Thermal Transport Regimes and Generalized Regime Diagram for High Energy Surface Melting Processes
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CONVECTION-DIFFUSION transport within the molten material pools is expected to bear profound influences on the morphological and microstructural features of the fusion welded joints and laser surfacetreated materials. In all these applications, the interacNILANJAN CHAKRABORTY, Lecturer, is with the Engineering Department, University of Liverpool, Liverpool L69 3GH, United Kingdom; SUMAN CHAKRABORTY, Assistant Professor, is with the Mechanical Engineering Department, Indian Institute of Technology, Kharagpur 721 302, India. Contact e-mail: suman@mech. iitkgp.ernet.in. Manuscript submitted Septemper 14, 2006.
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tion between momentum and energy transport mechanisms has been observed to play the most critical role in determining the molten pool morphology, because the thermal energy transport within the molten pool is a direct consequence of thermal diffusion and an advective melt flow. It is well known that the relative strength of momentum and thermal diffusion is characterized by the Prandtl number (Pr), which is defined as the ratio of kinematic viscosity m and thermal diffusivity, a = K/q c (where K is the thermal conductivity, q is the density, and c is the specific heat). It is interesting to recall here that the Prandtl numbers of molten metals are typically low, because of their large thermal diffusivities. This indicates that the thermal transport in molten metal pools is likely to be predominantly diffusion driven. However, contrary to this conjecture, a number of research investigations[1– 10] have demonstrated that the surface tension driven convection process plays a key role in determining the molten pool morphology. In this context, it is important to mention that most of the earlier numerical studies had presumed a laminar fluid flow in the molten pool. Only in recent times has it been established that for high energy surface melting operations, convection in the melt pool transport may become turbulent in nature, which is likely to have profound influence on the molten pool morphology.[11–17] It has also been demonstrated that the morphology predicted by employing a numerical model that is devoid of any turbulence considerations is significantly different from the morphology of the corresponding experimentally obtained macrostructure. The Reynolds number at which a transition from laminar to ‘‘turbulent flow’’ occurs in a molten pool transport is yet to be theoretically determined. Although, in principle, it is possible to estimate the transitional Reynolds number (Retr) by carrying out a hydrodynamic stability analysis, a complex geometry of the molten pool (often, irregular and time evolving) renders the pertinent mathematical exercise to be a somewhat prohibitive proposition, if not an impossible one. However, with the aid of order of magnitude estimates that have theoretically been established in the literature, it can be inferred that the transitional Reynolds number for the onset of turbulence in such cases of free surface molten material transport turns out to be of th
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