Effect of fluid viscosity on combined free forced convection flow phenomena in vertical pipes

Abstract

Physical property variations with temperature cause distortion of the fully developed parabolic velocity profile for laminar nonisothennal flow of a Newtonian fluid in a circular pipe. If the profile distortion is su5ciently great, flow instability may produce transition to fluctuating flow at very low Reynolds numbers. This transition has been investigated experimentally in vertical pipes for constant flux heating and cooling of water (3, 6, 9, 16, 17) and constant wall temperature heating and cooling of water (8,17) and it has also been observed for constant flux heating of air (2). Metais and Eckert (10) summarize much of this work and attempt to incorporate the combined free and forced convection transition phenomenon within the overall context of forced, mixed, and free convection regimes for heated pipe flows. Such an approach is of qualitative value, but individual results may deviate greatly from the generalized correlation because of significant differences in hydrodynamic entry length prior to heating, radial position of probe at transition, probe diameter, pipe diameter, mode of heating, and direction of forced flow, which are not parameters of the correlation.Theoretical analyses of the problem of flow field distortion with constant heat flux assumed have been presented for several cases. For the case where the fluid is Newtonian and only the density appearing in the gravity term of the equations of motion varies with temperature, it has been shown (3, 6, 8, 11, 12) that analytical solutions exist for the invariant fully developed velocity and temperature fields which are ultimately established in a long heat transfer section. In this case the maximum profile distortion occurs in the fully developed region and is a function only of the Grashof to Reynolds number ratio NGJNR, ( The apparent discrepancy between those water experiments which suggest attainment of a fully developed flow and those which indicate a continually developing flow even in long heat transfer sections may arise because of the much larger radial temperature gradients and hence viscosity gradients present in the latter experiments. The analysis of Lawrence and Chato is consistent with this interpretation but cannot be used to substantiate the apparently fully developed data of other investigators because the flow fields entering the heated sections do not correspond to the uniform velocity distribution assumed in the theory. On the other hand, there may be no discrepancy, for it is not certain that the flow has been truly fully developed in any experiments because agreement be-

Non-Newtonian Flow Stability in a Heated Pipe at Low Reynolds Numbers

“…For both Polyox solutions tested, transition to disturbed flow occurred in much the same manner as described for Newtonian fluids (Greene and Scheele, 1970). Transition occurred at low Reynolds numbers when the ratio of heat input to flow rate (NgZ/N-rZ in dimensionless form) was sufficiently large.…”

“…Greene (1966) obtained a mean extrapolated value between 26 and 30 for water at A7Re' = 0. For a more viscous 55% aqueous sucrose solution, which had a viscosity and viscosity-temperature dependence approximately equal to that of 0.2% Polyox, the limiting mean ratio was reduced to about 20 (Greene and Scheele, 1970). On the basis of the reduction in transition ratios from 33 to 20 for Newtonian liquids, a reduction from 24.5 to 16.5 for non-Newtonian liquids for a comparable increase in viscous effects seems plausible.…”

“…The experimental apparatus has been described in detail in connection with stability studies using water and aqueous sucrose solutions (Greene and Scheele, 1970).…”

“…Experiments with Newtonian fluids have demonstrated the feasibility of studying pipe flow instability by producing distorted flow fields through the constant flux heating of a fluid flowing at low Reynolds numbers in a vertical pipe (Greene and Scheele, 1970; Scheele and Hanratty, 1962). When natural convection effects predominate, fully developed distorted velocity profiles are approached far downstream in the heat transfer section.…”

“…For Newtonian fluids, a numerical analysis incorporating variable viscosity effects has been developed (Lawrence and Chato, 1966) but there is now no published analysis for non-Newtonian flow. The importance of the viscosity-temperature dependence on Newtonian flow stability has been demonstrated experimentally by comparing results for water with those for moderately low viscosity aqueous sucrose solutions (Greene and Scheele, 1970). Although careful choice of experimental conditions and fluids can minimize the viscosity effect, non-Newtonian solutions are generally sufficiently viscous that such effects cannot be ignored.…”