Numerical simulation of combined heat transfer phenomena (conduction, convection, and radiation). Application to he optimisation of thermal systems

Thermal systems interchanging heat and mass by conduction, convection, radiation (solar and thermal ) occur in many engineering applications like energy storage by solar collectors, window glazing in buildings, refrigeration of plastic moulds, air handling units etc. Often these thermal systems are composed of various elements for example a building with wall, windows, rooms, etc. It would be of particular interest to have a modular thermal system which is formed by connecting different modules for the elements, flexibility to use and change models for individual elements, add or remove elements without changing the entire code. A numerical approach to handle the heat transfer and fluid flow in such systems helps in saving the full scale experiment time, cost and also aids optimisation of parameters of the system. In subsequent sections are presented a short summary of the work done until now on the orientation of the thesis in the field of numerical methods for heat transfer and fluid flow applications, the work in process and the future work.

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.

Transplanted beta cell response to increased metabolic demand. Changes in beta cell replication and mass

We determined the capacity of transplanted beta cells to modify their replication and mass when stimulated by changes in metabolic demand. Five groups of Lewis rats were studied: group 1 (Tx-Px) had a 95% pancreatectomy 14 d after transplantation of 500 islets; group 2 (Px-Tx) had a 95% pancreatectomy 14 d before transplantation of 500 islets; group 3 (Tx) was transplanted with 500 islets; group 4 (Px) had a 95% pancreatectomy; and group 5 (normal) was neither transplanted nor pancreatectomized. Blood glucose was normal in Tx-Px and Tx groups at all times. Px-Tx and Px groups developed severe hyperglycemia after pancreatectomy that was corrected in Px-Tx group in 83% of rats 28 d after transplantation. Replication of transplanted beta cells increased in Tx-Px (1.15 +/- 0.12%) and Px-Tx (0.85 +/- 0.12%) groups, but not in Tx group (0.64 +/- 0.07%) compared with normal pancreatic beta cells (0.38 +/- 0.05%) (P < 0.001). Mean beta cell size increased in Tx-Px (311 +/- 14 microns2) and Px-Tx (328 +/- 13 microns2) groups compared with Tx (252 +/- 12 microns2) and normal (239 +/- 9 microns2) groups (P < 0.001). Transplanted beta cell mass increased in Tx-Px (1.87 +/- 0.51 mg) and Px-Tx (1.55 +/- 0.21 mg) groups compared with Tx group (0.78 +/- 0.17 mg) (P < 0.05). In summary, changes in transplanted beta cells prevented the development of hyperglycemia in Tx-Px rats. Transplanted beta cells responded to increased metabolic demand increasing their beta cell mass.

Measurement of the specific heat and determination of the thermodynamic functions of relaxed amorphous silicon

The specific heat, cp, of two amorphous silicon (a-Si) samples has been measured by differential scanning calorimetry in the 100–900K temperature range. When the hydrogen content is reduced by thermal annealing, cp approaches the value of crystalline Si (c-Si). Within experimental accuracy, we conclude that cp of relaxed pure a-Si coincides with that of c-Si. This result is used to determine the enthalpy, entropy, and Gibbs free energy of defect-free relaxed a-Si. Finally, the contribution of structural defects on these quantities is calculated and the melting point of several states of a-Si is predicted

A Thermokinetic approach to radiative heat transfer at the nanoscale

Radiative heat exchange at the nanoscale presents a challenge for several areas due to its scope and nature. Here, we provide a thermokinetic description of microscale radiative energy transfer including phonon-photon coupling manifested through a non-Debye relaxation behavior. We show that a lognormal-like distribution of modes of relaxation accounts for this non-Debye relaxation behavior leading to the thermal conductance. We also discuss the validity of the fluctuation-dissipation theorem. The general expression for the thermal conductance we obtain fits existing experimental results with remarkable accuracy. Accordingly, our approach offers an overall explanation of radiative energy transfer through micrometric gaps regardless of geometrical configurations and distances.

Beta cell mass and growth after syngeneic islet cell transplantation in normal and streptozocin diabetic C57BL/6 mice

In islet transplantation, nonimmunological factors such as limited growth capacity or increased death rate could reduce the beta cell mass in the graft and lead to failure of the transplant. We studied the evolution of beta cell replication and mass after transplantation of insufficient, minimally sufficient, or excessive islet tissue. Streptozocin diabetic C57BL/6 mice received 150 or 300 syngeneic islets under the kidney capsule and normal mice received 300 islets. In streptozocin diabetic mice 300 islets restored normoglycemia; beta cell replication in transplanted islets was similar to replication in normal pancreas and beta cell mass in the graft remained constant. In contrast, 150 islets were insufficient to achieve normoglycemia; beta cell replication was increased initially but not by 18 or 30 d despite persistent hyperglycemia, and beta cell mass fell progressively. When islets were transplanted into normal recipients, beta cell replication remained normal but beta cells underwent atrophy and mass in the graft was substantially reduced. Therefore, with a successful islet transplant, in diabetic mice beta cell replication and mass remain constant. In contrast, when insufficient islet tissue is transplanted an initial increase in beta cell replication can not compensate for a decline in beta cell mass. When excessive islet tissue is transplanted, beta cell mass is reduced despite normal beta cell replication.