The Stationary Thermal Field in a Multilayer Elliptic Cylinder

An analytical–numerical method for determining the two-dimensional (2D) thermal field in a layer-inhomogeneous elliptic cylinder (elliptical roller) was developed in the article. A mathematical model was formulated in the form of a boundary problem for Poisson equations with an external boundary condition of the third kind (Hankel’s). The conditions of continuity of temperature and heat flux increment were assumed at the inner boundaries of material layers. The eigenfunctions of the boundary problem were determined analytically. Hankel’s condition was subjected to appropriate mathematical transformations. As a result, a system of algebraic equations with respect to the unknown coefficients of the eigenfunctions was obtained. The above-mentioned system of equations was solved numerically (iteratively). As an example of an application of the aforementioned method, an analysis of the thermal field in an elliptical electric wire was presented. The system consists of an aluminum core and two layers of insulation (PVC and rubber). In addition to the field distribution, the steady-state current rating was also determined. The thermal conductivities of PVC and rubber are very similar to each other. For this reason, apart from the real model, a test system was also considered. Significantly different values of thermal conductivity were assumed in individual layers of the test model. The temperature distributions were presented graphically. The graphs showed that the temperature drop is almost linear in the insulation of an electrical conductor. On the other hand, in the analogous area of the test model, a broken line was observed. It was also found that the elliptical layer boundaries are not isothermal. The results obtained by the method presented in this paper were verified numerically

The Distribution of the Thermal Field in an Elliptical Electric Conductor Coated with Insulation

The paper determines the stationary thermal field in an elliptical cross-section electric conductor coated with insulation. Heat is generated by the flow of alternating current (AC) through the conducting core, and then dissipated from the insulation surface via convection and radiation. The authors have developed an original method for hybrid (analytical–numerical) modeling of a field. This method has been used to solve the relevant boundary problem of Poisson’s equation. While the eigenfunctions of the Laplace operator were determined analytically, the coefficients of the eigenfunctions were calculated by iteratively solving an appropriate system of algebraic equations. The proposed method enables the analysis of systems with an elliptical geometry and a heterogeneous layered structure (e.g., air, aluminum alloy, PCV), and does not require area discretization (grid). The developed analytical–numerical (AN) method has been positively verified using finite elements (FEs). The determined thermal field is illustrated graphically. The obtained solution has a good physical interpretation

An analytical-numerical method for calculating the stationary thermal field in electrical systems with elliptical cross-sections

In this article, an analytical-numerical approach to calculating a stationary thermal field in the elliptical region is presented. The eigenfunctions of the Laplace operator were determined analytically, whereas the coefficients of the eigenfunctions were obtained numerically. The cooling was modeled with 3rd kind (Hankel’s) boundary condition, where the total heat transfer coefficient was the sum of the convective and radiative components. The method was used to analyze the thermal field in an elliptical conductor and a dielectrically heated elliptical column. The basic parameters of these systems, i.e. their steady-state current rating and the maximum charge temperature, were determined. The results were verified using the finite element method and have been presented graphically

The thermal characteristics of ACCR lines as a function of wind speed – an analytical approach

The paper has investigated the effect of wind speed on selected thermal characteristics of the contemporary ACCR line. As wind speed functions, heating curves, stationary temperature profiles, steady-state current ratings and thermal time constants, have been determined. The composite core (Al–Al2O3) and the Al–Zr alloy braid were modeled as porous solids. As a result, the physical model is composed of a solid cylinder and a hollow cylinder with different material parameters of the above-mentioned elements. The mathematical model was formulated as the boundary-initial problem of the parabolic heat equation. The problem was solved by the state-superposition of and variable-separation method. On this basis, a computer program was developed in the Mathematica 10.4 environment and the velocity characteristics sought for were plotted. The results obtained analytically were positively verified by the finite-element method in the NISA v.16 environment. The physical interpretation of the determined characteristics has been given

The Stationary Thermal Field in a Multilayer Elliptic Cylinder

An analytical–numerical method for determining the two-dimensional (2D) thermal field in a layer-inhomogeneous elliptic cylinder (elliptical roller) was developed in the article. A mathematical model was formulated in the form of a boundary problem for Poisson equations with an external boundary condition of the third kind (Hankel’s). The conditions of continuity of temperature and heat flux increment were assumed at the inner boundaries of material layers. The eigenfunctions of the boundary problem were determined analytically. Hankel’s condition was subjected to appropriate mathematical transformations. As a result, a system of algebraic equations with respect to the unknown coefficients of the eigenfunctions was obtained. The above-mentioned system of equations was solved numerically (iteratively). As an example of an application of the aforementioned method, an analysis of the thermal field in an elliptical electric wire was presented. The system consists of an aluminum core and two layers of insulation (PVC and rubber). In addition to the field distribution, the steady-state current rating was also determined. The thermal conductivities of PVC and rubber are very similar to each other. For this reason, apart from the real model, a test system was also considered. Significantly different values of thermal conductivity were assumed in individual layers of the test model. The temperature distributions were presented graphically. The graphs showed that the temperature drop is almost linear in the insulation of an electrical conductor. On the other hand, in the analogous area of the test model, a broken line was observed. It was also found that the elliptical layer boundaries are not isothermal. The results obtained by the method presented in this paper were verified numerically

Intraarterial CT angiography using ultra low volume of iodine contrast : own experiences

BACKGROUND: High volume of intravenous contrast in CT-angiography may result in contrast-induced nephropathy. Intraarterial ultra-low volume of contrast medium results in its satisfactory blood concentration with potentially good image quality. The first main purpose was to assess the influence of the method on function of transplanted kidney in patients with impaired graft function. The second main purpose of the study was to evaluate the usefulness of this method for detection of gastrointestinal and head-and-neck haemorrhages. MATERIAL AND METHODS: Between 2010 and 2013 intraarterial CT-angiography was performed in 56 patients, including 28 with chronic kidney disease (CKD). There were three main subgroups: 18 patients after kidney transplantation, 10 patients with gastrointestinal hemorrhage, 8 patients with head-and-neck hemorrhage. Contralateral or ipsilateral inguinal arterial approach was performed. The 4-French vascular sheaths and 4F-catheters were introduced under fluoroscopy. Intraarterial CT was performed using 64-slice scanner. The scanning protocol was as follows: slice thickness 0.625 mm, pitch 1.3, gantry rotation 0.6 sec., scanning delay 1-2 sec. The extent of the study was established on the basis of scout image. In patients with CKD 6-8 mL of Iodixanol (320 mg/mL) diluted with saline to 18-24 mL was administered at a speed of 4-5 mL/s. RESULTS: Vasculature was properly visualized in all patients. In patients with impaired renal function creatinine/eGFR levels remained stable in all but one case. Traditional arteriography failed and CT-angiography demonstrated the site of bleeding in 3 of 10 patients with symptoms of gastrointestinal bleeding (30%). In 8 patients with head-and-neck bleeding CT-angiography did not prove beneficial when compared to traditional arteriography. CONCLUSIONS: 1. Ultra-low contrast intraarterial CT-angiography does not deteriorate the function of transplanted kidneys in patients with impaired graft function. 2. 3D reconstructions allow for excellent visualization of vascular anatomy of renal transplants. 3. Intraarterial CT-angiography is useful for detection of the bleeding site