Heat transfer in vertical perl mills

A model of heat transfer during grinding in vertical multi-disk perl mills has been proposed. Heat transfer intensity in such mills depends on thermal resistance in a boundary layer formed at the inner surface of mill tank wall. The layer thickness changes depending on process variables. Results obtained are presented in the form of a dimensionless correlation equation.List of Symbols C ball filling of the mill, - c _pw specific heat of cooling water, kJ/(kg K) - d disk diameter, m - d _k ball diameter, m - D inner diameter of the mill tank, m - G _w mass flow rate of cooling water, kg/s - h distance between impeller disks, m - n revolutions frequency of the impeller shaft, s^–1 - q heat flux density, kW/m² - Q _c total heat energy emitted in the mill, W - T temperature, K - T _w1 temperature of cooling water at the cooling jacket inlet, K - T _w2 cooling water temperature at the outlet, K - T _m average temperature inside the mill, K - T _s average temperature of the tank wall, K - u peripheral speed of the impeller disk, m/s - heat transfer coefficient, kW/(m²K) - boundary layer thickness, m - porosity of the lying bed, - _m porosity of the suspended bed, - _c liquid dynamic viscosity, Pa s - _cs liquid dynamic viscosity at wall temperature, Pa s - _c thermal conductivity coefficient of liquid, W/(mK) - _c liquid density, kg/m³ - _s solid density, kg/m³ Dimensionless Numbers Reynolds number for mixing process - Reynolds number for liquid parameters - Nusselt number for liquid parameters - Prandtl number for liquid parameters - modified Euler number