S., Huang, B., (1994) Viscous dissipation effects in entrance region heat transfer for a power law fluid flowing between parallel plates. (1987) Non-Newtonian fluids, Chapter 2 in Handbook of Heat Transfer Applications, 2nd edn. A discussion of these aspects is beyond the scope of this text.Ĭho, Y. Heat transfer and pressure drop results for power law fluids flowing in various noncircular ducts, including effects of temperature-dependent viscosity as well as viscous dissipation are available in Etemad (1995). It is interesting to note the influence of rounding the corners of a square duct for example, rounding the square duct with a radius one-sixth the side of the duct results in an increase of NuT from 3.19 to 3.43 for n = 0.5. These results were obtained by Etemad (1995) by a finite element solution of the governing conservation equations for Re = 500 and Pr = 10. For noncircular ducts the Reynolds number is based on the hydraulic diameter of the duct cross-section. Table 1 below compares the fully-developed Nusselt numbers (Nu T and Nu H2) for twelve different cross-sectional geometries. (a) Isothermal wall, (b) Constant heat flux at wall. The interested reader is referred to the excellent textbook by Skelland (1967) for a thorough analysis of non-Newtonian flow and heat transfer.įigure 2. Simultaneously developing flow and heat transfer in square duct for Re = 500 and Pr = 10. have been discussed in the literature, e.g., Mashelkar (1988), Lawal and Mujumdar (1989), and Etemad and Mujumdar (1994), among others.
Effects of viscous dissipation, variable apparent viscosity, effect of buoyancy, chemical reactions, external flow, turbulence, etc. We further restrict attention to rectilinear ducts of uniform cross-section. Therefore we focus on the case of fully developed velocity profiles, considering a number of geometric configurations, e.g., circular pipe, parallel plates, rectangular ducts, cylindrical annuli and several non-circular cross section ducts.
Since most non-Newtonian fluids have high viscosities, the hydrodynamic entrance length beyond which the flow becomes independent of axial distance is shorter than the thermal entrance length.
Also, except in the hydrodynamically developing entrance region of the duct or channel fluid elasticity has little influence on the flow since the elastic stresses do not change in the flow direction. Time-dependent fluids which undergo significant shearing before entry into the channel or duct are affected by the time-dependency only over short times of deformation. External flows involving non-Newtonian fluids are generally of less practical interest than internal flows. Since most non-Newtonian fluids are highly viscous, laminar flow is often encountered in industrial applications. Further, we will examine only internal flow through smooth, straight conduits of circular and noncircular cross-section. Due to space limitations, we confine our attention to steady convective heat transfer to pseudoplastic or dilatant fluids described by the well known Ostwald-de-Waele power law model (τ = Kγ n or η a = Kγ n−1 n 1 for dilatant fluids). It is affected by viscous dissipation due to the very high viscosities coupled with high shear rates, and the temperature-dependence of the apparent viscosity as well as by thermal conductivity, possible chemical reactions, etc. industries.Ĭonvective heat transfer to such fluids depends on the rheology of the fluid. The following chart presents a rheological classification of non-Newtonian fluids encountered in the chemical, food, petrochemical, detergent, printing inks, coatings, etc. Viscoelastic fluids display properties of both fluids and elastic solids. The apparent viscosity of Non-Newtonian Fluids, η a = τ/γ, is not a material property (as is the case for Newtonian Fluids) but may depend on the rate of shear and previous flow history of the fluid. Convective heat transfer to such fluids depends on the fluid rheology, geometric configuration of the flow domain as well as the flow regime (e.g., laminar, turbulent, etc). Most slurries, suspensions, dispersions, solutions of polymeric materials and melts exhibit complex flow behavior which cannot be described by Newton's law of viscosity τ = ηγ, where τ is the shear stress, γ is the shear rate and the constant of proportionality η is the material property called Viscosity.
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