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The purpose of this paper is to examine the effect of non-linear thermal radiation, Joule heating and viscous dissipation on the mixed convection boundary layer flow of MHD nanofluid flow over a thin moving needle.

The equations directing the flow are reduced into ODEs by implementing similarity transformation. The Runge–Kutta–Fehlberg method with a shooting technique was implemented.

Numerical outcomes for the coefficient of skin friction and the rate of heat transfer are tabulated and discussed. Also, the boundary layer thicknesses for flow and temperature fields are addressed with the aid of graphs.

Till now, no numerical study investigated the combined influence of Joule heating, non-linear thermal radiation and viscous dissipation on the mixed convective MHD flow of silver-water nanofluid flow past a thin moving needle. The numerical results for existing work are new and their novelty verified by comparing them with the work published earlier.

The purpose of this paper is to explore the effects of binary chemical reaction and activation energy on nano Casson liquid flow past a stretched plate with non-linear radiative heat, and also, the effect of a novel exponential space-dependent heat source (ESHS) aspect along with thermal-dependent heat source (THS) effect in the analysis of heat transfer in nanofluid. Comparative analysis is carried out between the flows with linear radiative heat process and non-linear radiative heat process.

A similarity transformation technique is utilised to access the ODEs from the governed PDEs. The manipulation of subsequent non-linear equations is carried out by a well-known numerical approach called Runge–Kutta–Fehlberg scheme. Obtained solutions are briefly discussed with the help of graphical and tabular illustrations.

The effects of various physical parameters on temperature, nanoparticles volume fraction and velocity fields within the boundary layer are discussed for two different flow situations, namely, flow with linear radiative heat and flow with non-linear radiative heat. It is found that an irregular heat source/sink (ESHS and THS) and non-linear solar radiation play a vital role in the enhancement of the temperature distributions.

The problem is relatively original to study the effects of activation energy and binary chemical reaction along with a novel exponential space-based heat source on laminar boundary flow past a stretched plate in the presence of non-linear Rosseland radiative heat.

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.

This paper aims to focus on linear and non-linear convection in a lid-driven square cavity with isothermal and non-isothermal bottom surface.

It is assumed that the top moving wall is adiabatic and the bottom wall is heated in two modes, and the rest of the walls are maintained at uniform cold temperature. The coupled governing non-linear partial differential equations are solved numerically with MAC algorithm for conducting a parametric study with uniform and non-uniform temperature bottom wall.

The numerical results are depicted in the form of streamlines, temperature contours and variation of local Nusselt number. The local Nusselt number at the bottom wall of the cavity increases in presence of non-linear temperature parameter as compared with linear temperature parameter and heat transfer reduces with increasing of Ha for uniform and non-uniform heating of bottom wall.

The numerical investigation is conducted for unsteady, two-dimensional natural convective flow in a square cavity. An extension of the present study with the effect of inclination of cavity, wavy walls and triangular cavity will be the interest of future work.

This work studies the effect of magnetic field in the presence of linear convection and non-linear convection. This study might be useful to cooling of electronic components, alloy casting, crystal growth and fusion reactors, etc.

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.

This paper aims to present two mathematical models to solve the Energy Management problem of a building microgrid (MG). In particular, it proposes a deterministic mixed integer linear programming (MILP) and non-linear programming (NLP) formulations. This paper focuses on the modelling process and the optimization performances for both approaches regarding optimal operation of near-zero energy buildings connected to an electric MG with a 24-h time horizon.

A general architecture of a MG is detailed, involving energy storage systems, distributed generation and a thermal reduced model of the grid-connected building. A continuous non-linear model is detailed along with linearizations for the mixed-integer liner formulation. Multi-physic, non-linear and non-convex phenomena are detailed, such as ventilation and air quality models.

Results show that both approaches are relevant for solving the energy management problem of the building MG.

Introduction and modelling of the thermal loads within the MG. The resulting linear program handles the mutli-objective trade-off between discomfort and the cost of use taking into account air quality criterion. Linearization and modelling of the ventilation system behaviour, which is generally non-linear and non-convex equality constraints, involving air quality model, heat transfer and ventilation power. Comparison of both MILP and NLP methods on a general use case provides a solution that can be interpreted for implementation.

The purpose of this paper is to access performance of existing computational techniques to model strongly non‐linear coupled thermo‐electric problems.

A thermistor is studied as an example of a strongly non‐linear diffusion problem. The temperature field and the current flow in the device are mutually coupled via ohmic heating and very rapid variations of electric conductivity with temperature and applied electric field, which makes the problem an ideal test case for the computational techniques. The finite volume fully coupled and fractional steps (splitting) approaches on a fixed computational grid are compared with a fully coupled front‐fixing method. The algorithms' input parameters are verified by comparison with published experiments.

It was found that fully coupled methods are more effective for non‐linear diffusion problems. The front fixing provides additional improvements in terms of accuracy and computational cost.

This paper for the first time compares in detail advantages and implementation complications of each method being applied to the coupled thermo‐electric problems. Particular attention is paid to conservation properties of the algorithms and accurate solutions in the transition region with rapid changes in material properties.

The paper presents the results of computer simulation of the process of induction heating with series transistor inverter. In the simulation of induction heating system the coupled harmonic electromagnetic and transient thermal fields were combined with the simulated real energy source. As a source, the transistor bridge inverter with series resonant circuit was applied. The source parameters (inductor voltage and frequency) depend on the load parameters obtained by numerical calculations of the coupled fields. As the examples, the induction heating before hardening of stationary cylindrical workpiece and of the moving flat workpiece were considered. The simulation results were compared with these obtained in the simulation at constant inductor voltage and frequency.

This paper aims to deal with the experimental and numerical investigations of the fire protection performance of a waterborne intumescent coating (IC) on structural steel in case of natural fires. Based on own small-scale laboratory tests, an advanced numerical model is developed to simulate the fire protection performance of the investigated coating in case of arbitrary fire scenarios. The insulation efficiency of the coating is described within the model by temperature and heating rate-dependent material properties, such as expansion factors, thermal conductivity and heat capacity. The results of the numerical model are compared to own large-scale fire tests of an unloaded I-section beam and column.

As natural fires can show arbitrary regimes, the material properties of the waterborne IC are investigated for various heating rates. Based on these investigations, a material model for the IC is implemented in the finite element program ABAQUS. With the help of user subroutines, the material properties of the coating are introduced for both the heating and cooling phase of natural fires, allowing for two- and three-dimensional thermomechanical analyses of coated steel elements.

The results of the performed small-scale laboratory tests show a heating rate-dependent behavior of the investigated coating. The mass loss as well as the expansion of the coating change with the heating rate. Moreover, the material properties obtained on small scale are valid for large scale. Therefore, a material model could be developed that is suitable to reproduce the results of the large-scale fire tests. Additionally, with the help of the numerical model, a dimensioning approach for the dry film thickness (DFT) of the investigated coating is derived for arbitrary natural fires.

The material properties presented in this paper are only valid for the investigated waterborne IC and the parameter area that was chosen. However, the developed modeling approach for the fire protection performance of ICs is general and can be applied for every coating that is part of the intumescent product family.

Until now, only few research works have been carried out on the fire protection performance of ICs under non-standard fire exposure. This paper deals extensively with the material properties and the material modeling of a waterborne IC exposed to natural fires. Especially, the laboratory examinations and the numerical simulations are unique and allow for new evaluation possibilities of ICs.

Concrete arch structures are commonly constructed for various civil engineering applications. Despite their frequent use, there is a lack of research on the response and performance of concrete arches when subjected to fire loading. Hence, this paper aims to investigate the response and in-plane failure modes of shallow circular concrete arches subjected to mechanical and fire loading.

This study is conducted through the development of a three-dimensional finite element (FE) model in ANSYS. The FE model is verified by comparison to a non-discretisation numerical model derived herein and the reduced modulus buckling theory, both used for the non-linear inelastic analysis of shallow concrete arches subjected to uniformly distributed radial loading and uniform temperature field. Both anti-symmetric and symmetric buckling modes are examined, with analysis of the former requiring geometric imperfection obtained by an eigenvalue buckling analysis.

The FE results show that anti-symmetric bifurcation buckling is the dominant failure mode in shallow concrete arches under mechanical and fire loading. Additionally, parametric studies are presented which illustrate the influence of various parameters on fire resistance time.

Fire response of concrete arches has not been reported in the open literature. The authors have previously investigated the stability of shallow concrete arches subjected to mechanical and uniform thermal loading. It was found that temperature greatly reduced the buckling loads of concrete arches. However, this study was limited to the simplifying assumptions made which include elastic material behaviour and uniform temperature loading. The present study provides a realistic insight into the fire response and stability of shallow concrete arches. The findings herein may be adopted in the fire design of shallow concrete arches.