Solution of Thermal Conductivity Problem of a Finite Dimensions Plate with Two Heat Sources

Research in the basic sciences is a critical factor in the development of the civil engineering industry. Solving the problems of radiation-convective heat transfer from heated surfaces has always aroused interest from the point of view of science and practical engineering application of knowledge. However, analytical solutions to these problems are obtained for elementary cases, for example, for infinite plates heated uniformly, or the propagation of heat waves in them obeys certain laws. The solution of the coupled problem of radiation-convective transfer from the surface of these panels is complicated not only by the geometric shape, but also by the openness of the entire thermophysical system, which includes the transfer of thermal energy from the coolant (coolant for cooling systems) to the surface of the thermal panel, from the panel to the room air by convection, and radiation to surrounding bodies (enclosing structures, furniture, people). In turn, additional heat exchange by convection occurs between the air and the enclosing structures. This article considers the possibility of obtaining an analytical solution to the problem of temperature distribution on the surface of a plate with two heat sources. When deriving the formulas, the classical equations of thermodynamics (Newton-Richmann, Fourier’s law, Helmholtz equation) were used. The general solution of the differential equation, in this case, is a linear combination of the Infeld and MacDonald functions. The research results can be applied to various areas of technical sciences: cooling of microprocessors, renewable sources of thermal energy, thermal and cooling panels for industrial production, automotive, marine shipbuilding, and of course heating and air conditioning systems for buildings and transport.

Non-Uniform Temperature Distribution in Multilayer Thermal Protective Coating with Curved Interfaces

In this work, the thermal conductivity problem is solved for fourth layer plate at the heat flux action on one of surfaces. The interfaces between layers are assumed non ideal that leads to appearance of thermal resistances between layers. Additionally thermal resistances are inhomogeneous due to curved surfaces of materials. The existence of curved surfaces and porosity of layers are connected with the way of specimen manufacturing. Thermal conductivity coefficients of layers can by changed when their porosity changes. The problem is solved numerically. It was found that curved interfaces and thermal resistance affect process only at initial stage of the heating. Temperature gradients depend essentially on porosity and thickness of layers.

Modeling of the Heat and Kinetic Phenomena Accompanying the Different Material Joining Using Solid-Phase Synthesis

Two-dimensional model of different material joining using solid-phase synthesis has been formulated. The model represents two-dimensional coupled thermal conductivity problem with allowance for the heat release due to chemical reaction course in an adhesive composition. The problem has been solved numerically with the help of a non-explicit difference scheme, coordinate splitting and linear double-sweep method. The influence of thermophysical parameters difference on the temperature and conversion degree fields, reaction zone width and conversion zone propagation velocity have been determined.

Analytical Solution of Nonlinear Boundary Value Problem for Fin Efficiency of Convective Straight Fins with Temperature-Dependent Thermal Conductivity

We have employed homotopy analysis method (HAM) to evaluate the approximate analytical solution of the nonlinear equation arising in the convective straight fins with temperature-dependent thermal conductivity problem. Solutions are presented for the dimensionless temperature distribution and fin efficiency of the nonlinear equation. The analytical results are compared with previous work and satisfactory agreement is noted.