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The present paper describes the applicability of hybrid transfinite element modelling/analysis formulations for non‐linear heat conduction problems involving phase change. The methodology is based on application of transform approaches and classical Galerkin schemes with finite element formulations to maintain the modelling versatility and numerical features for computational analysis. In addition, in conjunction with the above, the effects due to latent heat are modelled using enthalpy formulations to enable a physically realistic approximation to be effectively dealt computationally for materials exhibiting phase change within a narrow band of temperatures. Pertinent details of the approach and computational scheme adapted are described in technical detail. Numerical test cases of comparative nature are presented to demonstrate the applicability of the proposed formulations for numerical modelling/analysis of non‐linear heat conduction problems involving phase change.

Two analytical solutions of thermal problems connected with the disposal of nuclear waste are presented. Non‐linear diffusion problems are analysed. The use of the Kirchhoff transformation and the transformation of coordinates are made along with a numerical solution. Also comparison is made for the exact and numerical solutions for temperature histories at a nuclear waste site. A time dependent heat source is considered.

Derives a first order perturbation algorithm for the computation of mean values and (co‐) variances of the transient temperature field in conduction heated materials with random field parameters. Considers both linear as well as non‐linear heat conduction problems. The algorithm is advantageous in terms of computer time compared to the Monte Carlo method. The computer time can further be reduced by appropriate transformation of the random vectors resulting from the discretization of the random fields.

In this paper, a class of nonlinear heat‐conduction equations is derived. The properties of these heat‐conduction equations are analyzed. It is shown that the solutions of these equations contain singularity. That is, when T = T_m, discontinuity, i.e. blown‐up, occurs to the solutions. The occurrence of the blown‐ups is closely related the abnormal distribution of the initial ground temperatures, and so there might be some connections between blown‐ups and earthquakes.

We report on the progress in the development and application of a coupled boundary element/finite volume method temperature‐forward/flux‐back algorithm developed to solve conjugate heat transfer arising in 3D film‐cooled turbine blades. We adopt a loosely coupled strategy where each set of field equations is solved to provide boundary conditions for the other. Iteration is carried out until interfacial continuity of temperature and heat flux is enforced. The NASA‐Glenn explicit finite volume Navier‐Stokes code Glenn‐HT is coupled to a 3D BEM steady‐state heat conduction solver. Results from a CHT simulation of a 3D film‐cooled blade section are compared with those obtained from the standard two temperature model, revealing that a significant difference in the level and distribution of metal temperatures is found between the two. Finally, current developments of an iterative strategy accommodating large numbers of unknowns by a domain decomposition approach is presented. An iterative scheme is developed along with a physically‐based initial guess and a coarse grid solution to provide a good starting point for the iteration. Results from a 3D simulation show the process that converges efficiently and offers substantial computational and storage savings.

The purpose of this paper is to present novel search formulations in gradient‐type methods for prediction of boundary heat flux distribution in two‐dimensional nonlinear heat conduction problems.

The performance of gradient‐type methods is strongly contingent upon the effective determination of the search direction. Based on the definition of this parameter, gradient‐based methods such as steepest descent, various versions of both conjugate gradient and quasi‐Newton can be distinguished. By introducing new search techniques, several examples in the presence of noise in data are studied and discussed to verify the accuracy and efficiency of the present strategies.

The verification of the proposed methods for recovering time and space varying heat flux. The performance of the proposed methods via comparisons with the classical methods involved in its derivation.

The innovation of the present method is to use a hybridization of a conjugate gradient and a quasi‐Newton method to determine the search directions in gradient‐based approaches.

The Kirchhoff transformation, in conjunction with the finite element method, is proposed as a tool in solving non‐linear heat conduction problems. A very simple way to obtain the inverse Kirchhoff transformation is shown, using the contour lines of the Kirchhoff variable obtained from a finite element analysis.

The purpose of this paper is to determine the temperature distribution of a thin rectangular plate made of thermosensitive functionally graded (FG) material. By finding out thermal deflection and stress resultants, the thermal stresses have been obtained and analyzed.

Initially, the rectangular plate is kept at the surrounding temperature. The upper, lower and two parallel sides (y=0, b and z=0, c) are thermally insulated, while other parallel sides (x=0, a) are given convective-type heating, that is, the rate of change of the temperature of the rectangular plate is proportional to the difference between its own temperature and the surrounding temperature. The non-linear heat conduction equation has been converted to linear form by introducing Kirchhoff’s variable transformation and the resultant heat conduction equation is solved by integral transform technique with hyperbolic varying point heat source.

A mathematical model is prepared for FG ceramic–metal-based material, in which alumina is selected as the ceramic and nickel as the metal. The thermal deflection and thermal stresses have been obtained for the homogeneous and nonhomogeneous materials. The results are illustrated numerically and depicted graphically for comparison. During this study, one observed that variations are seen in the stresses, due to the variation in the inhomogeneity parameters.

The paper is constructed purely on theoretical mathematical modeling by considering various parameters and functions.

This type of theoretical analysis may be useful in high-temperature environments like nuclear components, spacecraft structural members, thermal barrier coatings, etc., as the effect of temperature and evaluation of temperature-dependent and nonhomogeneous material properties plays a vital role for accurate and reliable structural analysis.

In this paper, the authors have used thermal deflection and resultant stresses to determine the thermal stresses of a thin rectangular plate with temperature- and spatial variable-dependent material properties which is a new and novel contribution to the field.

The integral transform method is employed for the hybrid numerical‐analytical solution of two‐dimensional, steady‐state heat conduction within extended surfaces of variable longitudinal profile and temperature dependent thermal conductivity. Numerical results are then obtainable with automatic accuracy, allowing for the establishment of benchmark results and for the validation of approximate solutions. Convergence rates are illustrated for longitudinal fins with trapezoidal and parabolic profiles, and for different values of the governing parameters, Biot number and aspect ratio. In addition, the classical one‐dimensional approximate solutions are critically examined for these typical non‐straight profiles, and the applicability limits are investigated.

In the present work, we focus on developing an in-house parallel meshless local Petrov-Galerkin (MLPG) code for the analysis of heat conduction in two-dimensional and three-dimensional regular as well as complex geometries.

The parallel MLPG code has been implemented using open multi-processing (OpenMP) application programming interface (API) on the shared memory multicore CPU architecture. Numerical simulations have been performed to find the critical regions of the serial code, and an OpenMP-based parallel MLPG code is developed, considering the critical regions of the sequential code.

Based on performance parameters such as speed-up and parallel efficiency, the credibility of the parallelization procedure has been established. Maximum speed-up and parallel efficiency are 10.94 and 0.92 for regular three-dimensional geometry (343,000 nodes). Results demonstrate the suitability of parallelization for larger nodes as parallel efficiency and speed-up are more for the larger nodes.

Few attempts have been made in parallel implementation of the MLPG method for solving large-scale industrial problems. Although the literature suggests that message-passing interface (MPI) based parallel MLPG codes have been developed, the OpenMP model has rarely been touched. This work is an attempt at the development of OpenMP-based parallel MLPG code for the very first time.