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The thermal behavior at the interfaces (of the deposited strands) during fused filament fabrication (FFF) technique strongly influences bond formation and it is a time- and temperature-dependent process. The processing parameters affect the thermal behavior at the interfaces and the purpose of the paper is to simulate using temperature-dependent (nonlinear) thermal properties rather than constant properties.

Nonlinear temperature-dependent thermal properties are used to simulate the FFF process in a simulation software. The finite-element model is first established by comparing the simulation results with that of analytical and experimental results of acrylonitrile butadiene styrene and polylactic acid. Strand temperature and time duration to reach critical sintering temperature for the bond formation are estimated for one of the deposition sequences.

Temperatures are estimated at an interface and are then compared with the experimental results, which shows a close match. The results of the average time duration (time to reach the critical sintering temperature) of strands with the defined deposition sequences show that the first interface has the highest average time duration. Varying processing parameters show that higher temperatures of the extruder and envelope along with higher extruder diameter and lower convective heat transfer coefficient will have more time available for bonding between the strands.

A novel numerical model is developed using temperature-dependent (nonlinear) thermal properties to simulate FFF processes. The model estimates the temperature evolution at the strand interfaces. It helps to evaluate the time duration to reach critical sintering temperature (temperature above which the bond formation occurs) as it cools from extrusion temperature.

The main objective of this paper is to investigate the response of human skin to an intense temperature drop at the surface. In addition, this paper aims to evaluate the efficiency of finite difference and finite volume methods in solving the highly nonlinear form of Pennes’ bioheat equation.

One-dimensional linear and nonlinear forms of Pennes’ bioheat equation with uniform grids were used to study the behavior of human skin. The specific heat capacity, thermal conductivity and blood perfusion rate were assumed to be linear functions of temperature. The nonlinear form of the bioheat equation was solved using the Newton linearization method for the finite difference method and the Picard linearization method for the finite volume method. The algorithms were validated by comparing the results from both methods.

The study demonstrated the capacity of both finite difference and finite volume methods to solve the one-dimensional and highly nonlinear form of the bioheat equation. The investigation of human skin’s thermal behavior indicated that thermal conductivity and blood perfusion rate are the most effective properties in mitigating a surface temperature drop, while specific heat capacity has a lesser impact and can be considered constant.

This paper modeled the transient heat distribution within human skin in a one-dimensional manner, using temperate-dependent physical properties. The nonlinear equation was solved with two numerical methods to ensure the validity of the results, despite the complexity of the formulation. The findings of this study can help in understanding the behavior of human skin under extreme temperature conditions, which can be beneficial in various fields, including medical and engineering.

The purpose of this paper is to determine the fin efficiency of convective straight fins with temperature dependent thermal conductivity by using Homotopy Perturbation Method.

Most engineering problems, especially heat transfer equations are in nonlinear form. Homotopy Perturbation Method (HPM) has been applied to solve a wide series of nonlinear differential equations. In this paper, HPM is used for obtaining the fin efficiency of convective straight fins with temperature‐dependent thermal conductivity. Comparison of the results with those of Homotopy Perturbation Method, exact solution, numerical results and Adomian's decomposition method (ADM) were been done by Cihat Arslanturk.

Results show that both Homotopy Perturbation Method and ADM applied to the nonlinear equations were capable of solving them with successive rapidly convergent approximations without any restrictive assumptions or transformations causing changes in the physical properties of the problem. Moreover, adding up the number of iterations leads to explicit solution for the problem. The results are just obtained with two iterations. This shows the accuracy and great potential of this method. Finally, it can be seen that, with increase of thermo‐geometric fin parameter (v), the fin efficiency increases too.

The results demonstrate good validity and great potential of the HPM for Heat Transfer equations in engineering problems.

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.

The study aims to highlight the behaviour of one-dimensional and two-dimensional fin models under the natural room conditions, considering the different values of dimensionless Biot number (Bi). The effect of convection and radiation on the heat transfer process has also been demonstrated using the meshless local Petrov–Galerkin (MLPG) approach.

It is true that MLPG method is time-consuming and expensive in terms of man-hours, as it is in the developing stage, but with the advent of computationally fast new-generation computers, there is a big possibility of the development of MLPG software, which will not only reduce the computational time and cost but also enhance the accuracy and precision in the results. Bi values of 0.01 and 0.10 have been taken for the experimental investigation of one-dimensional and two-dimensional rectangular fin models. The numerical simulation results obtained by the analytical method, benchmark numerical method and the MLPG method for both the models have been compared with that of the experimental investigation results for validation and found to be in good agreement. Performance of the fin has also been demonstrated.

The experimental and numerical investigations have been conducted for one-dimensional and two-dimensional linear and nonlinear fin models of rectangular shape. MLPG is used as a potential numerical method. Effect of radiation is also, implemented successfully. Results are found to be in good agreement with analytical solution, when one-dimensional steady problem is solved; however, two-dimensional results obtained by the MLPG method are compared with that of the finite element method and found that the proposed method is as accurate as the established method. It is also found that for higher Bi, the one-dimensional model is not appropriate, as it does not demonstrate the appreciated error; hence, a two-dimensional model is required to predict the performance of a fin. Radiative fin illustrates more heat transfer than the pure convective fin. The performance parameters show that as the Bi increases, the performance of fin decreases because of high thermal resistance.

Though, best of the efforts have been put to showcase the behaviour of one-dimensional and two-dimensional fins under nonlinear conditions, at different Bi values, yet lot more is to be demonstrated. Nonlinearity, in the present paper, is exhibited by using the thermal and material properties as the function of temperature, but can be further demonstrated with their dependency on the area. Additionally, this paper can be made more elaborative by extending the research for transient problems, with different fin profiles. Natural convection model is adopted in the present study but it can also be studied by using forced convection model.

Fins are the most commonly used medium to enhance heat transfer from a hot primary surface. Heat transfer in its natural condition is nonlinear and hence been demonstrated. The outcome is practically viable, as it is applicable at large to the broad areas like automobile, aerospace and electronic and electrical devices.

As per the literature survey, lot of work has been done on fins using different numerical methods; but to the best of authors’ knowledge, this study is first in the area of nonlinear heat transfer of fins using dimensionless Bi by the truly meshfree MLPG method.

The purpose of this study is to investigate the bending analysis of metal (Ti-6Al-4V)-ceramic (ZrO₂) functionally graded material (FGM) sandwich plate with material property gradation along length and thickness direction under thermo-mechanical loading using inverse trigonometric shear deformation theory (ITSDT). FGM sandwich plate with a ceramic core and continuous variation of material properties has been modelled using Voigt’s micro-mechanical model following the power law distribution method. The impact of bi-directional gradation of material properties over the bending response of FGM plate under thermo-mechanical loading has been investigated in this work.

In this study, gradation of material properties for FGM plates is considered along length and thickness directions using Voigt’s micromechanical model following the power law distribution method. This type of FGM is called bi-directional FGMs (BDFGM). Mechanical and thermal properties of BDFGM sandwich plates are considered temperature-dependent in the present study. ITSDT is a non-polynomial shear deformation theory which requires a smaller number of field variables for modelling of displacement function in comparison to poly-nominal shear deformation theories which lead to a reduction in the complexity of the problem. In the present study, ITSDT has been utilized to obtain the governing equations for thermo-mechanical bending of simply supported uni-directional FGM (UDFGM) and BDFGM sandwich plates. Analytical solution for bending analysis of rectangular UDFGM and BDFGM sandwich plates has been carried out using Hamilton’s principle.

The bending response of the BDFGM sandwich plate under thermo-mechanical loading has been analysed and discussed. The present study shows that centre deflection, normal stress and shear stress are significantly influenced by temperature-dependent material properties, bi-directional gradation exponents along length and thickness directions, geometrical parameters, sandwich plate layer thickness, etc. The present investigation also reveals that bi-directional FGM sandwich plates can be designed to obtain thermo-mechanical bending response with an appropriate selection of gradation exponents along length and thickness direction. Non-dimensional centre deflection of BDFGM sandwich plates decreases with increasing gradation exponents in length and thickness directions. However, the non-dimensional centre deflection of BDFGM sandwich plates increases with increasing temperature differences.

For the first time, the FGM sandwich plate with the bi-directional gradation of material properties has been considered to investigate the bending response under thermo-mechanical loading. In the literature, various polynomial shear deformation theories like first-order shear deformation theory (FSDT), third-order shear deformation theory (TSDT) and higher-order shear deformation theory (HSDT) have been utilized to obtain the governing equation for bending response under thermo-mechanical loading; however, non-polynomial shear deformation theory like ITSDT has been used for the first time to obtain the governing equation to investigate the bending response of BDFGM. The impact of bi-directional gradation and temperature-dependent material properties over centre deflection, normal stress and shear stress has been analysed and discussed.

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.

The purpose of this study is the numerical prediction of the thermal and hydraulic characteristics (Nusselt number and shear stress) of a forced convection laminar flow through a rectangular micro-channel heat sink, using constant and temperature-dependent thermo-physical properties. The effects of the solids volume fraction and the size of the micro-channel on heat transfer enhancement have also been investigated.

The authors use the flow of a water-Al2O3 nanofluid and a single-phase approach. The equations are solved using the commercial code Fluent Version 6.3. This code uses the finite volume approach to solve the equations subject to the boundary conditions, which govern three-dimensional conjugate convection-conduction heat transfer model. The physical domain was meshed using the code GAMBIT. The mesh used is non-uniform and was obtained by sweeping in the Z direction an X-Y surface meshed with QUAD/pave type cells.

The results clearly show that the inclusion of nanoparticles produces a considerable increase in the heat transfer. Also, the temperature-dependent models present higher values of local and average Nusselt number than in the case of constant thermo-physical properties, and an increase in the channel dimensions leads to an important increase in heat transfer. Consequently, we ensure a better cooling of the base of the micro-channel heat sink.

Because of the settling of nanoparticles, the research results may not be generalized to high values of solids volume fraction. Therefore, researchers are encouraged to find other techniques of cooling when the heat loads exceed values that cannot be dissipated using nanonofluids.

The paper includes implications for the miniaturization of electronic devices such as in microprocessors or those used in robotics and automotive industries, where continually increasing power densities are requiring more innovative techniques of heat dissipation from a small area and small coolant requirements.

This paper shows the implementation of variable property nanofluid models in CFD commercial codes.

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.

Out‐of‐plane displacement (warpage) is one of the major thermomechanical reliability concerns for board‐level electronic packaging. The warpage and residual stresses can cause unreliability in the performance of electronic chip. An accurate estimation of the distortion and the residual stresses will help in selecting right combination of material for soldering and to determine the better assembly procedure of the chip. The purpose of this paper is to create a 3D nonlinear finite element model to predict the warpage, bending stresses, shear and peel stresses in a flip‐chip on board (FCOB).

A 3D finite element procedure has been developed considering the material nonlinearity during solidification for a FCOB assembly. Finite element results have been compared with the experimental values.

The present finite element method gives better approximation of residual warpage and stresses compared to analytical models available in the literature.

The 3D finite element approach considering the elasto‐plastic and temperature‐dependent material properties has not been attempted by any authors. Experiments have been conducted for the comparison of finite element values. The finite element results compare better than the methods available in the literature. Hence a better method for estimating the deformation and residual stresses in flip‐chip assembly has been suggested.