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This article proposes a new formulation of Fourier's heat conduction law by considering the size effect of functionally graded piezoelectric materials. Which contains the Caputo–Fabrizio type fractional-order heat transfer equation. The Kelvin–Voigt model was used to characterize the viscoelastic behavior of the material. The model is applied to the study of the thermodynamic behavior of functionally graded piezoelectric rods under thermal shock. It is assumed that the ends of the functionally graded piezoelectric rod are fixed and insulated, that there is no electric potential between the ends, and that the physical properties of the rod vary exponentially along the axial direction of the rod. The control equation is solved by the Laplace integral transformation and its numerical inverse transformation, and the distribution of the studied physics field is obtained, which is illustrated graphically. Finally, the effects of nonhomogeneity index, fractional-order derivatives, nonlocal parameters, and viscoelastic coefficients on the characteristics of the physical variables are investigated and discussed. [ABSTRACT FROM AUTHOR]

The dynamic response of a finite rod is investigated in the context of time-fractional strain and heat conduction theory. In order to perform a qualitative analysis of the problem, a rod fixed at both ends and subjected to a moving heat source is analyzed using the Laplace transform and its inverse. To verify the correctness of the derivations, degenerated results are compared with those obtained from previous literature. Then, the influence of the fractional order parameter, acting time, and moving velocity on the physical quantities is studied, respectively. Numerical results show that fractional order parameters and acting time have a significant influence on the physical quantities. [ABSTRACT FROM AUTHOR]

In this work, the coupled generalized thermoelasticity of two-dimensional finite domain subjected to moving heat source is investigated. The generalized thermoelasticity is based on Lord–Shulman (LS) theory, and the moving heat source is considered to move along the x -axis at the middle of the domain with constant velocity. The meshless method, because of continuous moving of approximations over the problem domain, is the best numerical method for problems with moving loads. So, for solving the governing equations, the meshless Galerkin weak form is employed. In the applied meshless method, the moving least square (MLS) shape functions are used for approximating the field variables in each influence domain. Also, for solving the final equations in the time domain, the Newmark time marching method is used. The results show that a moving source with a velocity equal to the temperature's wave speed exhibit the maximum peak values of temperature, displacement and stress in the domain, and when the temperature wave speed and the elastic wave speed are equal, the moving heat source at this speed drastically increases the peak values of stress, displacement and temperature. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the photo-thermoelastic response of homogeneous and isotropic finite thin slim strip that is exposed to a moving heat source, where both the ends are fixed. The novel thermo-viscoelastic theory is associated with the nonsingular relaxation kernel "Mittag-Leffler relaxation function". In the context of memory-dependent Moore–Gibson–Thompson (MGT) theory, the heat transport law is framed. Solutions of all the significant physical fields such as the displacement, carrier density, temperature, and thermal stress are evaluated in their dimensionless form in the Laplace transform domain. The distribution of the physical fields are found numerically in the real space-time domain implementing the Riemann-sum approximation technique. From the computational results and the corresponding graphical representations, significant effect of the effective parameters such as the nonlocality parameter, time-delay parameter has been reported. Also, significant effect for different choice of kernel function is indicated. Moreover, it is also proposed how a nonlinear kernel function is more superior compared to linear kernel in context of this new theory. [ABSTRACT FROM AUTHOR]

This investigation is devoted to exhibit the thermal damage of skin tissue exposed to a moving heat source. Modelling of the problem is performed by adopting dual phase lag theory of bio heat transfer in context of memory dependent derivative. Laplace transform technique has been adopted to represent the analytical solutions of temperature and thermal damage of skin tissue. Thermal damages to the tissues are calculated by the extent of the denatured protein employing with the Arrhenius equation. In order to predict the significance of memory dependent derivative approach, computational results of temperature and thermal damage are evaluated in the frame of different kernel functions as well as time-delay. For the purpose of exhibiting the attractiveness of the present model, obtained results are compared with the results corresponding to the absence of memory dependent derivative. Also, the impact of the velocity of moving heat source has been precisely investigated on temperature variation and thermal damage of skin tissue using quantitative results. Authors' believe that this study will be helpful to study the thermal treatment of several diseases such as hyperthermia. [ABSTRACT FROM AUTHOR]

Gas Tungsten Arc (GTA) welding employs to reduce the welding cost and produces the quality of the joint at the required positions. In this study, multipass GTA welding of SS316L was simulated, and experiments investigated its impacts on thermal analysis. An accurate and physically suitable heat flux simulation model is to be given as input for the analysis of welding processes. The transient thermal analysis was modeled using ANSYS with relevant APDL coding using Double Ellipsoidal moving heat flux models, providing boundary conditions. The temperatures of weldments were measured in real-time using infrared thermography and validated with simulation using ANSYS. Temperature readings were obtained from the analysis and the experiment, and the degree of agreement is less than 1%. [ABSTRACT FROM AUTHOR]

Presence of phase lags is found to be very efficient for predicting the realistic outcomes of the real world problems. The concept of phase lags exhibits the finite speed of thermal waves which is contrary to the concept of paradox of heat conduction. Present work is devoted to investigate the role of phase lags in the problem of magneto thermoelasticity with moving heat source inside a half-space medium. The governing equations are being developed in the context of generalized thermoelasticity involving three phase lags. A thermal shock has been applied on the traction free boundary of the medium. The Laplace transform technique has been employed for finding the analytical solutions. Physical variables such as temperature, displacement as well as stress have been determined in the time-domain. Computational results have been derived to predict the influence of the effective parameters such as phase lags and velocity of the heat source on the physical variables at different values of time. [ABSTRACT FROM AUTHOR]

In this paper, the thermoelastic behavior of a rod made of an isotropic material under the action of a moving heat source was investigated using a new theory of thermoelasticity related to fractional-order time with two relaxation times. A mathematical model of the one-dimensional thermoelasticity problem was established based on the new thermoelasticity theory. We considered the symmetry of the material, and the fractional-order thermoelasticity control equation was given. Subsequently, the control equations were solved and analyzed using the Laplace transform and its inverse transform. This study examined the effects of fractional-order parameters, time, two thermal relaxation times, and the speed of movement of the heat source on the displacement, temperature, and stress distribution patterns in the rod. [ABSTRACT FROM AUTHOR]

Sliding contact between wheel and rail will occur when the train is starting, braking, or passing through curved tracks and long-heavy down grades. In subways, the sliding contact is more frequent. The wear caused by sliding contact has a significant effect on the stress and friction heat of contact region. According to the numerical calculation method and friction heat transfer theory, a wheel-rail contact wear model and a friction heat transfer model are established. The wear-dependent contact stress is introduced, and a moving heat source is employed to simulate the friction heat. The temperature-dependent material parameters are adopted in models. The influences of wear on stress and temperature are studied. The results show that, with the increase of sliding distance, the wheel-rail contact patch becomes larger, the shape of contact patch changes from convex to flat, the maximum contact stress descends gradually, and the distribution of contact stress tends to be uniform. When the wear depth of wheel exceeds 0.2 mm, the node temperature values calculated by the initial contact stress are higher than those calculated by the wear-dependent contact stress. And as the sliding distance increases, the difference in temperatures increases gradually. At the end of sliding contact, the maximum temperatures of wheel and rail calculated by the initial contact stress are 113. 9 °C and 61.0 °C respectively higher than those obtained by the wear-dependent contact stress. The research results indicate that the wear obviously influences the contact stress and friction heat, and these influences should be fully considered when calculating the stress and friction heat. [ABSTRACT FROM AUTHOR]

Railroad vehicles require the use of disc brakes for safety purposes, however, the brakes are susceptible to thermal stress, which ultimately shortens their lifespan. Hence, to accurately predict the life of railway disc brakes in thermal load simulations, the availability of a model that considers spatial and temporal variations of temperature and thermal stress is essential. A non-axisymmetric moving heat source model was successfully developed to address spatial temperature variations (Deressa and Ambie in Urban Rail Transit 8(3–4):198–216, 2022. 10.1007/s40864-022-00176-9), and this study aims to extend this model to predict thermal stress and fatigue life, and assess its effectiveness. The analysis includes braking time thermal analysis, cooling time thermal analysis, and structural analysis. Spatially varying temperature is incorporated into the structural analysis to calculate thermal stress and strain. A fracture mechanics-based fatigue life estimation method is applied to critical areas of the friction surface. The model is implemented on two braking conditions (service and emergency) and two disc geometries (actual and modified). The model successfully resolves spatial heat considerations by estimating maximum stress variations of up to 46 MPa along the disc circumference. Stress differences of 3 MPa and 6 MPa are observed between the leading and trailing edges of the pad trace during late and mid-braking times, respectively. Fatigue life results identify critical positions and directions for fatigue life initiation. Additionally, these results are in accord with previous observations available in the literature. The proposed model can be easily implemented in various sliding friction applications such as drum brakes, engine pistons/cylinders, and camshafts. [ABSTRACT FROM AUTHOR]

Abstract Railroad vehicles require the use of disc brakes for safety purposes, however, the brakes are susceptible to thermal stress, which ultimately shortens their lifespan. Hence, to accurately predict the life of railway disc brakes in thermal load simulations, the availability of a model that considers spatial and temporal variations of temperature and thermal stress is essential. A non-axisymmetric moving heat source model was successfully developed to address spatial temperature variations (Deressa and Ambie in Urban Rail Transit 8(3–4):198–216, 2022. 10.1007/s40864-022-00176-9), and this study aims to extend this model to predict thermal stress and fatigue life, and assess its effectiveness. The analysis includes braking time thermal analysis, cooling time thermal analysis, and structural analysis. Spatially varying temperature is incorporated into the structural analysis to calculate thermal stress and strain. A fracture mechanics-based fatigue life estimation method is applied to critical areas of the friction surface. The model is implemented on two braking conditions (service and emergency) and two disc geometries (actual and modified). The model successfully resolves spatial heat considerations by estimating maximum stress variations of up to 46 MPa along the disc circumference. Stress differences of 3 MPa and 6 MPa are observed between the leading and trailing edges of the pad trace during late and mid-braking times, respectively. Fatigue life results identify critical positions and directions for fatigue life initiation. Additionally, these results are in accord with previous observations available in the literature. The proposed model can be easily implemented in various sliding friction applications such as drum brakes, engine pistons/cylinders, and camshafts.

Sliding friction is a common tribological effect that occurs between the contact surfaces of the inner components (inner race, outer race and balls) of a spindle rolling bearing during operation. This friction generally generates heat, which can affect the performance of the rolling bearing. To date, numerous studies have assumed that the contact surface between the inner components of the bearing is circular and stationary. While this assumption has yielded adequate results, it is not sufficient in the case of angular contact ball bearings, where the contact surfaces are elliptical and could be treated as either stationary or moving heat sources. This paper presents solutions for both, stationary and moving heat sources for elliptical contact surfaces in a spindle rolling bearing. The primary objective is to find the thermal contact resistances which are dependent on the shape of contact, the loads, the rotational speed and the material properties thereof, applying the mathematical expressions developed by Muzychka and Yovanovich. These expressions were used to calculate various thermal resistances, providing results applicable to the analysis of thermal models in spindle rolling elements. Through finite element analysis (FEA) performed in Ansys Workbench, the stationary and moving heat sources were compared, finding the heat distribution along the elements of the bearing. The findings herein are suitable for the creation of thermal networks in rolling bearings, which are essential to predict their thermal behaviour.

In order to explore the influence of moving heat sources in the deep roadway on the wind flow environment, with Xincheng Gold Mine as the engineering background, the wind temperature and wind speed monitoring of a transport roadway on a deep level was carried out, and the heat release of fuel equipment in the deep roadway of Xincheng Gold Mine was calculated by field investigation and theoretical formula.Based on Fluent finite element software, simulation of the dynamic response of moving heat source under different wind flow conditions, and the influence of moving heat source on deep roadway wind flow environment was analyzed.The results show that the average wind speed is 1.91 m/s and the average wind temperature is 33.38 ℃ in the monitoring section; when the heat source moves downwind, the wind temperature on both the front end and the tail end is affected.The wind temperature gradually decreases with the increase of distance and tends to be stable at 15 m at the front end of the heat source, and the stable wind temperature is 33.75 °C,high temperature is generated continuously within the 2 m range at the tail of heat sources; when the heat source moves against the wind, only the tail wind temperature is affected.The wind tempera-ture gradually decreases within the 0-20 m range of the tail of the heat source and becomes stable at 20 m of the tail of the heat source.The stable wind temperature is 34.12 °C;the range of influence of heat source on wind flow when moving upwind is larger than that when moving downwind, and the wind temperature when moving upwind is 0.37 ℃ higher than that when moving downwind. [ABSTRACT FROM AUTHOR]

In this paper, based on fractional order strain theory and nonlocal heat conduction theory, the thermoelastic response of an elastic rod rigidly fixed at both ends and subjected to a moving heat source is investigated. The nonlocal fractional order strain control equation is established, and the analytical expressions of dimensionless temperature, displacement, and stress are solved using the Laplace integral transformation and numerical inverse transformation. The distribution law of physical quantities such as temperature, displacement, and stress when the fractional parameters, heat source moving speed, and thermal nonlocal parameters change is obtained. The results show that strain parameters and thermal nonlocal parameters have less influence on thermal–mechanical waves, while heat source velocity has a significant influence on thermal–mechanical waves. [ABSTRACT FROM AUTHOR]

The computational model of phase change heat transfer analysis for anisotropic structures with moving heat sources is established using the element-free Galerkin method (EFGM), and the accuracy and superiority of the proposed model are verified by experimental results and two butt welding examples of anisotropic plates. The influence of off-angle and thermal conductivity factors on the temperature field, welding pool, and weld seam is investigated. The results show that EFGM temperature and welding pool have higher accuracy compared with the finite element method solutions. It is demonstrated that EFGM has a distinct advantage in the tracing of moving heat sources and dynamic phase interfaces during the butt welding process, whether along straight or complex paths. There is a high-quality welding pool and a uniform temperature in butt welding of anisotropic structures compared with isotropic structures. The increase of thermal conductivity factor can accelerate the phase change process and its reasonable range is suggested to be 2–4. It can reduce the temperature concentration and accelerate the solidification speed of weld seam when the off-angle is enlarged, and its recommended range is 30°–45°. [ABSTRACT FROM AUTHOR]

We systematically test families of explicit adaptive step size controllers for solving the diffusion or heat equation. After discretizing the space variables as in the conventional method of lines, we are left with a system of ordinary differential equations (ODEs). Different methods for estimating the local error and techniques for changing the step size when solving a system of ODEs were suggested previously by researchers. In this paper, those local error estimators and techniques are used to generate different types of adaptive step size controllers. Those controllers are applied to a system of ODEs resulting from discretizing diffusion equations. The performances of the controllers were compared in the cases of three different experiments. The first and the second system are heat conduction in homogeneous and inhomogeneous media, while the third one contains a moving heat source that can correspond to a welding process. [ABSTRACT FROM AUTHOR]

Enlightened by the memory dependent derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of the magnetic field and moving heat source in a rod in the context of three-phase lag theory of thermoelasticity based on Eringen's nonlocal elasticity. Both ends of the rod were fixed, and heat is insulated. Employing Laplace transform as a tool, the problem was transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain was obtained by applying the inverse Laplace transform. Numerical calculation for temperature, displacement and stress within the rod was carried out and displayed graphically. The effect of the moving heat source speed, time instance, memory dependent derivative, magnetic field and nonlocality on temperature, displacement, and stress was studied. Finally, three animated were added for easy understanding of the effect of moving the heat source on the studied fields. As per authors concern, the concept of the animated has been presented for the first time in this kinds of literature till now. [ABSTRACT FROM AUTHOR]

The analysis of rail/wheel sliding friction heat is a very important research field. The numerical simulation is often adopted to calculate the friction heat, and experimental method is relatively few. In this paper, an experimental machine is designed to simulate the rail/wheel sliding contact. At the same time, a rail/wheel contact wear model and a friction heat transfer model are established. The characteristics of temperature on rail/wheel sliding contact are analyzed by experimental test and numerical calculation. The research results show that the temperature rise of wheel and rail is quick in the initial sliding contact stage, then gradually slows down. The temperature of wheel is higher than that of rail at the same depth from the contact surface. In the initial sliding stage, the wheel temperature rises faster than the rail temperature, which is related to the size of contact surface and the concentration degree of friction heat. Moreover, the results of this paper show that the temperature values of the rail/wheel obtained through experimental test and numerical calculation are in good agreement. The experimental and numerical calculation methods used in this article can be adopted to analyze the contact problems of other sliding friction pairs. [ABSTRACT FROM AUTHOR]

The main concern of this article is to deal with the thermoelastic interaction in a functionally graded thermoelastic rod being enlightened by the memory-dependent derivative. This article investigates the transient phenomena due to the influence of an induced magnetic field of constant intensity and due to the presence of a moving heat source of constant velocity in the context of three-phase lag model of generalized thermoelasticity. Employing the Laplace and the Fourier transforms as tool, the problem has been constructed in the transformed domain. The inversions of the Fourier transform have been carried out using residual calculus whereas the numerical inversions of the Laplace transform have been performed employing the Riemann sum approximation method. Numerical computations for stress, displacement, and temperature within the rod are carried out and have been demonstrated graphically. The results also demonstrate how the nonhomogeneity parameter and the speed of the moving heat source influence the thermophysical quantities. It is observed that the temperature, thermally induced displacement, and stress of the rod are found to decrease at large source speed. Also, significant differences on the thermophysical quantities are revealed due to the influence of magnetic field, nonhomogeneity, and memory effect also. [ABSTRACT FROM AUTHOR]

• A new formulation of the plane problem of thermoelasticity is proposed. • Material property heterogeneity as a result of large temperature gradients. • Example: an external heat source traveling over a mixture of titanium and aluminum powders. • 3.5× higher stress for 500 °C increase assuming temperature dependence. The interaction of thermal and mechanical fields in modern technologies for the synthesis and processing of materials attracts more and more attention. This is due to the need to predict the behavior and properties of new materials and products depending on the conditions of their creation. In the present work, attention is focused on the comparison of the solutions to the thermoelasticity plane problems with and without accounting for the temperature dependence of the material properties. It is assumed that an external heat source traveling over the surface with a specific velocity and following a given trajectory is responsible for a significant temperature increase. It may correspond to a laser source, for example. The new way of problem formulation in stresses is used. The temperature dependence of the characteristics leads to nonlinear thermoelasticity equations when the equilibrium equations, the requirement of strain compatibility, and the Duhamel-Neuman relation for the plane stress state case are combined. To determine the temperature field, a nonlinear thermal conductivity equation is used. To solve the problem numerically, the use of an implicit finite-difference scheme and coordinate splitting for the thermal conductivity equation and the finite-difference method of successive over-relaxation with Chebyshev acceleration for the equations for stresses was made. As a result, the difference in the solution of linear and nonlinear problems is demonstrated for the considered cases. Using the example of a mixture of titanium and aluminum powders, numerical modeling demonstrated that some stress components can reach values up to 3.5 times higher than those obtained in the case of temperature-independent material properties when there is a 500-degree local temperature increase. [ABSTRACT FROM AUTHOR]

To extend the applicability and accuracy of the generalized thermoelasticity theory of thermoelasticity theory for one-dimensional problems involving a moving heat source, this study proposes a fractional-order thermoelasticity coupling theoretical model based on the Green-Lindsay theory and the Caputo-Fabrizio fractional-order derivative. The model's uniqueness and reciprocity are well established. To show its application, we analyzed the thermoelastic coupled dynamic response of a fixed-end rod subjected to a moving heat source. Using Laplace transforms and its numerical inverse method, the distribution patterns of non-dimensional displacement, temperature, and stress were obtained. A comprehensive analysis was conducted to investigate the effects of the fractional coefficient, two thermal relaxation time factors, and moving heat source speed on non-dimensional displacement, temperature, and stress. The findings reveal that the fractional coefficient and the speed of the moving heat source significantly influence all non-dimensional physical variables. While the two distinct thermal relaxation time factors have a minimal influence on the non-dimensional temperature, they exert a more pronounced effect on non-dimensional displacement and stress. [ABSTRACT FROM AUTHOR]

In this work, the fractional order theory of thermoelasticity is introduced to study a two-dimensional fiber-reinforced problem in a half-space. The governing equations are formulated by considering the effect of the magnetic field, gravity, and moving heat source on a fiber-reinforced linearly thermoelastic isotropic medium. These equations are then transformed into non-dimensional forms. The normal mode analysis is used to solve this problem to obtain the exact expressions of the non-dimensional temperature, displacement components, and stress. The distributions of these considered variables are obtained and illustrated graphically. Comparisons are taken with the results in the presence and absence of the magnetic field, gravity and heat source under the fractional order theory of thermoelasticity. The results show that the existence of the magnetic field, gravity, and heat source have significant influence on the distributions of the considered variables. [ABSTRACT FROM AUTHOR]

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This paper forecasts the transient thermal temperature history during girth welding with a single pass over the welded area on pipe ASME class 300 flange joints of low carbon steel using the moving heat source extension model. Using ANSYS ACT extension for the model of the moving, heat source is simulated for the forecast of the distribution of temperature over the welded region during the welding process like gas metal arc welding. Then due to the residual stress induced by the thermal load of the welding, heat source on the joints is analysed and then comparison of the various heat distribution by changing welding parameters is analysed for optimal welding parameters to reduce the stress. The analysis was carried out on transient thermal and transient structural processes to predict the temperature distribution and residual stress respectively. [ABSTRACT FROM AUTHOR]

Railway disc brake is vulnerable to surface damages including fade, wear, squeal, thermal cracks and fatigue being just few of them. To counteract these negative consequences, reliable thermal model that can accommodate space and time variables is essential. The aim of this study is to develop new non-axisymmetric moving heat source and compare its efficiency with pre-existing traditional models. Factors responsible for temperature spatial and temporal variation are identified first and then programmed in ANSYS APDL similar capability to a FORTRAN. Heat flux and convection coefficients are calculated by empirical equations and stored in parameters and arrays for later use, based on small time and pad angular increment. The modelling is to successfully solve the problems in traditional models by estimating surface temperature difference as high as 49 °C, within acceptable computation time. Besides, its consideration of radial distance reported variations from traditional models as high as 10% and 60% in moving heat source and axisymmetric, respectively. And, it is also verified with the literature within acceptable variation. Finally, it is suggested that the model can be applied in conducting pad geometry optimization, thermal stress and fatigue life of disc brake. [ABSTRACT FROM AUTHOR]

The current paper is concerned with a new size-dependent thermoelastic model where the constitutive and the motion equations are modified. The governing equations of the introduced model are derived based on the generalized dual-phase-lag thermoelastic model and non-local elasticity theory. Additionally, the present work is an attempt to investigate a thermoelastic interaction in an infinite medium with a cylindrical cavity based on the proposed model. The cavity surface is traction free and exposed to a time-dependent moving heat source. The analytical formulas for the field quantities are obtained first in the Laplace transform domain. To find the inverse Laplace transform into the physical quantities, a numerical technique is performed. The numerical results are discussed in different cases to highlight the effect of the size -scale parameter and the speed of the heat source on the studied thermo-physical fields. [ABSTRACT FROM AUTHOR]

The single track selective laser melting (SLM) of Ti6Al4V powder is characterized using numerical modelling. The main objective of this study is to understand the effect of laser process parameters such as laser power, scanning speed and beam size on the geometry characteristics of the melt zone. This was achieved by employing a moving heat source approach. The physical and geometrical characteristics of the laser melted zone were evaluated from the temperature solutions obtained through numerical analysis and compared with experimental results. The results presented in this paper are beneficial to realize homogenous layer formation in selective laser melting (SLM) processes. [ABSTRACT FROM AUTHOR]

One of the metallic (additive manufacturing) AM processes is directed energy deposition (DED), which utilizes a machine tool or robotic system for motion control. A laser heat source is used to melt the powder and substrate at the same time after the powder is fed through a powder feeder. Each layer of beads is deposited side by side, and then the layers are stacked over one another. During this process, parts are subjected to intense thermal cycles before reaching room temperature. This rapid heating and cooling, and subsequent expansion and contraction, leads to the generation of tensile and compressive residual stresses within the part. The accumulation of these thermal residual stresses has a detrimental effect on the final product quality. If the residual stresses exceed the yield strength of the material, this will lead to the non-uniform plastic deformation of the substrate as well as cracks, warping, and buckling. One of the influential factors on the amount and gradients of the residual stresses is the deposition or scanning pattern. Therefore, the depositions of the beads in each layer necessitate a careful analysis of the thermal history related to the scanning pattern in order to find the best path for bead deposition. It is desirable to minimize residual stresses and distortions. The purpose of this study was to investigate the thermo-mechanical characteristics for different scanning patterns for laser cladding-based additive manufacturing processes in three types of geometries. This study considered one-way, zigzag, spiral, and raster-angled pattern scans for various component configurations. The fabrication geometries are cross-type, a rectangular surface with a hole, and U-shape. These geometries account for different types of convection-conduction heat diffusion within the parts. The thermo-mechanical responses of the parts to different scanning patterns were assessed using an unsteady finite volume method with a one-way coupling with a finite element structural solver. The scanning patterns were derived from tool path geometry imported from commercial additive manufacturing software (APlus). According to the results, a high conduction zone during the last scan causes a non-uniform cooling rate while the latest scanning area experiences tensile stress. According to the study of different scanning patterns, geometry plays a role in determining which pattern performs best. Cross-type fabrication exhibits the best mechanical response to different scanning patterns. More research needs to be conducted to assess the influences of the geometry in tandem with scanning patterns, and unique AM tool paths may need to be introduced. [ABSTRACT FROM AUTHOR]

Hard-facing process is widely used for improving the wear resistance of mild steel. During the application of hard-facing, due to high temperatures, residual stresses and deformations may occur. The tensile residual stresses may cause crack propagation on the hard-faced part. The purpose of this study is to utilise minimum computer work for minimizing these residual stresses and deformations during the hard-facing of mild steel. The fully coupled transient heat transfer and structural analysis was performed for calculations. The double-ellipsoidal moving heat source was utilised to simulate the heat input from the gas metal arc welding (GMAW). Only eight numerical simulations were performed to minimize the computer work; the grey relational analysis was used for minimizing both the residual stresses and deformations. Welding speed, welding current, and welding pattern were considered as changing parameters. At the end of the numerical and statistical solutions, it is observed that heat input should be kept minimum to minimize the stresses and deformations. But it is obvious that the heat input must provide a temperature greater than the melting point. Straight patterns always produce better results for minimizing stresses and deformations. Transverse stress at the beginning and end of the longitudinal path gets higher significantly after cooling. Cooling does not affect the total deformation.

The generalized nonlocal thermoelastic model in the context of Eringen's nonlocal elasticity is applied to investigate the magnetothermoelastic interactions in a rod of finite length placed in a magnetic field with a moving source. With the use of the Laplace transform and numerical Laplace inversion techniques, the governing equations are solved, and the solutions in the time domain are obtained numerically. The distributions of the nonlocal thermal stress, temperature, and the displacement in the rod are obtained and presented graphically. The effects of the rotational speed and the speed of the moving heat source, nonlocal parameter, and the applied magnetic field intensity on the considered variables are discussed in detail. [ABSTRACT FROM AUTHOR]

Viscoelastic materials are used widely for seismic mitigation and vibration suppression in civil engineering, and have obvious advantages in energy dissipation. Viscoelastic materials and devices are often used in a thermoelastic coupling state. This paper investigated the thermodynamic behaviors of a viscoelastic plate for vibration control based on the generalized thermoviscoelastic theory. The plate was fixed on both surfaces and subjected to a moving heat source on the left. The governing equations of the plate were formulated considering the fractional order derivative heat conduction, material nonlocal effect, and temperature-dependent properties. The problem was solved numerically using the Laplace transform and its inverse transformation. The distribution of the nondimensional temperature, stress, and displacement along the thickness direction of the plate were determined and graphed. The impacts of the heat source moving speed, the fractional parameter, nonlocal effect parameter, and temperature-dependent parameter were discussed and analyzed. The thermodynamic behaviors of the plate are affected greatly by the considered parameters. [ABSTRACT FROM AUTHOR]

Classical thermo-viscoelastic models may be challenged to predict the precise thermo-mechanical behavior of viscoelastic materials without considering the memory-dependent effect. Meanwhile, with the miniaturization of devices, the size-dependent effect on elastic deformation is becoming more and more important. To capture the memory-dependent effect and the size-dependent effect, the present study aims at developing a modified fractional-order thermo-viscoelastic coupling model at the micro-scale to account for two fundamentally distinct fractional-order models which govern the memory-dependent features of thermal conduction and stress-strain relation, respectively. Then, the modified theory is used to study the dynamic response of a polymer micro-rod heated by a moving heat source. The governing equations are obtained and solved by the Laplace transform method. In calculation, the effects of the fractional-order parameter, the fractional-order strain parameter, the mechanical relaxation parameter, and the nonlocal parameter on the variations of the considered variables are analyzed and discussed in detail. [ABSTRACT FROM AUTHOR]

The advancement in additive manufacturing encourages the development of simplified tools for deep and swift research of the technology. Several approaches were developed to reduce the complexity of multi-track modeling for additive manufacturing. In the present work, a simple heat source model called concentrated heat source was evaluated for single- and multi-track deposition for directed energy deposition. The concentrated heat source model was compared with the widely accepted Goldak heat source model. The concentrated heat source does not require melt pool dimension measurement for thermal model simulation. Thus, it reduces the considerable time for preprocessing. The shape of the melt pool and temperature contour around the heat source was analyzed for single-track deposition. A good agreement was noticed for the concentrated heat source model melt pool, with an experimentally determined melt pool, using an optical microscope. Two heat source models were applied to multi-track 3D solid structure thermo-mechanical simulation. The results of the two models, for thermal history and residual stress, were compared with experimentally determined data. A good agreement was found for both models. The concentrated heat source model reported less than the half the computational time required for the Goldak model. The validated model, for 3D solid structure thermo-mechanical simulation, was used to analyze thermal stress evolution during the deposition process. The material deposition on the base plate at room temperature results in lower peak temperatures in the layers near the base plate. Consequently, the higher thermal stress in the layers near the base plate was found, compared to the upper layers during the deposition process. [ABSTRACT FROM AUTHOR]

The gas tungsten arc welding (GTAW) process is an excellent way of performing quality hard- -facing applications. The residual stresses and distortions are encountered in hard-facing. There are several methods to decrease residual stresses. Changing the welding pattern, changing thickness and preheating can be mentioned for this purpose. In this work, the influence of the welding pattern, plate thickness and preheating was investigated. The temperature distribution with the same welding conditions was used for validation of the numerical model. The total deformation in a 2mm plate was 15 times higher than in a 6mm plate with the same welding conditions. [ABSTRACT FROM AUTHOR]

In this paper, a closed-form analytical solution of hyperbolic Pennes bioheat equation is obtained for spatial evolution of temperature distributions during moving laser thermotherapy of the skin and kidney tissues. The three-dimensional cubic homogeneous perfused biological tissue is adopted as a media and the Gaussian distributed function in surface and exponentially distributed in depth is used for modeling of laser moving heat source. The solution procedure is Eigen value method which leads to a closed form solution. The effect of moving velocity, perfusion rate, laser intensity, absorption and scattering coefficients, and thermal relaxation time on temperature profiles and tissue thermal damage are investigated. Results are illustrated that the moving velocity and the perfusion rate of the tissues are the main important parameters in produced temperatures under moving heat source. The higher perfusion rate of kidney compared with skin may lead to lower induced temperature amplitude in moving path of laser due to the convective role of the perfusion term. Furthermore, the analytical solution can be a powerful tool for analysis and optimization of practical treatment in the clinical setting and laser procedure therapeutic applications and can be used for verification of other numerical heating models. [ABSTRACT FROM AUTHOR]

Based on the theory of fractional-order strains, the thermomechanical dynamic responses of 3D elastomers under moving heat sources were studied. The governing equations under the theory of fractional-order strains were applied to the 3D semi-space model, and solved by means of the Laplace transform, the double Fourier transform and its numerical reverse transform. The distributions of non-dimensional temperatures, stresses, strains and displacements were obtained under different heating source velocities and different fractional-order parameters. The results show that, the fractional-order strain parameters have significant effects on mechanical waves but minor effects on heat waves, and the heat source velocity has significant effects on thermomechanical waves. [ABSTRACT FROM AUTHOR]

The main concern of this article is to deal with the thermoelastic interaction in a thick plate subjected to a moving heat source and being enlightened by memory-dependent derivative (MDD). Due to the shortcomings of power law distributions in Taylor's series, some other forms of derivatives with few other kernel functions have been proposed. The present literature deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for a thermoelastic thick plate in which, the memory-dependent heat transport equation involves the Dual-phase (DP) lag model of generalized thermoelasticity. Employing the Laplace transform and Fourier transforms, the analytical results for the distributions of the thermophysical quantities have been derived. The numerical inversions of the respective transforms have been carried out using a suitable numerical scheme based on the Fourier series expansion technique. Numerical computations for stress, displacement and temperature within the plate have been carried out and have been demonstrated graphically. The results also demonstrate how the heat source moves with time and influences the thermophysical quantities according to its respective position by that time. Also, significant differences on the thermophysical quantities are revealed due to the influence of magnetic field, memory effect and time-delay also. [ABSTRACT FROM AUTHOR]

Hard-facing process is widely used for improving the wear resistance of mild steel. During the application of hard-facing, due to high temperatures, residual stresses and deformations may occur. The tensile residual stresses may cause crack propagation on the hard-faced part. The purpose of this study is to utilise minimum computer work for minimizing these residual stresses and deformations during the hard-facing of mild steel. The fully coupled transient heat transfer and structural analysis was performed for calculations. The double-ellipsoidal moving heat source was utilised to simulate the heat input from the gas metal arc welding (GMAW). Only eight numerical simulations were performed to minimize the computer work; the grey relational analysis was used for minimizing both the residual stresses and deformations. Welding speed, welding current, and welding pattern were considered as changing parameters. At the end of the numerical and statistical solutions, it is observed that heat input should be kept minimum to minimize the stresses and deformations. But it is obvious that the heat input must provide a temperature greater than the melting point. Straight patterns always produce better results for minimizing stresses and deformations. Transverse stress at the beginning and end of the longitudinal path gets higher significantly after cooling. Cooling does not affect the total deformation. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with a new mathematical model of three-dimensional generalized thermoelasticity which has been improved using Lord–Shulman theory. The governing equations on non-dimensional forms have been applied to a three-dimensional half-space subjected to a rectangular moving heat source and traction-free surface by using the Laplace and double Fourier transform techniques. The inverses of the double Fourier and Laplace transforms have been calculated numerically by applying the complex formula of inversion of the transform by of the Fourier expansion method. The numerical results of the temperature increment, strain, stress, and displacement distributions have been represented in graphs for various values of the heat source speed parameter to show its effect on the thermo-mechanical waves. The heat source speed parameter leads to significant effects on both the thermal and mechanical waves.

The temperature distribution characteristics of a moving annular hollow laser beam irradiated on the substrate are studied in this paper. First, through the linear superposition property of potential function, we derive the analytical solution of temperature distribution and the cooling rate of the moving ideal annular hollow heat source. The entransy dissipation rate per unit volume of the annular hollow laser beam is more uniform than that of the Gaussian laser beam. The "ω"-shaped profile of the cross-sectional melt temperature is predicted. Second, we set up an actual annular hollow heat source expression, and two parameters (hollow ratio and heat source hollow area) are defined to describe the heat transfer characteristics of the actual annular hollow heat source. Experiments are carried out to validate transient numerical results. The maximum relative error between the experiments and the simulations is 6.39%, and the average relative error is 3.16%. In the simulation, we compare the profile temperature field of the annular hollow heat source with that of the Gaussian heat source. The profile temperature field in simulation for the actual annular hollow heat source is in agreement with that predicted in the analytical solution for the ideal annular hollow heat source. The effects of scanning speed, power intensity, hollow ratio, and heat source hollow area on the temperature field are demonstrated. The obtained characteristics provide theoretical support for laser materials engineering applications. [ABSTRACT FROM AUTHOR]

Enlightened by the Caputo fractional derivative, this study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of dual-phase lag (DPL) theory of thermoelasticity based on Eringen's nonlocal elasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for temperature, displacement and stress within the rod is carried out and displayed graphically. The effect of moving heat source speed, time instance, memory-dependent derivative, magnetic-field and nonlocality on temperature, displacement and stress are studied. [ABSTRACT FROM AUTHOR]

• A simple analytical model allows predicting temperature rise during bone drilling, as a function of spindle speed. • The lateral friction during bone drilling plays a significant role in the duration of the temperature increase inside bone. • It is unsuitable to consider bone as an infinite medium inside thermal models, to reproduce temperature rise during drilling.. Predicting the bone thermal response in a surgical operation remains a major challenge. In the previous works, metal machining theory has frequently been used to predict bone temperature in drilling process. However, several experimental studies demonstrate that the chip formation process is very complex compared to metal cutting. In the present study, a simplified analytical model based on the moving heat source approach combined with the method of image sources is developed. The heat source due to the drill-bit tip was supposed to be proportional to the cutting energy. The friction at the tool-hole contact was also considered. An experimental study was performed on fresh femur pig bone for cutting speeds from 2 to 20 m/min. Temperature rise, drilling forces and bone volume fraction were measured. The experimental validation showed that the model reproduces satisfactorily the increase in temperature up to the maximum value while it overestimates the temperature during the cooling stage. A parametric study (thermal boundary conditions, lateral friction) was also performed. From the predicted results, it appears that the model can be improved by considering the effects of the bone volume fraction which can present a significant variation in the bone sample. [ABSTRACT FROM AUTHOR]