An Extended Analytical Solution of the Non-Stationary Heat Conduction Problem in Multi-Track Thick-Walled Products during the Additive Manufacturing Process

An analytical model has been developed for calculating three-dimensional transient temperature fields arising in the direct deposition process to study the thermal behavior of multi-track walls with various configurations. The model allows the calculation of all characteristics of the temperature fields (thermal cycles, cooling rates, temperature gradients) in the wall during the direct deposition process at any time. The solution of the non-stationary heat conduction equation for a moving heat source is used to determine the temperature field in the deposited wall, taking into account heat transfer to the environment. The method considers the size of the wall and the substrate, the change in power from layer to layer, the change in the cladding speed, the interpass dwell time (pause time), and the heat source trajectory. Experiments on the deposition of multi-track block samples are carried out, as a result of which the values of the temperatures are obtained at fixed points. The proposed model makes it possible to reproduce temperature fields at various values of the technological process parameters. It is confirmed by comparisons with experimental thermocouple data. The relative difference in the interlayer temperature does not exceed 15%.

Influence of extended heat sources on the temperature distribution in profiled polar-orthotropic annular plates with heat-insulated bases

The solution of the stationary heat conduction problem for profiled polar-orthotropic annular plates with heat-insulated bases from N extended heat sources at their external border is presented. The temperature distribution in such plates will be non-axisymmetric. The solution of the stationary heat conduction problem for anisotropic annular plates of an random profile is resolved through the solution of the corresponding Volterra integral equation of the second kind. The formula of a temperature calculations in anisotropic annular plates of an random profile is given. The exact solution of stationary heat conduction problem for polar-orthotropic annular plate of an exponential profile is recorded. The temperature distribution in such anisotropic plate from N extended heat sources at its outer border is more complex than in the case of temperature distribution from N point heat sources at their external border.

Heat Conduction Problems in a Homogeneous Pipe with Inner Nonhomogeneous Coating

The paper deals with the analysis of nonhomogeneous inner coatings for a homogeneous pipe with respect of heat loss from the outer pipe surface. Two kinds of the coatings in the form of ring layers are considered: (1º) with the thermal properties changing continuously along the coating thickness (called the coating A), (2º) multilayered coatings with piecewise continuous thermal properties (called the coatings B). The analysis is connected with the stationary heat conduction problems. Some special cases of the coatings A and B are investigated. The obtained analytical results and the comparison of the coatings are presented.

Stationary heat conduction in a solid with functionally graded thermal properties

In the paper the solutions for stationary heat conduction in a two dimensional composite with functionally graded heat properties were obtained. Numerical solutions for the taken boundary conditions are shown for several types of changes of composite’s thermal conductivity. The solutions were obtained with the use of the finite-difference method.

Production of three-layer steel bimetallic strips in the unit of continuous casting and deformation. Report 1

High technical and economic efficiency of the use of bimetals in chemical, oil, transport and energy engineering and other industries is described. The urgency of creating high-performance continuous processes for the production of bimetallic strips is substantiated. The authors have established the main technological tasks for development of the processes of obtaining bimetal of wide class. The paper describes resource-saving production technology of three-layer bimetals alloyed steel – constructional steel – alloyed steel at the unit of combined process of continuous casting and deformation. Possibilities of the proposed technology are outlined from the standpoint of improving the quality of bimetallic strips. The initial data are given to determine the temperature change over time of the main steel strip as it passes through the molten metal of the alloyed steel. The equations are given for non-stationary heat conduction, initial and boundary conditions for determining the temperature fields of main strip and cladding layer when obtaining a three-layer bimetallic strip on the unit of a combined process of continuous casting and deformation. The values of density, thermal conductivity and heat capacity for steel St3 were determined in a given temperature range. A procedure is described for calculating temperatures in the ANSYS package by solving a non-stationary heat conduction problem in a flat formulation by the finite element method. The authors have described the geometric model for calculating the temperature of strip and molten metal of the cladding layer. Values of the coefficient of heat transfer between the main strip and molten metal of the cladding layers of bimetallic strip are given adopted for calculation. Characteristic points are indicated in the model for calculating the temperatures of main strip and molten metal of the cladding layer. The graphs show temporal changes in these temperatures at production of a three-layer bimetallic strip on the unit of combined process of continuous casting and deformation. Calculated data on the time variation of temperature of main strip and molten metal of the cladding layer at characteristic points are given for different values of the contact heat transfer coefficient.

Stationary problem of heat conductivity for complex-shape multilayer plates

A method for calculating stationary temperature fields in a complex-shape multilayer plate when it is heated with film heat sources is proposed. Convective heat exchange takes place on the outer surfaces of the plate. The solution of the stationary heat conduction problem is obtained for a three-dimensional formulation based on the immersion method. A comparative analysis of the temperature distribution along the thickness of a square plate with the results obtained by finite element method has been carried out. As an example, the problem of stationary thermal conductivity for a five-layer glazing element of a vehicle when heated with a film heat source has been solved.