Transient Temperature Fields in Growing Bodies Subject to Discrete and Continuous Growth Regimes

The heat transfer problems for growing bodies is the is the subject of present research. Temperature distributions in growing bodies that appear during discrete and continuous growth are studied. The investigation is based on analytical and semianalytical solutions. Analytical solutions are of the form of spectral expansions. The applicability of the analytical solutions is limited to a narrow class for laws of evolution of growth boundaries. Semianalytical solutions have a wider range of applications. The calculation and analysis of temperature fields in the ball under the condition of central symmetry are provided. An analysis of the temperature behavior on the growth boundary shows that, depending on the accretion rate, the boundary can be considered as an isothermal boundary (for high values of the accretion rate) or a boundary with variable effective temperature determined in the process of solving the problem.