Nonisothermal laminar contracted flow

Abstract

Temperature and velocity profiles and pressure losses were computed for laminar, temperature-dependent Newtonian flow from a stream tube through an abrupt contraction into and through the entrance region of a smaller coaxial tube, in which the fluid was cooled or heated at constant wall temperature. The equations of motion and energy, including axial diffusion and viscous dissipation, were solved numerically for diameter ratios of one and two, a practical temperature range, and N p e and N R~ up to 100. Entrance temperatures and velocities are far from uniform, and pressure losses are greater than those computed using simplified equations and uniform entrance temperatures and velocities. E. B. CHRISTIANSEN and S. J. KELSEY Department of Chemical EngineeringThe University of Utuh Salt Lake City, Utah 841 12 SCOPEThe purpose of the presently reported study was to provide more accurate means for predicting pressure losses and the nature of the velocity and temperature fields at the entrance of and in the tubes of such equipment as shell-and-tube heat exchangers, chemical and nuclear reactors, and similar devices. Improved means for predicting such pressure losses and temperature and velocity fields should provide a basis for more effective and economical heat-exchanger design. Also, the nature of these temperature and velocity fields has an important influence on the progress of a chemical reaction and is important in the design and analysis of data from tubular chemical reactors.Recent as well as earlier theoretical and experimental studies of flow in a tube accompanied by heat exchange with the tube walls have demonstrated that the dependence of viscosity on temperature can importantly affect pressure losses and heat transfer. In some recent numerical solutions of the equations of motion and energy in which the dependence of viscosity on temperature is accounted for, it was assumed that flow at the tube entrance is parabolic and that radial convection, inertial terms, axial diffusion, and viscous dissipation are negligible. Some improved numerical solutions account for temperature-dependent viscosity, radial flow, and inertial effects but are restricted to uniform tube-entrance velocities and temperatures. Although these solutions approximate some situations, it is known that entrance velocity profiles are not flat in laminar, isothermal flow, particularly in the flow geometry of concern here, and that axial diffusion and viscous dissipation may have important effects. The effects of temperature-dependent flow, combined with those of axial diffusion and viscous dissipation, for the case of interest here have not, to our knowledge, been clearly defined in previous reports.In the presently reported study, flow from the header into the tubes of a shell-and-tube heat exchanger or reactor was approximated by flow from a larger stream tube (a stream tube has a frictionless wall) through an abrupt contraction into and through the flow-and temperaturedevelopment region of a smaller coaxial tube. The wall of the small tube...