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The purpose of this paper is to investigate the heat transfer attributes of annular fins with quarter circle profile in terms of the Biot number Bi and the radius ratio r_r. The latter corresponds to the internal radius of the tube divided by the length of the fin in question.

To this end, the governing two-dimensional (2-D) heat conduction equation in cylindrical coordinates is numerically solved via finite element analysis for different Bi (i.e., 0.1, 1 and 5) and r_r (i.e., 0.5, 1 and 2).

The obtained results for the mid-plane and surface temperatures show that these profiles, which exhibit nearly r_r-independent responses, only present one-dimensional (1-D) radially linear distributions for the case Bi = 1. For Bi = 0.1, the temperature profiles also possess a 1-D character but with a clearly defined concave pattern. Finally, for Bi = 5, a 2-D temperature field in a wide zone from the fin base is achieved with a convex pattern for the mid-plane and surface temperatures.

Exhaustive assessment of the heat transfer in annular fins with quarter circle profile in terms of different Biot numbers and radius ratios

The purpose of this paper is to address unsteady heat conduction in two subsets of ordinary bodies. One subset consists of a large plane wall, a long cylinder and a sphere in one dimension. The other subset consists of a short cylinder and a large rectangular bar in two dimensions. The prevalent assumptions in the two subsets are: constant initial temperature, uniform surface heat flux and thermo-physical properties invariant with temperature. The engineering applications of the unsteady heat conduction deal with the determination of temperature–time histories in the two subsets using electric resistance heating, radiative heating and fire pool heating.

To this end, a novel numerical procedure named the enhanced method of discretization in time (EMDT) transforms the linear one-dimensional unsteady, heat conduction equations with non-homogeneous boundary conditions into equivalent nonlinear “quasi–steady” heat conduction equations having the time variable embedded as a time parameter. The equivalent nonlinear “quasi–steady” heat conduction equations are solved with a finite difference method.

Based on the numerical computations, it is demonstrated that the approximate temperature–time histories in the simple subset of ordinary bodies (large plane wall, long cylinder and sphere) exhibit a perfect matching over the entire time domain 0 < t < ∞ when compared against the rigorous exact temperature–time histories expressed by classical infinite series. Furthermore, using the method of superposition of solutions in the convoluted subset (short cylinder and large rectangular crossbar), the same level of agreement in the approximate temperature–time histories in the simple subset of ordinary bodies is evident.

The performance of the proposed EMDT coupled with a finite difference method is exhaustively assessed in the solution of the unsteady, one-dimensional heat conduction equations with prescribed surface heat flux for: a subset of one-dimensional bodies (plane wall, long cylinder and spheres) and a subset of two-dimensional bodies (short cylinder and large rectangular bar).

A phase‐change temperature‐based formulation including general latent heat effects is presented. These effects are taken into account by means of an explicit “phase‐change function” (or liquid fraction‐temperature relationship in a more specific context) defined analytically or based on experimental measurements. The behaviour of different functions is studied and compared. The finite element equations of this formulation are also described. Finally, a numerical example is analysed to illustrate the performance of the proposed methodology.

An integrated formulation for the analysis of casting processes is presented in this work. This model involves the description of the evolution and the coupled interactions of the flow, thermal and mechanical fields occurring during the liquid‐solid transformation of the solidifying metal. The corresponding discretized formulation is solved in the context of a fixed‐mesh finite element method. Numerical results applying this methodology in two cylindrical casting specimens are first presented to assess the influence of different phenomena occurring during the process. Moreover, these simulations are compared with available experimental data.

The modelling of steady‐state natural and mixed convection in obstructed channels is presented. The two‐dimensional numerical analysis is carried out with a finite element thermally coupled incompressible flow formulation written in terms of the primitive variables of the problem and solved via a generalized streamline operator technique. Natural convection is studied in several vertical channel configurations for a wide range of Rayleigh numbers while mixed convection is analysed in a horizontal channel with a built‐in rectangular cylinder for different Reynolds and Grashof numbers. The results obtained in this work are validated with available experiments and other existing numerical solutions.

This work is devoted to the experimental analysis, numerical modelling and validation of ice melting processes.

The thermally coupled incompressible Navier‐Stokes equations including water density inversion and isothermal phase‐change phenomena are assumed as the governing equations of the problem. A fixed‐mesh finite element formulation is proposed for the numerical solution of such model. In particular, this formulation is applied to the analysis of two different transient problems.

The numerical results computed with the finite element formulation have been found to be very similar to the corresponding predictions, also obtained in this study, provided by a finite volume enthalpy‐based technique. Both numerical results, in turn, satisfactorily approached the available experimental measurements expressly conducted in the context of this work for validation purposes.

They are mainly due to some model simplifications (e.g. no volume changes are considered during the solid‐liquid transformation) and to the inherent difficulties associated with the experimental measurements.

This study may be relevant for a better understanding of the phenomena occurring in different engineering applications involving phase‐change in water: food freezing, ice formation in pipes, freezing/melting processes in soils, ice growth in plane wings, etc.

The study is mainly focused on the validation of the numerical predictions obtained with the finite element formulation mentioned above with other results provided by a well‐known finite volume technique and, in addition, with available laboratory measurements carried out in the context of this work.

The purpose of this paper is to present a 2D numerical simulation of natural convection and phase‐change of succinonitrile in a horizontal Bridgman apparatus. Three different heat transfer mechanisms are specifically studied: no growth, solidification and melting.

The analysis is carried out with a preexisting thermally coupled fixed‐mesh finite element formulation for generalized phase‐change problems.

In the three cases analyzed, the predicted steady‐state liquid‐solid interfaces are found to be highly curved due to the development of a primary shallow cell driven by the imposed furnace temperature gradient. In the no growth case, the heating and cooling jackets remain fixed and, therefore, a stagnant liquid‐solid interface is obtained. On the other hand, the phase transformation in the solidification and melting cases is, respectively, controlled by the forward and backward movement of the jackets. In these last two growth conditions, the permanent regime is characterized by a moving liquid‐solid interface that continuously shifts with the same velocity of the jackets. The numerical results satisfactorily approach the experimental measurements available in the literature.

The numerical simulation of the no growth, solidification and melting cases in a horizontal Bridgman apparatus using a finite element based formulation is the main contribution of this work. This investigation does not only provide consistent results with those previously computed via different numerical techniques for the no growth and solidification conditions but also reports on original numerical predictions for the melting problem. Moreover, all the obtained solid‐liquid interfaces are validated with experimental measurements existing in the literature.

The present work is an experimental and numerical study of a sloshing problem including baffle effects. The purpose of this paper is to assess the numerical behavior of a Lagrangian technique to track free surface flows by comparison with experiments, to report experimental data for sloshing at different conditions and to evaluate the effectiveness of baffles in limiting the wave height and the wave propagation.

Finite element simulations performed with a fixed mesh technique able to describe the free surface evolution are contrasted with experimental data. The experiments consist of an acrylic tank of rectangular section designed to attach baffles of different sizes at different distance from the bottom. The tank is filled with water and mounted on a shake table able to move under controlled horizontal motion. The free surface evolution is measured with ultrasonic sensors. The numerical results computed for different sloshing conditions are compared with the experimental data.

The reported numerical results are in general in good agreement with the experiments. In particular, wave heights and frequencies response satisfactorily compared with the experimental data for the several cases analyzed during steady state forced sloshing and free sloshing. The effectiveness of the baffles increases near resonance conditions. From the set of experiments studied, the major reduction of the wave height was obtained when larger baffles were positioned closer to the water level at rest.

Model validation: evaluation of the effectiveness of non-massive immersed baffles during sloshing.

The value of the present work encompass the numerical and experimental study of the effect of immersed baffles during sloshing under different imposed conditions and the comparison of numerical results with the experimental data. Also, the results shown in the present work are a contribution to the understanding of the role in the analysis of the proposed problem of some specific aspects of the geometry and the imposed motion.

The purpose of this paper is to address a novel method for solving parabolic partial differential equations (PDEs) in general, wherein the heat conduction equation constitutes an important particular case. The new method, appropriately named the Improved Transversal Method of Lines (ITMOL), is inspired in the Transversal Method of Lines (TMOL), with strong insight from the method of separation of variables.

The essence of ITMOL revolves around an exponential variation of the dependent variable in the parabolic PDE for the evaluation of the time derivative. As will be demonstrated later, this key step is responsible for improving the accuracy of ITMOL over its predecessor TMOL. Throughout the paper, the theoretical properties of ITMOL, such as consistency, stability, convergence and accuracy are analyzed in depth. In addition, ITMOL has proven to be unconditionally stable in the Fourier sense.

In a case study, the 1-D heat conduction equation for a large plate with symmetric Dirichlet boundary conditions is transformed into a nonlinear ordinary differential equation by means of ITMOL. The numerical solution of the resulting differential equation is straightforward and brings forth a nearly zero truncation error over the entire time domain, which is practically nonexistent.

Accurate levels of the analytical/numerical solution of the 1-D heat conduction equation by ITMOL are easily established in the entire time domain.