien Oberfläche eines halb-unendlichen Mediums mit bekannter Oberflächen-Reflektivität wird bestimmt mit Hilfe der Methode der mehrfachen Zusammenstöße. Die zeitabhängige skalare Intensität auf der freien Oberfläche wurde berechnet für verschiedene Reflektivitäten und Albedos, mit Benützung der entsprechenden stationären Lösung.

---

---

Consiglio Nazionale Delle Ricerche (CNR) Visiting Professor at the University of Bologna.     

On eigenvalue calculations for radiative transfer models that include polarization effects

Several representations of the dispersion matrix (z) basic to analytical solutions for a theory of radiative transfer that includes the effects of polarization are reported, and a method for computing the zeros of det (z) is discussed. Numerical results are given for several specific models.

---

Zusammenfassung Verschiedene Darstellungen der Dispersionsmatrix (z), welche grundlegende Bedeutung für die analytischen Lösungen der Theorie der Strahlungsübertragung mit Polarisation hat, werden angegeben. Eine Methode zur Berechnung der Nullstellen von det (z) wird diskutiert. Es werden numerische Ergebnisse für verschiedene Modelle angegeben.