Volume 43, Issue 4

A new formula has been proposed for the Landsberg–Tonge function χ(ε)\chi (\varepsilon ) entering the entropy density flux of the diluted blackbody radiation of dilution factor ε . Two models have been proposed for the conversion of diluted blackbody radiation energy into work. The Carnot and Petela–Landsberg–Press relationships do not provide accurate upper bounds for the real conversion efficiency and in some cases they wrongly estimate positive output work when the converter of radiation energy into work does not operate. Four upper bounds for the conversion efficiency have been derived. The most accurate upper bound efficiency requires the numerical solution of an algebraic equation for the optimum absorber temperature while the second best upper bound efficiency has the advantage that it is a simple analytical formula.

Suppose that a vertical tube is composed of two chambers that are separated by a retractable thermally insulated thin membrane. The upper and lower chambers are filled with an incompressible fluid and maintained at temperatures Tc{T_{c}} and Th>Tc{T_{h}}>{T_{c}}, respectively. Upon removal of the membrane, the two fluid masses form an unstably stratified Rayleigh–Taylor-type configuration with cold and heavy fluid overlying a warmer and lighter fluid and separated by an interface across which there is a discontinuity in the density. Due to the presence of an initial discontinuity between two homogeneous states, this problem is mathematically homologous to that of the shock tube problem with the thermal expansion playing the role of pressure. When the two fluid regions are brought directly into contact with each other and the transient interfacial fluctuations have subsided, we show the emergence of a stationary state of convection through a supercritical bifurcation provided a threshold value for the temperature difference is exceeded. We suggest a possible way for the experimental testing of the theoretical results put forth in this paper.

Thermodynamically isolated systems normally relax to equilibria characterized by single temperatures; however, in recent years several systems have been identified that challenge this presumption, demonstrating stationary temperature gradients at equilibrium. These temperature gradients, most pronounced in systems involving epicatalysis, can be explained via an underappreciated symmetry in the Van ’t Hoff equation.

This work was motivated by the need to understand the passivation of metal surfaces to provide resistance against chemical degradation, given that corrosion is a major limiting factor in the operational lifetime of metals and their alloys. In this study, a unified analysis for an oxide growth model was presented. The oxide growth model was consistent with the literature and accounted for the transport of oxygen defects through a growing oxide film, as well as the electrochemical reactions of oxygen defects at the metal/oxide and oxide/environment interfaces. A linear potential profile across the oxide film was assumed. The model was analyzed for different rate limiting steps in the physicochemical process and perturbation techniques were utilized when necessary. The investigation yielded the well-known linear, parabolic, logarithmic and integral rate laws and the conditions that led to these rate laws were discussed.

We aimed at examining the magnetohydrodynamic (MHD) radiative non-aligned stagnation point motion of non-Newtonian liquid over a stretched surface. The heat transfer mechanism is investigated in the presence of variable heat sink/source, non-linear Rosseland approximation and Biot number. Appropriate transmutations are exploited to metamorphose the flow equations into ODEs. The acquired non-linear ODEs are highly coupled. These are tackled with the consecutive implication of fourth-order Runge–Kutta and shooting techniques. The variations of flow governing parameters on the dimensionless velocity, micro-rotation and temperature plus the measure of heat transport, couple stress coefficient and friction factor are thoroughly explained using plots and tables. Outcomes stipulate that increasing the values of the stretching ratio parameter causes the thermal field to decline and the velocity field to inflate. Also, an upsurge in the micropolar parameter produces an increase in the rate of heat transport but an opposite outcome is detected with the couple stress coefficient. To the best of our knowledge the non-orthogonal stagnated motion of micropolar liquid with radiation as non-linear and variable heat source/sink has never before been scrutinized.

We present a kinetic model for the reaction mechanism of acid-catalyzed twin polymerization. Our model characterizes the reaction mechanism not by the reactants, intermediate structures, and products, but via reaction-relevant moieties. We apply our model for three different derivatives of 2,2’-Spirobi[4 H -1,3,2-benzodioxasiline] and determine activation energies, reaction enthalpies, and reaction rate constants for the reaction steps in our mechanism. We compare our findings to previously reported values obtained from density functional theory calculations. Furthermore, with this approach we are also able to follow the time development of the concentrations of the reaction-relevant moieties.

Transient analysis of phonon cross-plane transport across two consecutively placed thin films is considered, and a new approach is introduced to obtain the semi-analytical solution for the equation of phonon radiative transport. The orthogonality properties of trigonometric functions are used in the mathematical analysis. Silicon and diamond thin films are used to resemble the consecutively placed thin films. The films are thermally disturbed from its edges to initiate the phonon transport, and thermal boundary resistance is introduced at the films interface. Equivalent equilibrium temperature is incorporated to quantify the phonon intensity distribution in the films. It is found that the results of the analytical solution agree well with their counterparts obtained from the numerical simulations. Phonon intensity at the film edges and interface reduces significantly due to boundary scattering. The analytical solution captures phonon scattering at boundaries and interface correctly, and provides considerable simplification of the numerical treatment of the equation for phonon radiative transport. It also reduces significantly the numerical efforts required for solving the transient phonon radiative transport equation pertinent to the cross-plan transport across the thin films in terms of program size and run-time.