Integral transform method solution for heat transfer in polymer melt flow in a parallel plate single screw channel with periodic inlet temperature

摘要

This work investigates the capacity of a particular class of flows, namely drag and pressure driven flows, to propagate and distorts a transient sinusoidal temperature disturbance occurring at the inlet of the metering zone of a polymer processing screw channel. The integral transform method is applied to the forced convection heat transfer problem in a parallel plate channel with a general drag and pressure driven flow velocity profile for a Newtonian fluid, with the pressure gradient as an adjustable flow parameter. We follow closely the procedure outlined by Cotta and Ozisik in their seminal paper [5]. We found that the knowledge of the lowest eigenvalue in the solution is sufficient to characterise the dampening efficiency of an inlet temperature fluctuation by the flow and that a higher level of positive pressure difference is indeed improving the thermal homogeneity in the flow. Moreover, we found that for any given flow, the higher frequency disturbances are dispersed more efficiently than the lower frequency disturbances.