scholarly journals Heat Transfer Process with Solid-solid Interface: Analytical and Numerical Solutions

2021 ◽  
Vol 20 ◽  
pp. 404-414
Author(s):  
Diana Rubio ◽  
Domingo A. Tarzia ◽  
Guillermo F. Umbricht

This work is aimed at the study and analysis of the heat transport on a metal bar of length L with a solid-solid interface. The process is assumed to be developed along one direction, across two homogeneous and isotropic materials. Analytical and numerical solutions are obtained under continuity conditions at the interface, that is a perfect assembly. The lateral side is assumed to be isolated and a constant thermal source is located at the left-boundary while the right-end stays free allowing the heat to transfer to the surrounding fluid by a convective process. The differences between the analytic solution and temperature measurements at any point on the right would indicate the presence of discontinuities. The greater these differences, the greater the discontinuity in the interface due to thermal resistances, providing a measure of its propagation from the interface and they could be modeled as temperature perturbations. The problem of interest may be described by a parabolic equation with initial, interface and boundary conditions, where the thermal properties, the conductivity and diffusivity coefficients, are piecewise constant functions. The analytic solution is derived by using Fourier methods. Special attention is given to the Sturm-Liouville problem that arises when deriving the solution, since a complicated eigenvalue equation must to be solved. Numerical simulations are conducted by using finite difference schemes where its convergence and stability properties are discussed along with physical interpretations of the results.

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.


2021 ◽  
pp. 1-4
Author(s):  
Iyad Said Hamadi ◽  
Lubna Lutfi ◽  
Asma Anan Mohammed ◽  
Zahr Alkhadem

Branchial cleft cysts are congenital anomalies that most commonly arise from a failure of fusion of the second branchial arch during embryonic life. They usually present as a swelling in the lateral side of the neck, below the mandible. In this article, we present a case of a 28-year-old female patient with a right branchial cyst measuring 7 × 6 × 5 cm, who presented with an asymptomatic, rapidly growing mass in the right anterior triangle of the neck that abutted the right external carotid artery, leading to stenosis of the vessel that is preceded by dilatation above the site of compression. She underwent excision of the cystic mass with preservation of the facial nerve and presented no active complaints on follow-up a few weeks postoperatively.


2021 ◽  
Vol 23 (3) ◽  
pp. 123
Author(s):  
MajedAbdul Basit Momin ◽  
Nagendra Mahendra ◽  
Abhijeet Ingle ◽  
ShumailaAbdul Rehman ◽  
DharmendraKumar Borad
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Author(s):  
Jairo Rodríguez-Padilla ◽  
Daniel Olmos-Liceaga

The implementation of numerical methods to solve and study equations for cardiac wave propagation in realistic geometries is very costly, in terms of computational resources. The aim of this work is to show the improvement that can be obtained with Chebyshev polynomials-based methods over the classical finite difference schemes to obtain numerical solutions of cardiac models. To this end, we present a Chebyshev multidomain (CMD) Pseudospectral method to solve a simple two variable cardiac models on three-dimensional anisotropic media and we show the usefulness of the method over the traditional finite differences scheme widely used in the literature.


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