Heat transfer to non-newtonian fluids

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. 

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. 

Metzner, A. B., and D. F. Gluck. 1960. Heat Transfer to Non-Newtonian Fluids Under Laminar Flow Conditions. Chem. Eng. Science, 12, 3 Oune), 185-190. 

U. Gkigull, Heat Transfer to Non-Newtonian Fluids for Laminar Flow Through Tubes, Chem.-Ingr.-Tech. 28, (8/9), 553-556 (1956). 

Heat transfer involving non-Newtonian fluids has not been studied in rotating devices. Models have been developed for gravity-driven heat transfer for power-law fluids (46). These models may be useful as a starting point to evaluate performance in higher-gravity fields. 

W. H. Suckow, P. Hrycak, and R. G. Griskey, Heat Transfer to Non-Newtonian Dilatant (Shear-Thickening) Fluids Flowing Between Parallel Plates, AIChE Symp. Ser. (199/76) 257,1980. 

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]. 

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. 

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 ... 

U. K. Ghosh, S. N. Upadhyay, and R. P. Chhabra, Heat and Mass Transfer from Immersed Bodies to Non-Newtonian Fluids, Advances in Heat Transfer (25) 252-321,1994. 

A significant heat-transfer enhancement can be obtained when a nonckcular tube is used together with a non-Newtonian fluid. This heat-transfer enhancement is attributed to both the secondary flow at the corner of the nonckcular tube (23,24) and to the temperature-dependent non-Newtonian viscosity (25). Using an aqueous solution of polyacrjiamide the laminar heat transfer can be increased by about 300% in a rectangular duct over the value of water (23). 

Hartnett, ). P., Kostic, M., Heat tranfer to Newtonian and non-Newtonian fluids in rectangular ducts, Adv. Heat Transfer 19 (1989) 247-356. 

Two experimental publications (B6, C3) and one theoretical paper (P5) are available in the field of heat transfer to liquids which are appreciably non-Newtonian in behavior. The data of Bonilla et al. (B6) have frequently been used by workers in the field of heat transfer to dilute suspensions but may more properly be treated here along with other fluids whose heat transfer characteristics are appreciably influenced by their departure from Newtonian behavior. 

The velocity profiles of pseudoplastic non-Newtonian fluids (Fig. 8) in laminar flow deviate from the Newtonian parabola in the same way as the velocity profile of Newtonian liquids changes when heat is being transferred to them (M4, p. 229), since in both cases the viscosity of the fluid is lower at the wall than at the center of the tube. For the Newtonian... 

The rates of heat transfer between the fermentation broth and the heat-transfer fluid (such as steam or cooling water flowing through the external jacket or the coil) can be estimated from the data provided in Chapter 5. For example, the film coefficient of heat transfer to or from the broth contained in a jacketed or coiled stirred-tank fermentor can be estimated using Equation 5.13. In the case of non-Newtonian liquids, the apparent viscosity, as defined by Equation 2.6, should be used. 

Fluid flow, heating and composition, which change by reaction or by transfer at one interface, represent the specificity of the chemical engineering processes. The response of a system to the applied effects that generate the mentioned cases depends on the nature of the materials involved in the process. All the properties of the materials such as density, viscosity, thermal capacity, conductivity, species diffusivity or others relating the external effects to the process response must be included as variables. The identification of these variables is not always an easy task. A typical case concerns the variation of the properties of the materials, in a nonlinear dependence with the operation variables. For example, when studying the flow of complex non-Newtonian fluids such as melted polymers in an externally heated conduct, their non-classical properties and their state regarding the effect of temperature make it difficult to select the properties of the materials. 

Rao and Anantheswaran (1988) reviewed studies on convective heat transfer to canned fluids in detail. Here, the dimensionless groups and relationships applicable to both Newtonian and non-Nervtonian fluids are reviewed in brief The rotational Reynolds Reg number is defined as... 

Anantheswaran and Rao (1985a, 1985b) developed the following respective correlations for heat transfer to cans under end-over-end agitation for Newtonian and non-Newtonian fluids ... 

Heat transfer to canned liquids being heated in a Steritort was examined by Rao et al. (1985). Both Newtonian (water, and 30,40, 50, and 60% w/v, aqueous sucrose solutions) and non-Newtonian fluids (0.3, 0.4, 0.5, and 0.75% aqueous guar gum... 

You saw how the equations governing energy transfer, mass transfer, and fluid flow were similar, and examples were given for one-drmensional problems. Examples included heat conduction, both steady and transient, reaction and diffusion in a catalyst pellet, flow in pipes and between flat plates of Newtonian or non-Newtonian fluids. The last two examples illustrated an adsorption column, in one case with a linear isotherm and slow mass transfer and in the other case with a nonlinear isotherm and fast mass transfer. Specific techniques you demonstrated included parametric solutions when the solution was desired for several values of one parameter, and the use of artificial diffusion to smooth time-dependent solutions which had steep fronts and large gradients. 

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