Publisher Summary This chapter focuses on heat transfer in non-Newtonian fluids. This chapter illustrates that useful engineering studies which deal with transport processes in non-Newtonian fluids have been underway for the past several years. Earlier heat transfer reviews therefore serves primarily to separate a very small number of useful contributions from the substantial mass of trivial, misleading or even incorrect concepts and interpretations available at that time. This chapter provides the general survey of rheological behavior necessary for an understanding of transport processes in non-Newtonian fluids. The fluid classification system of interest is based on the form of the constitutive equations used to describe the properties of real fluids quantitatively. The chapter discusses all or more recent publication of work on heat transfer to non-Newtonian fluids since 1954 and provides an overview of the current state of the art. The chapter also describes fluid mechanical studies dealing with non-Newtonian materials.

Heat Transfer in Non-Newtonian Fluids

Pressure losses in non‐Newtonian entrance flows

A review is presented of the current status of non- Newtonian fluid mechanics. Emphasis is placed on attempts to formulate rheological equations of state which are mathematically acceptable. A number of exact and approximate solutions to the equation of non-Newtonian motion are listed. Difficulties as well as possibilities which are associated with future progress in non-Newtonian fluid mechanics are cited.

Non-Newtonian Viscosities and the Equation of Motion

An experimental study has been made of the pressure drop in the conical entrance region to a capillary tube. Two fluids, a Newtonian oil and a viscoelastic polymer solution , were used. The entrance half angle was varied from 10.8° to 90° ; the wall shear rate in the capillary was varied from 50 sec: 1 to 1000 sec;1 • For Newtonian flow, Oka's creeping flow solution was shown to be of the correct form to predict viscous pressure drop effects, although it gave quantitative agreement only at the larger half angles (46.7°). An adaptation of this solution to the power law viscosity model provided a satis­ factory prediction of non-Newtonian viscous effects. Weissberg's solution for flow in a sharp-edged entrance (�=900) gave excellent agreement with experimental data. For viscoelastic flow, the data were correlated semiempirically using an equation that involved a non­ linear viscous term and an elastic term. An attempt to solve the conical flow problem using the theory of Bernstein, Kearsley, and Zapas yielded an intractable result , but it was possible. to. identify a group with the character of a dimensionless norma.Ldeformation rate. This group, which .also has the·properties of a Deborah number, was found to characterize the elastic pressure drop reasonably well. iv

An Experimental Study of Viscoelastic Flow in a Conical Entrance Region

According to Prandtl's suggestion, the author calculated the velocity distribution and the pressure gradient of the non-Newtonian laminar flow in the region near the entrance of a circular pipe. The results are summarized as follows:1) Though the inlet length for the Newtonian flow, when n=1, was not in agreement with the results of the author's calculation, the change in the inlet length for the non-Newtonian flow, when the values of n were varied, could be roughly estimated as shown in Fig. 3.2) The pressure loss in the Newtonian flow, when n=1, was in good agreement with the results of the author's calculation. Therefore, on the assumption that the pressure loss in the non-Newtonian flow with different values of n would be in good agreement with the experimental results, too, the correction of the pressure loss Δq for different values of n was made as shown in Fig. 5

On the Non-Newtonian Laminar Flow in the Region near the Entrance of a Circular Pipe

Although the studies on the heat transfer in non-Newtonian flow are increasing in recent years, the law of similarity of the heat transfer is not yet established. It is true that the previous investigators tried to find correlation between the experimental data on the heat transfer and various dimensionless numbers, but there is observed no consistency between them.In this paper, the author describes the law of similarity of the heat transfer in non-Newtonian flow which he has derived, using the fundamental equation. The results may be summarized as follows:(1) Pseudoplastic and dilatant fluid:(a) Natural ConvectionNu=f1(Gr, Pr2)(b) Forced convectionNu=f2(Re, Pr1):(2) Bingham fluid:(a) Natural convectionNu=f3(Gr, cGr, Pr, cPr)(b) Forced convectionNu=f4(Re, cRe, Pr, cPr)

https://www.jstage.jst.go.jp/article/kakoronbunshu1953/23/2/23_2_66/_pdf

Yukio Tomita

Papers

On the Non-Newtonian Laminar Flow in the Region near the Entrance of a Circular Pipe

On the Law of Similarity of the Heat Transfer in Non-Newtonian Flow