Chemical Engineering Science 54 (1999) 999—1013 Analysis of nonisothermal screw extrusion processing of viscoplastic fluids with significant back flow Adeniyi Lawal*, Dilhan M. Kalyon  Department of Chemical Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia  Department of Chemical, Biochemical, and Materials Engineering, Highly Filled Materials Institute, Stevens Institute of Technology, Castle Point, Hoboken, NJ 07030, USA Received 30 May 1997; accepted 29 October 1998 Abstract Analytical solutions are developed for the flow and heat transfer in nonisothermal screw extrusion processing of viscoplastic fluids with pressure back flow. The screw geometry is assumed to be shallow and the flight width small, thus enabling the flow to be modeled as that occurring between two infinitely long parallel plates, i.e., the generalized Couette flow. The constitutive equation is the generalized Newtonian fluid and the Herschel—Bulkley viscosity function is used to describe the rheology of the viscoplastic fluid, and the interfacial boundary condition of wall slip is incorporated in the analysis. For the temperature problem, the shear viscosity of the fluid is taken to be independent of temperature, and the equation of conservation of energy is reduced to an eigenvalue problem. The eigenfunctions and eigenvalues are determined using the Runge—Kutta method. The analytical solutions in terms of pressure gradient, and temperature distributions show good agreement with numerical and experimental results in the literature for power law fluids. The analytical results are also compared with experimental data collected from twin screw extrusion processing of a concentrated suspension which exhibits viscoplasticity, and wall slip, with the mass flow rate sufficiently low for the pressure back flow to be significant.  1999 Published by Elsevier Science Ltd. All rights reserved. Keywords: Nonisothermal extrusion; Viscoplastic; Slip backflow 1. Introduction The single-screw and twin-screw extruders are used for a variety of continuous processing tasks such as melting, pressurization, mixing, blending, compounding, and re- active extrusion. They rely on drag-induced flow, and pressurization whereby the fluid is conveyed and pressur- ized by the action of a moving surface. The highly viscous nature of processed materials generally encountered including concentrated suspensions and polymeric com- posites implies significant viscous dissipation in ex- truders. The isothermal extrusion flow of polymeric fluids has been studied by a number of investigators (Denson and Hwang, 1980; Wang and White, 1989; Kalyon et al., 1988; Lai-Fook et al., 1989; Lawal and Kalyon, 1994a) using different mathematical models, and Fenner (1969) investigated the various solution methods * Corresponding author. Tel.: 00966 03 860 2205; fax: 00966 03 860 4234. E-mail address: awlawal@dpc.kfupm.edu.sa (A.Lawal). available for the flow and deformation occurring in the single-screw extruder and compared the findings with experimental results. The geometry of the extruder is usually unwound in the channel direction, and the curva- ture effects neglected. Zamodits and Pearson (1969) presented screw characteristic curves for a rectangular channel for different values of the power-law index. De- nson and Hwang (1980), using the finite element method (FEM), analyzed the flow in the twin-screw extruder for several actual channel geometries, but the fluid was as- sumed to be Newtonian. For shallow-screw geometries, the curvature effects in single-screw and twin-screw ex- truders can be neglected without incurring significant errors, and for such screw geometries, the flow so ob- tained, i.e., the generalized plane Couette flow appears to provide an excellent model description of the flow. Closed-form analytical expressions can then be easily worked out for the velocity distribution, and hence the functional dependence of the throughput rate on the pressure generated, for various design parameters and operating conditions. For constant property fluids, the 0009-2509/99/$ — see front matter  1999 Published by Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 8 ) 0 0 4 4 6 - 1