Dimensionless correlations for convective heat transfer to liquid and particles in cans subjected to end-over-end rotation

Dimensionless correlations, for estimating forced convection heat transfer coefficients in cans with end-over-end rotation, were investigated using multiple regression of significant dimensionless groups. Data on overall heat transfer coefficient, U, and fluid to particle heat transfer coefficient, h(fp), were obtained for several processing conditions, and analyzed separately for single and multiple particles in the can. Heat transfer to a single particle was modeled based on particle settling theory, with terminal velocity resulting from the combined forces of gravity, buoyancy, centrifugal and drag acting on it, during end-over-end rotation. In the presence of multiple particles, heat transfer to the moving liquid/particles system was modeled as in a packed bed. Attempts were made to account for the particle shape and size effects on U and h(fp) by including particle sphericity (psi = surface area of an equivalent sphere/surface area of the particle) and particle equivalent diameter (as diameter of sphere of volume equal to that of particle, d(e)) into the correlation equation. For U with a single particle in the can, the Nusselt number (Nu) was related to Reynolds number (Re), Prandtl number (Pr) and relative can headspace; while with multiple particles, Re, Pr, d(e), the ratio of particle to liquid concentration and psi were found to be significant. For h(fp) with a single particle in the can, Nu was related to Re [or Froude number (Fr)], Pr, density simplex (a), relative can headspace and the ratio of the sum of the diameter of rotation and diameter of the can to the can diameter, while with multiple particles, Re (or Peclet number), ratio of particle to liquid thermal conductivity, the particle to liquid concentration ratio and particle sphericity were found to be significant parameters.