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The proposed work is devoted to the application of the direct method to the study of heat transfer processes in a multilayer flat structure. It is assumed that each layer is made of isotropic material of different thickness. There is an imperfect thermal contact between them, and the layers have internal heat sources. In this case, the isothermal surfaces are parallel planes, i.e the temperature changes in only one direction. On the outer surfaces of the structure there is a convective heat exchange with the environment, i.e the boundary conditions of the third kind are fulfilled. The coefficients of the thermal conductivity equation are considered to be piecewise constant with respect to the spatial coordinate. This is the first time the problem has been solved in this setting. The solution of the problem is realized by applying the method of reduction using the concept of quasi-derivatives and applying the theory of systems of differential equations with impulse action. The following is the procedure for separating Fourier variables using a modified method of eigenfunctions.Based on the physical content of the problem, the differential equation of thermal conductivity was written in the Cartesian coordinate system, but the solution scheme presented here without any fundamental difficulties extends to similar problems for multilayer bodies of basic geometric shapes by switching to appropriate coordinate systems. To illustrate the proposed method, a model example of finding the distribution of a nonstationary temperature field in a seven-layer flat structure under the influence of the hydrocarbon temperature of the fire is solved. The condition of ideal or non-ideal thermal contact is fulfilled between two adjacent layers. In addition, some layers have internal heat sources. The results of the calculations are presented in the form of a graph of temperature changes depending on timeand spatial coordinates.

This article is focused on the influence of the learning rate parameter on the training results of pre-trained transformer models: BERT, DistilBERT, ALBERT, and XLM-RoBERTa. As data for models training and testing dataset from HuggingFace portal is used. This dataset contains labeled data for both testing and training purposes. Moreover, it contains unlabeled data for unsupervised models and algorithms. Instead of direct training and testing, Trainer and TrainingArgument classes from the HuggingFace portal were used. For batch formation, DataColator class was utilized. Different metrics of model training efficiency were considered: learning time, the output of validation and training loss functions. Work result allows comparing the efficiency of every observed model in binary text classification tasks standalone or in assembly with other models.

Introduction. Solving the problem of heat transfer in multilayer structures devoted a large number of works. The vast majority of them are limited to the case of perfect thermal contact between the layers. However, according to the authors, the problems of thermal conductivity in multilayer structures using into account the imperfect thermal contact are insufficiently studied. The number of such studies is quite limited. Also, known studies are usually limited to two layers. That is because the increase in the number of layers (given the choice of methods of practical implementation) leads to several computational difficulties. Therefore, the problem of constructing an effective analytical scheme for the study of heat transfer processes in multilayer structures in the presence of imperfect thermal contact between the layers remains an urgent task.Purpose. Application of the direct method to the study of heat transfer processes in the system "continuous cylinder inside a multilayer cylindrical shell" with imperfect thermal contact.Methods. An auxiliary problem set for the distribution of the temperature field in a multilayer solid cylindrical hollow body (a cylinder of the sufficiently small radius is "removed") taking into account the imperfect thermal contact between the individual layers. According to the already known scheme of the direct method solve this problem.Results. Boundary transition obtained the solution of the original problem. Boundary transition: the radius of the"removed" cylinder, with the centre at the origin, goes to zero. This approach established that the solution to the problemis limited in the whole structure. In this case, the solution obtained explicit formulas.Conclusions. Effective analytical scheme constructed for application of the direct method to the study of heattransfer processes in multilayer hard cylindrical solids taking into account the non-ideal thermal contact between thelayers. The number of layers, their size and arrangement are considered arbitrary.