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Gas insulated systems, such as gas insulated lines (GIL), use insulating gas, mostly sulfur hexalfluoride (SF₆), to enable a higher dielectric strength compared to e.g. air. However, under high voltage direct current conditions, charge accumulation and electric field stress may occur, which may lead to partial discharge or system failure. Therefore, numerical simulations are used to design the system and determine the electric field and charge distribution. Although the gas conduction shows a more complex current–voltage characteristic compared to solid insulation, the electric conductivity of the SF₆ gas is set as constant in most works. The purpose of this study is to investigate different approaches to address the conduction in the gas properly for numerical simulations.

In this work, two approaches are investigated to address the conduction in the insulating gas and are compared to each other. One method is an ion-drift-diffusion model, where the conduction in the gas is described by the ion motion in the SF₆ gas. However, this method is computationally expensive. Alternatively, a less complex approach is an electro-thermal model with the application of an electric conductivity model for the SF₆ gas. Measurements show that the electric conductivity in the SF₆ gas has a nonlinear dependency on temperature, electric field and gas pressure. From these measurements, an electric conductivity model was developed. Both methods are compared by simulation results, where different parameters and conditions are considered, to investigate the potential of the electric conductivity model as a computationally less expensive alternative.

The simulation results of both simulation approaches show similar results, proving the electric conductivity for the SF₆ gas as a valid alternative. Using the electro-thermal model approach with the application of the electric conductivity model enables a solution time up to six times faster compared to the ion-drift-diffusion model. The application of the model allows to examine the influence of different parameters such as temperature and gas pressure on the electric field distribution in the GIL, whereas the ion-drift-diffusion model enables to investigate the distribution of homo- and heteropolar charges in the insulation gas.

This work presents numerical simulation models for high voltage direct current GIL, where the conduction in the SF₆ gas is described more precisely compared to a definition of a constant electric conductivity value for the insulation gas. The electric conductivity model for the SF₆ gas allows for consideration of the current–voltage characteristics of the gas, is computationally less expensive compared to an ion-drift diffusion model and needs considerably less solution time.

To develop new and existing coupled thermal and mechanical models of electromagnetic solids for the simulation of coupled field problems based on a consistent theoretical and computational framework.

The finite element computational models we describe involve the combination of classical electrodynamics, continuum mechanics, and thermodynamics. In order to create consistent coupled models, we employ the fundamental principles of thermodynamics as a common framework.

Our procedure requires the necessary thermodynamical considerations for building consistent multiphysics models and develops some novel implementation issues that are important from the designers' point of view. Additionally, efficient numerical algorithms for solving the arising static and dynamic nonlinearities are discussed.

The paper targets the simulation of coupled problems in macroscopic electromagnetic continua.

The application areas of the coupled field models are identified and illustrated by the solution of complex industrial problems.

We introduce new computational models and techniques for the solution of some coupled field problems in electromagnetic solids. While some elements of these computational models and techniques have been used for decades, the complete theoretical and computational framework is presented for the first time here.

In high voltage direct current cable systems, cable joints are known as the least reliable components due to the use of multiple dielectrics. Resulting from the electric field and temperature depending conductivity of the different dielectrics, field enhancement at critical areas, e.g. triple points, may result in accelerated aging and the failure of the component. To reduce the stress, different field grading techniques are applied. The purpose of this study is to investigate different grading techniques for cable joints. Different shapes of the electrode and a varying nonlinear conductivity of field grading materials (FGM) are used for the simulation of the electric field.

Coupled electro-thermal field simulations are applied for different joint geometries, to obtain the stationary electric field. Electric field simulations in cable joint using geometric and nonlinear field grading techniques are shown.

Using the geometric field grading, the shape of the stress cone determines the field values in critical areas (triple points). High stress reduction is obtained for a certain curvature of the stress cone. For the nonlinear stress control, materials with a higher conductivity in comparison to the cable and the joint material are used. A field reduction is obtained by increasing the total conductivity. On the other hand, this is also increasing the insulation losses within the total FGM. More applicable is the decrease of the switching field or the increase of nonlinearity, which is only locally increase the conductivity and the insulation losses. Furthermore, simulations results show that an approximately constant field reduction is obtained, if the nonlinearity is above a certain threshold.

This study is restricted to a field dependency of FGM only. For impulse voltages, high temperature and electric conductivity values my result in a thermal runaway. Furthermore, only direct current field grading techniques are studied.

The field grading of cable joints, using geometric and nonlinear techniques, is analyzed. A comparison between the electric field, by varying the curvature of the ground stress cone or the FGM conductivity constants in a complex joint geometry is novel. With its effect on the electric fields, general requirements for the geometry (geometric field grading) or the values of the FGM constants (nonlinear field grading) are defined to obtain a sufficient field grading.

It is well known that the prefabricated vertical drain (PVD) installation process generates a significant soil disturbance around PVD. This disturbed zone significantly affects the rate of settlement and excess pore pressure dissipation. However, the characteristics of these zones were still uncertain and difficult to quantify; there remains large discrepancy among researchers. This study aims to develop a simple analytical solution for radial consolidation analysis of PVD-installed deposit considering mandrel-induced disturbance.

The proposed solution takes into account the nonlinear distributions of both horizontal hydraulic conductivity and compressibility toward the drain. The proposed solution was applied to analyze field behavior of test embankment in New South Wales, Australia.

Both effects significantly increased the time required to achieve a certain degree of consolidation. The effect of hydraulic conductivity on the consolidation rate was more significant than the effect of compressibility variation. And, the increased compressibility in the soil-disturbed zone due to mandrel installation significantly increased vertical strain of the PVD-improved soil deposit. The predicted results using the proposed analytical solution were in good agreement with the field measurements.

A geotechnical engineer could use the proposed analytical solution to predict consolidation behavior of drainage-installed ground.

Consolidation behavior of PVD-installed ground could be reasonably predicted by using the proposed solution with considering variations of both hydraulic conductivity and compressibility due to PVD installation.

The purpose of this paper is to study the thermal behaviour of a fully wet porous fin of longitudinal profile. The significance of radiative and convective heat transfer has been scrutinised along with the simultaneous variation of surface emissivity, heat transfer coefficient and thermal conductivity with temperature. The emissivity of the surface and the thermal conductivity are considered as linear functions of the local temperature between fin and the ambient. Darcy’s model was considered to formulate the heat transfer equation. According to this, the porous fin permits the flow to penetrate through it and solid–fluid interaction occurs.

Runge–Kutta–Fehlberg fourth–fifth-order method has been used to solve the reduced non-dimensionalized ordinary differential equation involving highly nonlinear terms.

The impact of pertinent parameters, such as convective parameter, radiative parameter, conductivity parameter, emissivity parameter, wet porous parameter, etc., on the temperature profiles were elaborated mathematically with the plotted graphs. The heat transfer from the fin enhances with the rise in convective parameter.

The wet nature of the fin enhances heat transfer and in many practical applications the parameters, such as thermal conductivity, heat transfer coefficient as well as surface emissivity, vary with temperature. Hence, the main objective of the current study is to depict the significance of simultaneous variation in surface emissivity, heat transfer coefficient and thermal conductivity with respect to temperature under natural convection and radiation condition in a totally wetted longitudinal porous fin.

This work seeks to analyze the heat transfer phenomena of anisotropic thermal conductivity fabrics containing electric conductive yarns.

A numerical program, based on a spectral element method, is used to assess the heating fabric with a temperature control model. The study determines suitable parameters for the fabric by evaluating the temperature uniformity on the fabric surface. Effective thermal conductivities of the fabric are obtained by comparing the experimental and numerical results with each other, using a nonlinear least‐square fitting method.

The results indicate that employing high effective thermal conductivity of non‐electric conductive yarns in a direction perpendicular to electric conductive yarns helps to increase temperature uniformity. However, the effect of the high effective thermal conductivity of electric conductive yarns is not evident. Adopting a short distance between the electric conductive yarns and a thick fabric is also beneficial in increasing temperature uniformity. If the heating fabric is applied in a place where there is easy energy transfer between the surface of the fabric and moving air, collocation with high heating power is needed to maintain the temperature. Choosing an appropriate heating source is essential when considering temperature uniformity and energy savings using a temperature controller.

The findings will be useful in the design of heating fabrics.

This paper aims to study nonlinear heat transfer through a longitudinal fin of three different profiles.

A truly meshfree method is used to undertake a nonlinear analysis to predict temperature distribution and heat-transfer rate.

A longitudinal fin of three different profiles, such as rectangular, triangular and concave parabolic, are analyzed. Temperature variation, along with the fin length and rate of heat transfer in steady state, under convective and convective-radiative environments has been demonstrated and explained. Moving least square (MLS) approximants are used to approximate the unknown function of temperature T(x) with Th(x). Essential boundary conditions are imposed using the penalty method. An iterative predictor–corrector scheme is used to handle nonlinearity.

Modelling fin in a convective-radiative environment removes the assumption of no radiation condition. It also allows to vary convective heat-transfer coefficient and predict the closer values to the real problems for the corresponding fin surfaces.

The meshless local Petrov–Galerkin method can solve nonlinear fin problems and predict an accurate solution.

This paper aims to use the Laplace Adomian decomposition method (LADM) to investigate the effects of thermal convection, thermal conduction, surface emissivity and thermal radiation on the heat dissipated by a continuously moving plate undergoing thermal processing.

In performing the analysis, it is assumed that the thermal conductivity and surface emissivity of the plate are both temperature-dependent. The accuracy of the LADM solutions is confirmed by comparing the results obtained for the temperature distribution within the plate with those reported in the literature based on the differential transformation method.

It is shown that the heat dissipated from the plate reduces as the Peclet number increases. By contrast, the dissipated heat increases as any one of the non-dimensionalized parameters of the system, i.e. Nc, Nr and B, increases. In addition, the temperature drop along the length of the plate reduces as parameter A increases owing to a more rapid heat transfer.

The results provide a useful source of reference for the choice of suitable materials and cooling fluids in a variety of practical applications.

This paper aims to study the magneto-radiative gas (water vapor) on an unsmooth boundary.

This paper provided a numerical treatment via the implicit Chebyshev pseudo-spectral method to investigate unsteady compressible magneto-radiative gas (water vapor Pr = 1) flow near a heated vertical wavy wall through porous medium in the presence of inclined magnetic field. The impacts of viscous dissipation, temperature-dependent fluid properties, thermal conductivity and viscosity in the presence of nonlinear thermal radiation are studied. The sinusoidal surface is transformed into a flat one using a suitable transformation. The comparison figures of published data with the present outcomes illustrate a good match. The present steady-state outcomes are presented for the temperature, velocity, Nusselt number and the shearing stress through figures for several interested physical parameters, namely, compressibility, magnetic, radiation, viscosity–temperature variation, thermal conductivity–temperature variation, surface sinusoidal waveform and porous parameters.

The present numerical outcomes confirm the importance of applying nonlinear thermal radiation cases in all studies that investigate heat transfer under the influence of thermal radiation.

A mathematical model is established for a wavy boundary, and Chebyshev pseudo-spectral method is adopted for the numerical study.

In high-voltage direct current (HVDC) cable systems, space charges accumulate because of the constant applied voltage and the nonlinear electric conductivity of the insulating material. The change in the charge distribution results in a slowly time-varying electric field. Space charges accumulate within the insulation bulk and at interfaces. With an operation time of several years of HVDC systems, typically the stationary electric field is of interest. The purpose of this study is to investigate the influence of interfaces on the stationary electric field stress and space charge density.

An analytic description of the stationary electric field inside cable insulation is developed and numerical simulations of a cable joint geometry are applied, considering spatial variations of the conductivity in the vicinity of the electrodes and interfaces.

With increasing conductivity values toward the electrodes, the resulting field stress decreases, whereas a decreasing conductivity results in an increasing electric field. The increased electric field may cause partial discharge, resulting in accelerated aging of the insulation material. Thus, interfaces and surfaces are characterized as critical areas for the reliability of HVDC cable systems.

This study is restricted to stationary electric field and temperature distributions. The electric field variations during a polarity reversal or a time-varying temperature may result in an increased electric conductivity and electric field at interfaces and surfaces.

An analytical description of the electric field, considering surface effects, is developed. The used conductivity model is applicable for cable and cable-joint insulations, where homo- and hetero-charge effects are simulated. These simulations compare well against measurements.