Based on the Green's function method, a mathematical model allowing for the latent heat of fusion and solidification is developed to describe the steady state, two-dimensional heat flow during welding of thin plates. It is demonstrated that the latent heat has a pronounced effect on shape and size of the weld pool and mushy zone. The thermal efficiency of base metal fusion by a line heat source g t can exceed 0 . 4839 considerably if the latent heat is taken into account. It is shown that the known simplified approaches for considering the latent heat can introduce large errors into the estimation of g t . The calculated and experimental weld pool shapes are compared.A L cross-sectional area of fused metal, m 2 a thermal diffusivity, m 2 s 21 c specific heat capacity of liquid and solid phases, J kg 21 K 21 c ma maximum specific heat capacity including latent heat, J kg 21 K 21 d diameter of constant density heat source, m D hs heat source area, m 2 D mz mushy zone area, m 2 f Green's function, K W 21 f L liquid fraction h plate thickness, m H enthalpy per unit mass, J kg 21 DH latent heat of fusion and solidification, J kg 21 i, iz1 iteration levels K 0 modified Bessel function of second kind of zero order L total latent heat of fusion and solidification, J kg 21 Pe Peclet number Pr Prandtl number q 2 net heat flow density, W m 22 q net net heat input (net power), W Ste Stefan number T temperature, K T 0 initial temperature, ambient temperature, K T L liquidus temperature at which solid formation commences, K T S solidus temperature at which full solidification is achieved, K v welding speed, m s 21 W weld width, m x, y Cartesian frame travelling with source, m a coefficient of heat transfer from plate to ambient air, W m 22 K 21 b dimensionless heat transfer parameter e 1 , e 2 dimensionless heat input j, g coordinates of reference point for Green's function g t thermal efficiency of base metal fusion l thermal conductivity, W m 21 K 21 l ma maximum thermal conductivity including latent heat, W m 21 K 21 L dimensionless latent heat of fusion and solidification r density, kg m 23 v iteration parameter
IntroducionIn analysis of thermal processes, the known functionanalytical solutions of the heat conduction problem, which do not include the latent heat of phase transformations, are usually used. 1-4 The major advantage of these solutions is the ease of implementation; the major disadvantage is a large calculation error for the high temperature region. Whereas the latent heat of solid-solid transformation is relatively low and can be neglected, the energy stored in the latent heat of fusion for aluminium alloys can be as much as 40% of the energy required to bring the material to its melting