We present a model for plasma heating produced by time-dependent, spatiallylocalized reconnection within a flare current sheet separating skewed magneticfields. The reconnection creates flux tubes of new connectivity whichsubsequently retract at Alfv\'enic speeds from the reconnection site. Heatingoccurs in gas-dynamic shocks which develop inside these tubes. Here we presentgeneralized thin flux tube equations for the dynamics of reconnected fluxtubes, including pressure-driven parallel dynamics as well as temperaturedependent, anisotropic viscosity and thermal conductivity. The evolution oftubes embedded in a uniform, skewed magnetic field, following reconnection in apatch, is studied through numerical solutions of these equations, for solarcoronal conditions. Even though viscosity and thermal conductivity arenegligible in the quiet solar corona, the strong gas-dynamic shocks generatedby compressing plasma inside reconnected flux tubes generate large velocity andtemperature gradients along the tube, rendering the diffusive processesdominant. They determine the thickness of the shock that evolves up to asteady-state value, although this condition may not be reached in the shorttimes involved in a flare. For realistic solar coronal parameters, thissteady-state shock thickness might be as long as the entire flux tube. Forstrong shocks at low Prandtl numbers, typical of the solar corona, thegas-dynamic shock consists of an isothermal sub-shock where all the compressionand cooling occur, preceded by a thermal front where the temperature increasesand most of the heating occurs. We estimate the length of each of thesesub-regions and the speed of their propagation.
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