Variable-viscosity flows in heated and cooled channels

Abstract

An asymptotic description is given of Newtonian fluid flow in a channel which is suddenly heated or cooled. The viscosity is assumed to be purely a function of temperature. The asymptotic approximation is that the downstream viscosity at the channel wall differs by an order of magnitude from that in the upstream flow. Although we make the drastic assumption that viscous dissipation is negligible, we can analyse flows where the viscosity depends either algebraically or exponentially on the temperature.

Numerical study on a vertical plate with variable viscosity and thermal conductivity

“…Hence the velocity components U and V both are negligible for small time t. During this initial transient regime, the heat transfer are dominated by pure heat conduction, and hence for constant viscosity and thermal conductivity. Equation (8) reduces to Thus, for short times, it is noted that for a given Prandtl number, the temperature profile is a function of time only and normal distance from the wall. Setting Pr = 1, the solutions of Eq.…”

“…As expected the agreement between the two solutions is good at early times (t = 0.1 and t = 0.2) and this shows that the current method is valid for this types of transient problems. Figures 5,6,7,8,9,10,11,12,13,14,15,16,17,18, shows that the variation of velocity and temperature at their transient, temporal maximum and steady state against the co-ordinate Y at the leading edge of the plate viz., X = 1.0 for different viscosity, thermal conductivity variation parameters and Prandtl numbers. The fluid velocity increases and reached its maximum value at very near to the wall (i.e., 0 ≤ Y ≤ 2) and then decreases monotonically to zero as Y becomes large for all time t. It is also observed that the velocity and temperature increases with time t, reaches a temporal maximum and consequently it reaches the steady state.…”

“…The following forms are proposed by Slattery [21], Ockendon and Ockendon [8], Elbashbeshy and Ibrahim [10], Wilson and Duffy [16], and Seddeek and Abdelmeguid [19].…”

Study of cooling with solidification of a laminar thermodependent Herschel-Bulkley fluid flow in a convectively cooled annular duct

“…This result was also observed by Nouar et al [8] in the case of laminar thermal convection (heating situation) in a pipe for a thermodependent yield stress fluid. In fact, if we consider (i) a large Prandtl number, so that the mechanical relaxation length along the annular duct is insignificant compared with the thermal relaxation length, and (ii) X + << 1, the temperature variations are small everywhere, except in a very thin thermal layer by the outer cylinder wall (Ockendon et al [9], Richardson [10] ). As a result, viscosity variations are not sufficiently large to cause significant variation in the pressure gradient.…”

Free convective flow in a vertical rectangular duct filled with porous matrix for viscosity and conductivity variable properties

“…Different relations between the physical properties of fluids and temperature were given by Kays and Crawford [11]. Ockendon and Ockendon [12] presented an analysis for suddenly heated or cooled channel flow of Newtonian fluids with viscosity either algebraically or exponentially dependent on temperature. Gary et al [13] studied the effects of significant viscosity variation on convective heat transport in water-saturated porous media.…”