Study of Non-Stationary Thermomechanical Processes in the Structure Elements of the Construction Taking into Accounting for the Local Surface Heat Exchanges
Abstract
The aim of the work was to develop a methodology for taking into account the presence of local surface heat exchanges in rods of finite length, often taking place in studies of the non-stationary phenomenon of thermal conductivity. The proposed methodology was oriented to the subsequent creation of a computational algorithm and its implementation on a personal computer using the universal DELPHI programming tool. This allowed the authors to complete the initial stage of the research works, which will subsequently take into account the internal heat sources in the rods of finite length and constant cross-section in the study of non-stationary thermal conductivity, as well as to develop new methods, approaches and models associated with them.
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Introduction
In mechanical engineering, in particular, in instrument engineering, plastic engineering, and also in other areas, physicotechnical processes often arise, where, any structural element in the form of a rod of finite length is suddenly exposed to thermomechanical loading [1]. Thermomechanical load can be in the form of local temperatures, heat fluxes or heat exchanges, where, in the case of their action on rods of finite length and constant cross-section, non-stationary thermal conductivity can occur in the system, as well as other non-stationary thermoelastic processes [2].
In practice, such phenomena are often encountered at the start of gas-generating, nuclear, hydrogen power plants, rocket and hydrogen engines, as well as internal combustion engines. In transient, unsteady heat conduction processes in the loadbearing elements of these power plants or engines, a complex non-stationary thermally stressed deformed state arises. Herewith, in order to study these processes, many load-bearing elements of the above-mentioned structures can be taken as rods of finite length with a constant cross-section along the entire length. For an adequate description of a non-stationary heat conduction process arising in the rod under the action of dissimilar types of heat sources, taking into account the presence of local thermal insulation, it is necessary to use the classical laws of energy conservation [3], because, the application of energy conservation laws describing such complex non-stationary processes of thermal conductivity in rods of finite length that are exposed to dissimilar kinds of heat sources allows us to take into account natural boundary conditions. As a result, the results obtained will have high accuracy [4]. This, in turn, will contribute to a correct evaluation of the thermally steadystate behavior of the bearing elements [5]. In connection with this, therefore, the development of special effective methods for investigating the non-stationary processes of thermal conductivity of load-bearing elements in the form of rods of finite length and constant cross-section is an actual problem of the applied non-stationary theory of thermoelasticity. At the same time, the development of a complex of applied DELPHI programs that allow studying the classes of non-stationary heat conduction processes for the above systems under the influence of dissimilar types of heat sources, taking into account the presence of local thermal insulation, is of independent scientific interest.
Conclusion
Based on the energy conservation laws, a technique is developed that simultaneously takes into account the presence of local surface heat exchanges for the non-stationary heat conduction problem occurring in a rod of finite length and the constancy of its cross-sectional area. Applying the quadratic approximation function of the form from the energy conservation law by the method of minimizing it through the node temperature values, we obtain solving systems of first-order linear ordinary equations that take into account the natural boundary conditions. Due to this, the results obtained have a high degree of accuracy. The developed methodology and the corresponding computational algorithm allowed to realize calculations in a personal computer on the object-oriented Delphi-7 programming language, and thus to solve the non-stationary heat conduction problem for a rod of finite length under the influence of local heat exchange along the lateral surface.