Large Prandtl Number Fluids Research Articles

Viscous dissipation effects on convective instability and heat transfer in plane poiseuille flow heated from below

The effects of viscous dissipation on the onset of instability for longitudinal vortices in the thermal entrance region of a horizontal parallel-plate channel are studied by a numerical method for the case when the lower plate is heated isothermally and the upper one is cooled isothermally. Numerical results are obtained for Pr=0.1, 0.7, 10 and 100. It is found that viscous heating has a destabilizing influence. The effect is significant for large Prandtl number fluid (Pr≳10) but is insignificant for small Prandtl number fluid (Pr≲0.7). The viscous dissipation effects on thermal entrance region heat transfer for basic flow (without secondary flow) are also studied.

On the upper bounding approach to thermal convection at moderate Rayleigh numbers, II. Rigid boundaries

Abstract Numerical solutions for two upper bounding problems for thermal convection in a horizontal layer of fluid contained between perfectly conducting rigid boundaries are presented. Problem I was first introduced by Howard (1963) and yields an upper bound on the heat transport which is independent of Prandtl number. The numerical solutions of this problem indicate that the boundary layer approach used by Howard overestimates this upper bound somewhat; in addition, solutions with two horizontal wavenumbers, first discussed by Busse (1969), exist for Rayleigh numbers larger than 32400. These solutions are also investigated, and a transition to solutions with three horizontal wavenumbers is found to occur at a Rayleigh number of about 63000. Problem II, which is valid for large Prandtl number fluids, yields an upper bound on the heat transport which is smaller than that given by Problem I. No transitions to solutions with multiple horizontal wavenumbers occur for Rayleigh numbers as large as 10 6 .

Natural convection effects on graetz problem in horizontal rectangular channels with uniform wall temperature for large Pr

The effect of buoyancy forces on laminar forced convective heat transfer in the thermal entrance region of horizontal rectangular channels with uniform wall temperature is studied by a numerical method for the case of large Prandtl number fluids. The numerical results are presented for the aspect ratios (width/height) 0·5, 1, 2 and Rayleigh numbers 0 ~ 5 × 10 5. The correlation equations for the prediction on the onset of significant free convection effect are developed. The asymptotic behavior of local Nusselt number is compared against the known asymptote for the uniform wall temperature boundary condition. The entrance region where the free convection effect is significant is clearly established and the classical Graetz problem is shown to be a limiting case and is applicable only when Ra ⩽ 10 3.

Buoyancy effects on laminar heat transfer in the thermal entrance region of horizontal rectangular channels with uniform wall heat flux for large prandtl number fluid

The Graetz problem for fully developed laminar flow in horizontal rectangular channels with uniform wall heat flux is extended by including buoyancy effects in the analysis for the case of large Prandtl number fluid. A general formulation valid for all Prandtl numbers is presented and the limiting case of large Prandtl number is approached by a numerical method. The typical developments of temperature profile, wall temperature and secondary flow in the thermal entrance region are presented for the case of square channel γ = 1. Local Nusselt number variations are presented for the aspect ratios γ = 0.2, 0.5, 1, 2 and 5 with Rayleigh number as parameter. Due to entry and secondary flow effects, a minimum Nusselt number occurs at some distance from the entrance, depending on the magnitude of Rayleigh number. This behavior is similar to that observed in the thermal entrance region where the transition from laminar to turbulent flow occurs. The effect of Rayleigh number is seen to decrease the thermal entrance length, and the Graetz solution, neglecting buoyancy effects, is found to be applicable only when Rayleigh number is less than about 10 3. A study of the practical implications of large Prandtl number on heat transfer results for hydrodynamically and thermally fully developed case reveals that the present heat transfer results are valid for Prandtl number ranging from order 10 to infinity.

Thermal Instability in Differentially Heated Inclined Fluid Layers

In an inclined adversely heated fluid layer confined between two rigid boundaries in a slot of large aspect ratio it is found that the unicellular base flow in the conduction regime becomes unstable with the formation of stationary secondary rolls with their axes along the line of inclination (x-rolls) for large Prandtl number fluids and axes perpendicular to the line of inclination (y-rolls) for small Prandtl number fluids. However, for angles near the vertical, the curve of the critical Rayleigh number versus inclination for x-rolls rises above that for y-rolls even for large Prandtl number fluids so that in a vertical fluid layer only cross rolls (y-rolls) could develop. The stability equations, as well as the results, reduce to those available for the horizontal fluid layer for which x-rolls are as likely to occur as y-rolls. It is seen that even a small inclination to the horizontal is enough to assign a definite direction for these two-dimensional cells, this direction depending on the Prandtl number. It is hoped that this basic information will be of help in the determination of the magnitude of the secondary cells in the postinstability regime and the heat transfer characteristics of the thin fluid layer.

An asymptotic solution for large Prandtl number free convection

The set of ordinary differential equations governing free convection boundary layer flow past an isothermal semi-infinite vertical flat plate is solved for large Prandtl numbers by means of the method of matched asymptotic expansions. The analysis leads to an expression for heat transfer which contains the Prandtl number explicitly and which is very accurate for sufficiently large values of the Prandtl number. On the other hand the analysis also has qualitative assets. Before choosing the mathematical method of solution, the physical aspects of the large Prandtl number free convection boundary layer are investigated. The mathematical solution serves to enlarge our understanding of the physical implications of a free convection boundary layer in a large Prandtl number fluid.