On the width of cold fronts in clusters of galaxies due to conduction

We consider the impact of thermal conduction in clusters of galaxies on the (unmagnetized) interface between a cold gaseous cloud and a hotter gas flowing over the cloud ( the so-called cold front). We argue that near the stagnation point of the flow conduction creates a spatially extended layer of constant thickness Delta, where Delta is of the order of similar to root kR/U, where R is the curvature radius of the cloud, U is the velocity of the flow at infinity and k is the conductivity of the gas. For typical parameters of the observed fronts, one finds Delta << R. The formation time of such a layer is similar to R/U. Once the layer is formed, its thickness only slowly varies with the time and the quasi-steady layer may persist for many characteristic time-scales. Based on these simple arguments, one can use the observed width of the cold fronts in galaxy clusters to constrain the effective thermal conductivity of the intra-cluster medium.