At first the hydraulic jump is created when the liquid metal enters the sleeve. insert the calculations for the time scale for hydraulic jump creation As the liquid metal level in the sleeve rises, the location of the jump moves closer to the impinging center. At certain point, the jump disappears due to the liquid depth level (the critical depth level). put estimate on when hydraulic jump disappear. At this stage, air bubbles are entrained in the liquid metal which augment the heat transfer. At present, we have an extremely limited knowledge about the heat transfer during process and of course less about minimization of it.
The heat transfer from the liquid metal to the surroundings is affected by the velocity and the flow patterns since the mechanism of heat transfer is changed from a like natural convection to a like force convection. In addition the liquid metal jet surface is also effected by heat transfer to some degree by change in the properties. to make graph for the estimated h and velocity in that case As first approximation the radius of the jet changes due to the velocity change. For a laminar flow a plug flow, why? the velocity goes as where x is the distance from the ladle. For a constant flow rate assumption A good assumption? show change of density effect? the radius will change as . Note that this relationship is not valid vary near the ladle proximity ( (why?)). The heat transfer increases as a function of for these two reasons.
The heat transfer to the sleeve in the impinging area is the most significant and at present only very limited knowledge is available due complexity.