Cross-plane heat conduction in thin solid films

Cross-plane heat transport in thin films with thickness comparable to the phonon mean free paths is of both fundamental and practical interest. However, physical insight is difficult to obtain for the cross-plane geometry due to the challenge of solving the Boltzmann equation in a finite domain. Here, we present a semi-analytical series expansion method to solve the transient, frequency-dependent Boltzmann transport equation that is valid from the diffusive to ballistic transport regimes and rigorously includes frequency-dependence of phonon properties. Further, our method is more than three orders of magnitude faster than prior numerical methods and provides a simple analytical expression for the thermal conductivity as a function of film thickness. Our result enables a more accurate understanding of heat conduction in thin films

Radiant interchange in a non-isothermal rectangular cavity

Radiant interchange between non-isothermal, gray diffuse surfaces with non-uniform radiosity has been determined for a rectangular cavity. Temperature distribution and heat flux as thermal specifications for the parallel surfaces of the cavity have been considered separately. Ambarzumian\u27s method has been used for the first time to solve a radiant interchange problem. According to the method, the integral equation for the radiosity is first transformed into an integro-differential equation and then into a system of ordinary differential equations. Initial conditions required to solve the differential equations are the H-functions. The H-functions represent the radiosity at the edge of the cavity for various temperature profiles. Applying Ambarzumian\u27s Method a closed-form expression for radiosity and heat transfer are obtained in terms of universal functions. Heat transfer from the cavity can be determined without knowing the radiosity inside the cavity. The numerical results for the H-functions, radiosity, local heat flux, overall heat transfer, local and overall apparent emittance for the cavity have been presented in the form of tables and graphs --Abstract, page iii

Surface chemistry in the Interstellar Medium II. H2\mathrm{H}_2 formation on dust with random temperature fluctuations

The $\mathrm{H}_2$ formation on grains is known to be sensitive to dust temperature, which is also known to fluctuate for small grain sizes due to photon absorption. We aim at exploring the consequences of simultaneous fluctuations of the dust temperature and the adsorbed H-atom population on the $\mathrm{H}_2$ formation rate under the full range of astrophysically relevant UV intensities and gas conditions. The master equation approach is generalized to coupled fluctuations in both the grain's temperature and its surface population and solved numerically. The resolution can be simplified in the case of the Eley-Rideal mechanism, allowing a fast computation. For the Langmuir-Hinshelwood mechanism, it remains computationally expensive, and accurate approximations are constructed. We find the Langmuir-Hinshelwood mechanism to become an efficient formation mechanism in unshielded photon dominated region (PDR) edge conditions when taking those fluctuations into account, despite hot average dust temperatures. It reaches an importance comparable to the Eley-Rideal mechanism. However, we show that a simpler rate equation treatment gives qualitatively correct observable results in full cloud simulations under most astrophysically relevant conditions. Typical differences are a factor of 2-3 on the intensities of the $\mathrm{H}_2$ $v=0$ lines. We also find that rare fluctuations in cloud cores are sufficient to significantly reduce the formation efficiency. Our detailed analysis confirms that the usual approximations used in numerical models are adequate when interpreting observations, but a more sophisticated statistical analysis is required if one is interested in the details of surface processes.Comment: 21 pages, 28 figures, accepted in A&

Extensions of Green\u27s Function Discretization for Modeling Acoustics in Inhomogeneous Media

This research examines two new methods to numerically model linear field equations with spatially varying coefficients, with a particular focus on the acoustic velocity potential equation. The methods are based on a new field discretization technique, Green\u27s function discretization (GFD), which was primarily developed to model the Hehnholtz equation for frequency domain acoustics problems in homogeneous media. GFD can be used to model acoustics in inhomogeneous media by assuming constant media properties across each computational stencil. The methods presented herein correct GFD for variations in the media across each stencil in two distinct ways: via a Fredholm volume integral, and by a particular solution to a perturbation expansion. To evaluate these methods, boundary value problem test cases have been numerically evaluated to determine gains in accuracy in one and two dimensions. The results demonstrate that the ability of GFD to model the effects of an inhomogeneous medium on acoustics can be significantly increased using corrections factors computed from these new methods

Proceedings of the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11), 10-11 July 2017, Nottingham Conference Centre, Nottingham Trent University

This book contains the abstracts and papers presented at the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11), held at Nottingham Trent University in July 2017. The work presented at the conference, and published in this volume, demonstrates the wide range of work that is being carried out in the UK, as well as from further afield

A study of radiative heat transfer from a spherical layer

The problem of radiative heat transfer from a spherical layer of absorbing-emitting gas has been studied. First, the medium is assumed to be gray and then nongray. A thorough survey of literature from fields other than heat transfer, such as astrophysics and neutron transport has been made to stimulate further interest in this important area. To gain some insight into the effect of various parameters on the heat transfer, simple physical situations involving isothermal medium are considered. Comparison of the results obtained for the flux from the spherical and planar layers reveal that the curvature becomes increasingly important as the inner to outer optical radii ratio decreases. The study of a particular nonisothermal case shows that the temperature variations are important and cannot be neglected. In the study of the nongray problem, a simplified rectangular model for the spectral absorption coefficient is first considered. The expressions developed for the simplified rectangular model turns out to be similar to the expressions for the gray analysis. With a small amount of additional computational time one can obtain the results for the simplified rectangular model. Carbon monoxide example is studied in order to illustrate how the rectangular model can be used to analyze radiative heat transfer in a nongray gas. The results of this example reveals that the influence of the \u27windows\u27 is quite profound, thus exposing the limitations of the gray analysis. In order to determine the effect of line or band shape on the radiative transfer, five different models for the absorption coefficient representing the rectangular, triangular, Doppler, exponential and Lorentz profiles are considered. The results obtained for the dimensionless flux reveal that the rectangular profile has the smallest numerical value of all the profiles. The effect of the wings of the Doppler, exponential and Lorentz profiles is evident only for large values of optical thickness. The limiting cases of the functions on which the expressions for the local radiative flux (both from gray and nongray medium) depends are also studied. All the results (except for carbon monoxide example) reported graphically as well as in tabular form in this study are obtained using double precision --Abstract, pages ii-iii