Approximate analytical solution to the stationary two-dimensional heat conduction problem on infinite bar with the source of heat

3rd International Scientific and Technical Conference “Energy Systems”

Tkachev, V.K.^1

Department of Industrial Heat and Power, Samara State Technical University, Molod-ogvardeyskaya St.244, Samara

443100, Russia^1

关键词: Approximate analytical solutions;    Axis of symmetry;    Complementary boundary conditions;    Deformation load;    Heat conduction problems;    Industrial facilities;    Production process;    Two-dimensional heat conduction problems;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/552/1/012009/pdf
DOI  :  10.1088/1757-899X/552/1/012009

来源: IOP

【 摘 要 】

An approximate analytical solution to the boundary-value heat conduction problem for an infinite bar with a heat source was obtained with the use of the integral method of heat balance, by introducing a complementary required function and complementary boundary conditions. The boundary-value problem for a partial differential equation is reduced to an ordinary differential equation with respect to this function due to the complementary required function that characterizes the change in temperature along the axis of symmetry in the cross-section of the bar. The complementary boundary conditions determined by the initial differential equation and the given boundary conditions are found so that their satisfaction is equivalent to the solution of the initial equation of the boundary value problem at the boundary points. The fulfilment of the equation at the boundary points as well as the heat balance integral results in the fulfilment of the initial equation inside the domain. The approximate analytical solution obtained can be used to identify the amount of internal heat generated by various production processes (vibration and deformation loads, electromagnetic fields effects, etc.) in thermal and nuclear power plants, in the rocket and space industry and other industrial facilities.