Abstract
Nonlinear nonstationary heat conduction problem for infinite circular cylinder under a complex heat transfer taking into account the temperature dependence of thermophysical characteristics of materials is solved numerically by the method of lines. Directing it to the Cauchy’s problem for systems of ordinary differential equations studied feature which takes place on the cylinder axis. Taken into account the dependence on the temperature coefficient of heat transfer that the different interpretation of its physical content makes it possible to consider both convective and convective-ray or heat ray. Using the perturbation method, the corresponding thermoelasticity problem taking into account the temperature dependence of mechanical properties of the material is construed. The influence of the temperature dependence of the material on the distribution of temperature field and thermoelastic state of infinite circular cylinder made of titanium alloy Ti-6Al-4V by radiant heat transfer through the outer surface has been analyzed.
Highlights
It is of interest to consider the condition of convective heat transfer coefficient depending on the temperature of heat transfer t t t n t t tc S (1)Here t t —coefficient of thermal conductivity, which depends on the temperature; tc —temperature environment, which washes the body surface S ; n -external normal to the surface S
Nonlinear nonstationary heat conduction problem for infinite circular cylinder under a complex heat transfer taking into account the temperature dependence of thermophysical characteristics of materials is solved numerically by the method of lines
The influence of the temperature dependence of the material on the distribution of temperature field and thermoelastic state of infinite circular cylinder made of titanium alloy Ti-6Al-4V by radiant heat transfer through the outer surface has been analyzed
Summary
T t —coefficient of thermal conductivity, which depends on the temperature; tc —temperature environment, which washes the body surface S ; n -external normal to the surface S. That kind of heat transfer conditions considers heating or cooling the body by radiation, or heat when carried out simultaneously by convection and radiation. For radiation heat transfer coefficient t is called the coefficient of radiation heat transfer, it has the same dimension as the coefficient of convective heat transfer is:. Transient heat transfer body will be called convective heat transfer with temperature depending on the heat transfer coefficient. In the study of processes of heat conduction in solids, which are shaped circular cylinder radius r0 using a cylindrical coordinate system r, , z. If the temperature is independent of and z (the case of axial symmetry), the heat equation has the form:. The solution of Equation (4) satisfies the initial condition t r,0 tp ,. The growth temperature T Tp denoted by T , where Tp t p t0
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