Heat Transfer of Non-Newtonian Fluids

Most of the studies on heat transfer, with fluids have been done with Newtonian fluids. However, a wide variety of non-Newtonian fluids are encountered in the industrial chemical, biological, and food processing industries. To design equipment to handle these fluids, the flow property constants (rheological constants) must be available or must be measured experimentally. Section 3.5 gave a detailed discussion of rheological constants for non-Newtonian fluids. Since many non-Newtonian fluids have high effective viscosities, they are often in laminar flow. Since the majority of non-Newtonian fluids are pseudoplastic fluids, which can usually be represented by the power law, Eq. (3.5-2), the discussion will be concerned with such fluids. For other fluids, the reader is referred to Skelland (S3). 

Laminar flow in tubes. A large portion of the experimental investigations have been concerned with heat transfer of non-Newtonian fluids in laminar flow through cylindrical tubes. The physical properties that are needed for heat transfer coefficients are density, heat capacity, thermal conductivity, and the rheological constants K and n or K and n. 

In heat transfer in a fluid in laminar flow, the mechanism is one of primarily conduction. However, for low flow rates and low viscosities, natural convection effects can be present. Since many non-Newtonian fluids are quite viscous, natural convection effects are reduced substantially. For laminar flow inside circular tubes of power-law fluids, the equation of Metzner and Gluck (M2) can be used with highly viscous non-Newtonian fluids with negligible natural convection for horizontal or vertical tubes for the Graetz number Nq, 20 and n 0.10. 

Solution The solution is trial and error since the outlet bulk temperature of the fluid must be known to calculate /i from Eq. (4.12-2). Assuming Tjp = 54.4°C for the first trial, the mean bulk temperature 7 is (54.4 -h 37.8)/2,or46.1°C. 

Plotting the two values of K given at 37.8 and 93.3°C as log K versus T°C and drawing a straight line through these two points, a value of of 

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S.6. Equations of Motion and Heat Transfer of Non-Newtonian Fluids 345... 

M. L. Ng, An Experimental Study on Natural Convection Heat Transfer of Non-Newtonian Fluids from Horizontal Wires, Ph.D. thesis, University of Illinois at Chicago, 1985. 

In Chapter 6 we consider problems of hydrodynamics and mass and heat transfer in non-Newtonian fluids and describe the basic models for Theologically complicated fluids, which are used in chemical technology. Namely, we consider the motion and mass exchange of power-law and viscoplastic fluids through tubes, channels, and films. The flow past particles, drops, and bubbles in non-Newtonian fluid are also analyzed. 

Since the power-law and the Bingham plastic fluid models are usually adequate for modelling the shear dependence of viscosity in most engineering design calculations, the following discussion will therefore be restricted to cover just these two models where appropriate, reference, however, will also be made to the applications of other rheological models. Theoretical and experimental results will be presented separately. For more detailed accounts of work on heat transfer in non-Newtonian fluids in both circular and non-circular ducts, reference should be made to one of the detailed surveys [Cho and Hartnett, 1982 Irvine, Jr. and Kami, 1987 Shah and Joshi, 1987 Hartnett and Kostic, 1989 Hartnett and Cho, 1998]. 

In conclusion, it should be emphasised that most of the cmrently available information on heat transfer to non-Newtonian fluids in stirred vessels relates to specific geometrical arrangements. Few experimental data are available for the independent verification of the individual correlations presented here which, therefore, must be regarded somewhat tentative. Reference should also be made to the extensive compilations [Edwards and Wilkinson, 1972 Poggermann et al., 1980 Dream, 1999] of other correlations available in the literature. Although the methods used for the estimation of the apparent viscosity vary from one correlation to another, especially in terms of the value of ks, this appears to exert only a moderate influence on the value of h, at least for shear-thinning fluids. For instance, for n = 0.3 (typical of suspensions and polymer solutions), a two-fold variation in the value of ks will give rise to a 40% reduction in viscosity, and the effects on the heat transfer coefficient will be further diminished because Nu [Pg.371]

The heating or cooling of process streams is frequently required. Chapter 6 discusses the fundamentals of convective heat transfer to non-Newtonian fluids in circular and non-circular tubes imder a range of boundary and flow conditions. Limited information on heat transfer from variously shaped objects - plates, cylinders and spheres - immersed in non-Newtonian fluids is also included here. 

Lev que s problem was extracted from the rescaled mass balance in Equation 8.28. As can be seen, this equation is the basis of a perturbation problem and can be decomposed into several subproblems of order 0(5 ). The concentration profile, the flux at the wall, and consequently the mixing-cup concentration (or conversion) can all be written as perturbation series on powers of the dimensionless boundary layer thickness. This series is often called as the extended Leveque solution or Lev jue s series. Worsoe-Schmidt [71] and Newman [72] presented several terms of these series for Dirichlet and Neumann boundary conditions. Gottifredi and Flores [73] and Shih and Tsou [84] considered the same problem for heat transfer in non-Newtonian fluid flow with constant wall temperature boundary condition. Lopes et al. [40] presented approximations to the leading-order problem for all values of Da and calculated higher-order corrections for large and small values of this parameter. 

Gottifredi JC. Flores AF. Extended Leveque solution for heat transfer to non-Newtonian fluids in pipes and flat ducts. International Journal of Heat and Mass Transfer 1985 28 903-908. 

English-Chinese dictionary of Rheology, Science Press Staff, Er. Eur., 1990, 49.95 Free liquid jets and films hydrodynamics and Rheology interaction of mechanics and mathematics, Yarin A, John Wiley Sons, A 246 Fundamentals of heat transfer in non-Newtonian fluids, Chen J,... 

Computer modelling provides powerful and convenient tools for the quantitative analysis of fluid dynamics and heat transfer in non-Newtonian polymer flow systems. Therefore these techniques arc routmely used in the modern polymer industry to design and develop better and more efficient process equipment and operations. The main steps in the development of a computer model for a physical process, such as the flow and deformation of polymeric materials, can be summarized as ... 

Topics that acquire special importance on the industrial scale are the quality of mixing in tanks and the residence time distribution in vessels where plug flow may be the goal. The information about agitation in tanks described for gas/liquid and slurry reactions is largely apphcable here. The relation between heat transfer and agitation also is discussed elsewhere in this Handbook. Residence time distribution is covered at length under Reactor Efficiency. A special case is that of laminar and related flow distributions characteristic of non-Newtonian fluids, which often occiu s in polymerization reactors. 

This chapter deals with the most commonly encountered (empirical and semi-empirical) rheological models of non-Newtonian fluids. Typical problems of hydrodynamics and heat and mass transfer are stated for power-law fluids, and the results of solutions are given for these problems. 

So far we have considered nonisothermal flows of non-Newtonian fluids with allowance for dissipative heating and the dependence of the apparent viscosity on temperature. It has been assumed that the wall temperature is constant and convective heat transfer is absent. 

Acrivos, A., Shah, M. J., and Petersen, E. E., Momentum and heat transfer in laminar boundary-layer flows of non-Newtonian fluids past external surfaces, AIChE J., Vol. 6, No. 2, pp. 312-317, 1960. 

A. A. McKillop, Heat Transfer for Laminar Flow of Non-newtonian Fluids in Entrance Region of a TUbe, Int. J. Heat Mass Transfer (7) 853,1964. 

Heat transfer characteristics of non-Newtonian fluids in pipes... 

Much of the research activity in this area has related to heat transfer to inelastic non-Newtonian fluids in laminar flow in circular and non-circular ducts. In recent years, some consideration has also been given to heat transfer to/from non-Newtonian fluids in vessels fitted with coils and jackets, but little information is available on the operation of heat exchange equipment with non-Newtonian fluids. Consequently, this chapter is concerned mainly with the prediction of heat transfer rates for flow in circular tubes. Heat transfer in external (boundary layer) flows is discussed in Chapter 7, whereas the cooling/heating of non-Newtonian fluids in stirred vessels is dealt with in Chapter 8. First of all, however, the thermo-physical properties of the commonly used non-Newtonian materials will be described. 

The most important thermo-physical properties of non-Newtonian fluids are thermal conductivity, density, specific heat, surface tension and coefficient of thermal expansion. While the first three characteristics enter into virtually all heat transfer calculations, siuface tension often exerts a strong influence on boiling heat transfer and bubble dynamics in non-Newtonian fluids, as seen in Chapter 5. Likewise, the coefficient of thermal expansion is important in heat transfer by free convection. 

Thus a momentum and a thermal boimdaiy layer will develop simultaneously whenever the fluid stream and the inunersed surface are at different temperatures (Figure 7.3). The momentum and energy equations are coupled, because the physical properties of non-Newtonian fluids are normally temperature-dependent. The resulting governing equations for momentum and heat transfer require numerical solutions. However, if the physical properties of the fluid do not vary significantly over the relevant temperature interval, there is little interaction between the two boimdaiy layers and they may both be assumed to develop independently of one another. As seen in Chapter 6, the physieal properties other than apparent viscosity may be taken as constant for commonly encountered non-Newtonian fluids. 

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