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McNaught, J M, Macdonald equation, for fixed-bed pressure drop, Mach number, Macleod-Sugden method for surface tension Macrolayer consumption model for critical heat flux in pool boiling, Maddox, R N Magnetic fields, effect on properties of rheologically complex materials, Magnetic devices, for fouling mitigation, Magnetohydrodynamcs, inaugmentation of heat transfer in microfluidic systems, Margarine manufacture, crystallization of edible oils and fats in, scraped surface heat exchangers for, Marlotherm, heat transfer media, Martensitic stainless steels, Martin, H Martinelli and Boelter equations for combined free and forced convection, Martinelli and Nelson correlations: Mass absorption coefficient, Mass extinction coefficient, Mass fraction, in multicomponent mixtures, Mass scattering coefficient, Mass transfer: Mass transfer coefficient: Materials of construction, for heat exchangers, Low temperature operation, ASME VIII code guidelines for, Matovosian, Robert, Matrix inversion techniques, in radiative heat transfer, Maximum drag reduction Maximum velocities (in shell-and-tube heat exchangers) Maxwell model, for non-Newtonian fluid, Maxwell-Stefan equations, for multicomponent diffusion, Maxwell's equations, for electromagnetic radiation, Mean beam length concept, in radiative heat transfer: Mean phase content, Mean temperature difference: Measurement of fouling resistance, Mechanical design of heat exchangers: Mechanical draft cooling towers, Mechanical loads, specifications in EN13445, Mechanical vapour compression cycles in refrigeration, Mediatherm, heat transfer medium, Melo, L F, Melting, thermal conduction in, Melting point: Mercury: Merilo correlation, for critical heat flux in horizontal tubes, Merkel's equation, in cooling tower design, Mertz, R, Metais and Eckert diagrams, for regimes of convection: Metals: Metallurgical industry, kilns and furnaces for, Metastable equilibrium, of vapor and liquid, Methane: Methanol: Methyl acetate: Methylacetylene: Methyl acrylate: Methyl amine n-Methylaniline: Methyl benzoate: 2-Methyl-1,3-Butadiene (Isoprene): 2-Methylbutane (isopentane): Methylbutanoate: 2-Methyl-2-butene: Methylcyclohexane: Methylcyclopentane: Methylethylketone: Methyl formate: Metallurgical slag, use of submerged combustion in reprocessing of, Methyl fluorate: 2-Methylhexane: Methylisobutylketone: Methylmercaptan: 1-Methylnaphthalene: 2-Methylnaphthalene: 2-Methylpentane: 3-Methylpentane: 2-Methylpropane (isobutane): 2-Methylpropene: Methyl propionate: Methylpropylether: Methylpropyl ketone: Methyl salicylate: Methyl-t-butyl ether: Microbubbles, for drag reduction, Microchannels (see also microfluidics) Micro-fin tubes: Microfluidics, enhancement of heat transfer in, Mie scattering, in pulverized coal combustion, Miller, C J Miller, E R Mineral oils, as heat transfer media, physical properties of, Mineral wool production, submerged combustion systems for, Minimum fluidization velocity, Minimum heat flux in pool boiling: Minimum tubeside velocity, in shell-and-tube heat exchangers, Minimum velocity for fluidization, Minimum wetting rate, for binary mixtures, Mirror-image concept, in radiative heat transfer, Mirrors, spectral characteristics of reflectance from, Mishkinis, D, Mist flow: Mitigation of fouling, Mixed convection occurrence in horiozntal circular pipe, Metais and Eckert diagram for, Mixing (shell-side), in twisted tube heat exchangers, Mixing length, in turbulent flow, Mixtures: Modelling, of fouling: Models, theory of, Modulus of elasticity: Moffat, R S M, Molecular gas radiation properties, Molecular weight: Mollier chart, for humid air, Momentum equation: Monitoring, on line, of fouling, Monochloroacetic acid: Monte Carlo methods, in radiative heat transfer, Moody chart: Morris, M Mostinski correlations: Moving bed, heat transfer to, Muchowski, E, Mueller, A C Muller-Steinhagen, H Multicomponent mixtures: Multidimensional systems, heat conduction in, Multiflux methods, for radiative heat transfer in nonisothermal gases, Multipass shell-and-tube heat exchangers, Multiphase fluid flow and pressure drop: Multiple duties, in plate heat exchangers, Multiple effect evaporation, Multiple hairpin heat exchanger, Multistage flash evaporation (MSF) Multizone model, for furnaces,
N O P Q R S T U V W X Y Z

Heat Transfer for non-Newtonian Fluids

DOI 10.1615/hedhme.a.000179

2.5.12 Heat transfer for non-Newtonian fluids

A. Introduction

(by R. C. Armstrong and H. H. Winter)

Section 179 describes ways in which heat transfer in non-Newtonian fluids is different from that in Newtonian fluids. As polymers constitute the largest class of non-Newtonian fluids, we shall focus our attention on them. Moreover, we shall focus on differences in heat transfer characteristics between Newtonian and polymeric fluids that can be attributed to differences in viscous behavior between these two classes of fluids. These distinctions involve both the shear rate dependence that is commonly observed in non-Newtonian fluids and also the different magnitude of the viscosity in polymers as opposed to low-molecular-weight fluids. In addition to these viscous effects, it is clearly possible that many interesting changes in heat transfer problems could result from the "elastic" character of polymeric fluids. For example, in duct flows involving noncircular cross sections, certain non-Newtonian fluids show qualitatively different secondary velocity patterns than Newtonian fluids. These clearly have some effect on heat transfer. Very little can yet be said quantitatively about these "elastic" effects, however.*

In addition to these differences in heat transfer between Newtonian and non-Newtonian fluids, there are differences in the kinds of information that we are generally interested in for nonisothermal flows of these two classes of fluids. Let us break the possible calculations into two categories: global and local. For Newtonian fluids it is the global result, the evaluation of a heat transfer coefficient to relate bulk temperature differences to heat fluxes, that is of most interest. This heat transfer coefficient, which is used for sizing heat exchanger equipment and estimating bulk temperature changes, is not as useful for non-Newtonian fluids for two reasons: first, in problems with significant viscous heating, which are common for molten polymers, the heat transfer coefficient cannot be defined meaningfully; and second, because of the peculiar physical properties of polymers, heat transfer between a flowing polymer and its surroundings is generally ignored. There are, of course, exceptions to this last statement, such as cooling extruders for low-temperature extrusion of foamed polymers and cooling of polymerization reactors.

For polymeric fluids, evaluation of the local temperature field is usually of primary interest. Because of the sensitivity of the physical properties to temperature, the temperature field can have a pronounced effect on the flow field and therefore on the process itself. In addition, many polymers are temperature sensitive and will degrade at high temperatures, say, at Tdegrad. It is important to be sure that the local temperature never exceeds Tdegrad. Finally, relaxation phenomena in polymers are strongly temperature sensitive, and the amount and location of residual stress or strain in a polymeric product will depend on the local temperature history of the polymer.

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