Plane quasi-stationary thermal problems with convective boundary condition

A fundamental solution is given for the temperature field due to a line heat source that moves at a constant speed over the surface of a co-nvective half-space. On the basis of this solution approximate and exact solutions to the heat conductivity mixed boundary value problem for the quasi-static temperature field under convection conditions has been obtained. The influence of the coefficient of heat transfer and speed on the temperature distribution has been traced.