Abstract
The problem of axisymmetric heat conduction with internal surface solidification in the inlet regions of tubes is discussed. An approximate analytical solution is presented to this nonlinear, two-dimensional free-boundary problem. The analysis employs a variational technique which extends the Lagrangian formalism to treat the internal flow, two-dimensional moving-interface problems. The solution is expressed in terms of the short-time, asymptotic and steady-state components. Two forms of the variational solution are presented. One has limited validity in the entrance region of the tube, and the other, while less general, is more accurate. The results are compared with a finite-difference numerical solution. Agreement is of the order of 15 per cent.
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