Steady temperature fields associated with a moving rod in a medium with nonlinear thermal conductivity
The two-dimensional problem is considered of determining the temperature field when a rectangular rod of width h and at constant temperature moves at constant speed V in a medium with a temperature dependent thermal diffusivity D(T). It is assumed that \(Vh/D(T)\ll 1\) and the solution is first considered in the far field (``the outer solution'') where the problem is reduced to a nonlinear ordinary differential equation. Properties of this ``outer solution'' are then used to set a boundary condition at infinity for the ``inner problem'' of determining the temperature close to the rod. Finally, this inner problem is solved by using the Kirchhoff transformation to reduce the nonlinear equation to the Laplace equation valid close to the rod.
medium with a temperature dependent thermal diffusivity
nonlinear ordinary differential equation
scientific article; zbMATH DE number 4074644