Studies on heat transfer to Newtonian and non-Newtonian fluids in agitated vessel

Heat transfer studies to Newtonian and non-Newtonian fluids are carried out in a stirred vessel fitted with anchor/turbine impeller and a coil for heating/cooling with an objective of determining experimentally the heat transfer coefficient of few industrially important systems namely castor oil and its methyl esters, soap solution, CMC and chalk slurries. The effect of impeller geometry, speed and aeration is investigated. Generalized Reynolds and Prandtl numbers are calculated using an apparent viscosity for non-Newtonian fluids. The data is correlated using a Sieder–Tate type equation. A trend of increase in heat transfer coefficient with RPM in presence and absence of solids has been observed. Relatively high values of Nusselt numbers are obtained for non-Newtonian fluids when aeration is coupled with agitation. The contribution of natural convection to heat transfer has been accounted for by incorporating the Grashof number. The correlations developed based on these studies are applied for design of commercial scale soponification reactor. Power per unit volume resulted in reliable design of a reactor.     

Breakup of Newtonian and non-Newtonian fluids in air jets

The breakup of droplets of non-Newtonian fluids has been investigated by high speed photography and impaction following preliminary results of Newtonian fluids, which confirmed the suitability of the measurement techniques. Single droplets with diameters from 2.4 to 3.3 mm, were arranged to fall under gravity into a jet of air with velocities up to 36o m/s. The droplets of Newtonian fluids, water and Diesel oil, were atomised in the expected manner within three main regimes characterised by the Weber number of the droplet and air jet conditions, while similar droplets of non-Newtonian fluids were found not to atomise but to develop under shear and stretching into ligaments of fluid separated from a local region of their surface; these ligaments were elongated until breakup occurred, though not into small droplets as with the Newtonian fluids. Some of the non-Newtonian fluids (TEP with 7.5% and lo% K125, with and without water) were found not to break up at the maximum speed of the tests and they will be re-examined at higher jet velocities. Increase in the concentration of K125 in TEP resulted in higher critical speed for a given droplet diameter.The authors would like to thank Prof. J. H. Whitelaw of Imperial College for many discussions and useful suggestions during the course of this work, and Dr. G. Cambray of CBDE for his valuable administrative support     

Entropy generation in non-Newtonian fluids due to heat and mass transfer in the entrance region of ducts

A new solution for the Graetz problem (hydrodynamically developed forced convection in isothermal ducts) extended to power-law fluids and mass transfer with phase change at the walls is presented. The temperature and concentration spatial distributions in the corresponding entrance regions are obtained for two geometries (parallel-plates duct and circular pipe) in terms of appropriate dimensionless parameters. They are used to illustrate the effects of the fluid nature on the velocity, temperature and concentration distributions, on the axial evolution of the sensible and latent Nusselt numbers as well as on the local entropy generation rate due to velocity, temperature and concentration gradients.     

Cavitation-induced particle–wall interaction in Newtonian and non-Newtonian fluids

A novel hydrodynamic effect, namely, slow contactless motion of a heavy spherical particle along an inclined wall, accompanied by the formation of a finite particle–wall clearance under the action of a cavitation-induced lift force, is investigated. Similarity parameters controlling the particle motion, determined using the dimensionality theory, are validated experimentally. These parameters are related to the atmospheric pressure, the surface tension on the liquid–air interface, the density of the air dissolved in the fluid, the particle weight in the fluid, and the viscoelastic properties of the fluid.This paper was presented at the AERC 2005.     

Development of experimental heat transfer correlations using Newtonian fluids in helical coils

The experimental work was carried out using water, 10 and 20 % glycerol–water mixture as Newtonian fluids under isothermal and non-isothermal conditions in helical coils. The experiments were performed in laminar and turbulent flow regimes using four helical coils of coil curvature ratios as; δ = 0.055, 0.064, 0.0685 and 0.0757. For the first time, an innovative heat transfer correlations in terms of new dimensionless number ‘M’ are developed based on 135 and 183 tests conducted under isothermal and non-isothermal conditions. The developed heat transfer correlations were compared with the work of earlier investigators and are found to be in good agreement. Hence, M number could be used for characterization of fluid flow in helical coils for any types of fluids which is significant. Also, comparison of Nusselt numbers for water and glycerol–water mixtures under different experimental conditions is presented in this paper. It was observed that as helix diameter increases, Nusselt number decreases due to decrease in centrifugal force.     

Behaviors of flow mechanisms and heat transfer of non-Newtonian fluids through a spinneret

This investigation examines non-Newtonian flow mechanisms and heat transfer characteristics for a micro spinneret. The working fluid, Polyethylene terephthalate (PET), is the raw material of micro fiber, and a large-scale experimental test model was designed to visualize the complex viscous flow system in the micro spinneret. To visualize the complex convective flow system, an experimental test model was constructed, using glycerin instead of PET. The related parameters of PET were compared with those of glycerin. The power law correlates the shear strain with PET viscosity at various temperatures. The pressure distribution along the flow direction was measured and the flow pattern was visualized using polyethylene (PE) powder of 20–40 m. Similar configurations were calculated for micro spinneret physical parameters to determine the thermal flow characteristics. The Reynolds number in the test model is not less than 10^–2. In the non-Newtonian PET working fluid of practical micro spinneret, flows with Re = 10⁴ to 10^–2 are in the same low Reynolds number flow regime. Therefore, the working fluid is expected to have the same flow characteristic. A numerical solution covering the range of approximately Re = 10^–4 at PET confirms that the flow characteristics of glycerin are constant for Re = 1.228 × 10^–2. The Peclet number in the test model can be adjusted to a value similar to that in the micro spinneret. The flow visualization was compared with that of the numerical solution, and the friction factor and Nusselt number in the micro spinneret were analyzed. Finally, numerical results and friction factor with various exit angles of micro spinneret in a triangular zone flow system were also summarized.     

An analysis for forced convection heat transfer from external surfaces to non-Newtonian fluids

A theoretical analysis has been proposed for the forced convection heat transfer from external surfaces immersed in non-Newtonian fluids of the power-law model. The integral treatment previously introduced for Newtonian fluids has been successfully extended to the non-Newtonian fluids over a flat plate and a wedge of an arbitrary included angle. The integral momentum and energy equations are transformed into a pair of characteristic equations, which can readily be solved for the velocity shape factor and the boundary layer thickness ratio, once the exponents in the expressions for the power-law model, free stream velocity and wall temperature variation are specified. It has been also found that an asymptotic expression derived under the assumption of large Prandtl number, is valid practically for all power-law fluids, and hence, can be used for a speedy, and yet accurate estimation of the local heat transfer to non-Newtonian fluids.     

The free surface flow of Newtonian and non-Newtonian fluids trapped by surface tension

In this paper the position of the free surface of a swirling fluid held in by surface tension is calculated by the finite element method. A new locally mass-conserving quadratic velocity, linear pressure triangular element is used to overcome non-physical solutions produced by the well known Taylor-Hood element.     

Theoretical prediction of the mass transfer coefficients in bubble columns operating in churn-turbulent flow regime. Study in Newtonian and non-Newtonian fluids under different operation conditions

 A comprehensive experimental study of the volumetric transfer coefficient k _L a with Newtonian and non-Newtonian fluids in bubble columns using CO₂ as gas phase is the objective of this work. The evaluation of the hydrodynamic characteristics of the bubble columns and delineated the different hydrodynamic regimes considering column geometry, gas flow, liquid height and type of fluid (Newtonian and non-Newtonian) suggest a general applicability of the proposed model. An explanation about of the k _L a values in non-Newtonian fluid is offered take into account shear rate, column geometry, viscosity and results reported in the literature previously. Received on 31 July 1999     

Similarity solutions of unsteady laminar incompressible boundary layer equations for flow,heat and mass transfer in non-Newtonian fluids around axisymmetric bodies

Summary The possible existence of similarity solutions for the unsteady three-dimensional boundary layer flows with heat and mass transfer around stationary axisymmetric bodies which are fully immersed in purely viscous moving non-Newtonian fluids has been searched in general by the application of transformations, involving a single linear parameter. In particular, the cases involving rotational flows around stationary bodies and rotating bodies have been discussed as corollaries of the main analysis. The main analysis shows that the similarity solutions are possible only for the bodies for which where is a cross-sectional radius; and is the longitudinal distance from the nose point to the cross section. In case of rotating bodies, similarity solutions exist only for cones and disks. The analysis, as an example, has successfully been applied to the Powell-Eyring model. It is seen that for the same rate of shear, expenditure of energy for maintaining the rotation of the solid body is comparatively higher for a flow with a higher Eyring number where the Eyring numberEy=1/µBE. µ, B, andE are the material functions of the Powell-Eyring fluid.

---

Zusammenfassung Es wird die mögliche Existenz von Ähnlichkeitslösungen für instationäre drei-dimensionale Grenzschichtströmungen rein-viskoser nicht-newtonscher Flüssigkeiten mit Wärme- und Stoffübertragung um voll eingetauchte stationäre achsensymmetrische Körper in allgemeiner Weise untersucht. Hierbei werden Transformationen verwendet, die einen einzigen linearen Parameter enthalten. Als Spezialfälle der allgemeinen Analyse werden Rotationsströmungen um ruhende und rotierende Körper diskutiert. Die Hauptanalyse ergibt, daß Ähnlichkeitslösungen nur existieren für Körper mit , wo den Abstand von der Achse und den longitudinalen Abstand auf der Oberfläche von der Nase des Körpers aus bedeuten. Im Falle rotierender Körper existieren solche Lösungen nur für Kegel und Kreisscheiben. Die Analyse läßt sich erfolgreich auf das Beispiel einer Powell-Eyring-Flüssigkeit anwenden. Man findet, daß bei gleicher Schergeschwindigkeit der Energieverbrauch zur Aufrechterhaltung der Körperrotation mit wachsender Eyring-Zahl Ey= 1/µBE ansteigt, wobeiµ, B undE Materialfunktionen der Powell-Eyring-Flüssigkeit bedeuten.

---

---

With 1 figure and 1 table     

A unified compatibility method for exact solutions of non-linear flow models of Newtonian and non-Newtonian fluids

Criteria are established for higher order ordinary differential equations to be compatible with lower order ordinary differential equations. Necessary and sufficient compatibility conditions are derived which can be used to construct exact solutions of higher order ordinary differential equations subject to lower order equations. We provide the connection to generalized groups through conditional symmetries. Using this approach of compatibility and generalized groups, new exact solutions of non-linear flow problems arising in the study of Newtonian and non-Newtonian fluids are derived. The ansatz approach for obtaining exact solutions for non-linear flow models of Newtonian and non-Newtonian fluids is unified with the application of the compatibility and generalized group criteria.     

An analytical solution to non-axisymmetric heat transfer with viscous dissipation for non-Newtonian fluids in laminar forced flow

Forced convection heat transfer in a non-Newtonian fluid flow inside a pipe whose external surface is subjected to non-axisymmetric heat loads is investigated analytically. Fully developed laminar velocity distributions obtained by a power-law fluid rheology model are used, and viscous dissipation is taken into account. The effect of axial heat conduction is considered negligible. The physical properties are assumed to be constant. We consider that the smooth change in the velocity distribution inside the pipe is piecewise constant. The theoretical analysis of the heat transfer is performed by using an integral transform technique – Vodicka’s method. An important feature of this approach is that it permits an arbitrary distribution of the surrounding medium temperature and an arbitrary velocity distribution of the fluid. This technique is verified by a comparison with the existing results. The effects of the Brinkman number and rheological properties on the distribution of the local Nusselt number are shown.     

Pool boiling heat transfer performance of Newtonian nanofluids

Experimental measurements were carried out on the boiling heat transfer characteristics of γ-Al₂O₃/water and SnO₂/water Newtonian nanofluids. Nanofluids are liquid suspensions containing nanoparticles with sizes smaller than 100 nm. In this research, suspensions with different concentrations of γ-Al₂O₃ and SnO₂ nanoparticles in water were studied under nucleate pool boiling heat transfer conditions. Results show that nanofluids possess noticeably higher boiling heat transfer coefficients than the base fluid. The boiling heat transfer coefficients depend on the type and concentration of nanoparticles.     

Turbulent forced convection heat transfer of non-Newtonian nanofluids

Forced convection heat transfer of non-Newtonian nanofluids in a circular tube with constant wall temperature under turbulent flow conditions was investigated experimentally. Three types of nanofluids were prepared by dispersing homogeneously γ-Al₂O₃, TiO₂ and CuO nanoparticles into the base fluid. An aqueous solution of carboxymethyl cellulose (CMC) was used as the base fluid. Nanofluids as well as the base fluid show shear-thinning (pseudoplastic) rheological behavior. Results indicate that the convective heat transfer coefficient of nanofluids is higher than that of the base fluid. The enhancement of the convective heat transfer coefficient increases with an increase in the Peclet number and the nanoparticle concentration. The increase in the convective heat transfer coefficient of nanofluids is greater than the increase that would be observed considering strictly the increase in the effective thermal conductivity of nanofluids. Experimental data were compared to heat transfer coefficients predicted using available correlations for purely viscous non-Newtonian fluids. Results show poor agreement between experimental and predicted values. New correlation was proposed to predict successfully Nusselt numbers of non-Newtonian nanofluids as a function of Reynolds and Prandtl numbers.     

Mixed convective heat and mass transfer in a non-Newtonian fluid at a peristaltic surface with temperature-dependent viscosity

We investigate the problem of the unsteady mixed convection peristaltic mechanism. The flow includes a temperature-dependent viscosity with thermal diffusion and diffusion-thermo effects. The peristaltic flow is between two vertical walls, one of which is deformed in the shape of traveling transversal waves exactly like peristaltic pumping and the other of which is a parallel flat plate wall. The equations of momentum, energy, and concentration are subject to a set of appropriate boundary conditions by assuming that the solution consists of two parts: a mean part and a perturbed part. The solution of the perturbed part has been obtained by using the long-wave approximation. The mean part has been solved and coincides with the approximation of Ostrach. The mean part (zeroth order), the first order, and the total solution of the problem have been evaluated numerically for several sets of values of the parameters entering the problem. The skin friction, and the rate of heat and mass transfer at the walls are obtained and illustrated graphically.     

Heat transfer to non-Newtonian fluids in laminar flow through rectangular ducts

Heat transfer to non-newtonian fluids flowing laminarly through rectangular ducts is examined. The conservation equations of mass, momentum, and energy are solved numerically with the aid of a finite volume technique. The viscoelastic behavior of the fluid is represented by the Criminale-Ericksen-Filbey (CEF) constitutive equation. Secondary flows occur due to the elastic behavior of the fluid, and, consequently, heat transfer is strongly enhanced. It is observed that shear thinning yields negligible heat transfer enhancement effect, when compared with the secondary flow effect. Maximum heat transfer is shown to occur for some combinations of parameters. Thus, there are optimal combinations of aspect ratio and Reynolds numbers, which depend on the fluid's mechanical behavior. This result can be usefully explored in thermal designs of certain industrial processes.     

Quasi-linear heat and mass transfer

Flow, Turbulence and Combustion - From the assumption that the heat flux (mass flux with respect to the mass-average velocity) vector is an isotropic function of the temperature (mass-fraction)...     

Time-derivatives and frame-invariance beyond Newtonian fluids

Replacing the time-derivatives with spatial gradients is a quite useful and ordinary method to work with the Chapman–Enskog expansion when dealing with non-uniform fluids. However, to perform the substitution, approximated balance equations, which are not frame invariant, are usually used. Alternatively, frame-invariant but not frame-indifferent expansions may be derived. In this paper we analyze the possibility of deriving a Chapman–Enskog expansion both frame-invariant and frame-indifferent.