Search

In this work, the momentum and heat transfer characteristics of a time-dependent flow of Bingham plastic fluid over a heated isothermal sphere have been investigated numerically over wide ranges of conditions: Reynolds number, 5 ≤ Re ≤ 120, Bingham number, 0.1 ≤ Bn ≤ 100, Prandtl number, 0.7 ≤ Pr ≤ 100, frequency, π/4 ≤ ω* ≤ π and amplitude, 0 ≤ A ≤ 0.8. The influence of the fluid yield stress and inertia due to the imposed flow pulsations on the flow and thermal fields have been examined in detail. Detailed structure of the flow and temperature fields are analysed in terms of the instantaneous streamlines, isothermal contours, yielded/unyielded zones, surface pressure profiles, time-average drag coefficient and surface- and time-average Nusselt number. The influence of the frequency and amplitude of pulsations on the size of yielded (fluid-like) and unyielded (solid-like) zones is considered in order to understand convective heat transport. The size of yielded zones is seen to be in phase with the imposed pulsating velocity. However, the yield stress effects suppress the influence of flow pulsations. The temporal evolution of the drag coefficient and Nusselt number lag the imposed pulsating flow by different degrees thereby indicating the inherently different evolution of the momentum and thermal boundary layers. Broadly, the pulsating flow conditions may lead to up to 20% augmentation in heat transfer provided there is a moderate degree of advection and/or when the fluid yield stress effects are weak, i.e., small Bingham numbers. Thus, the maximum benefits of pulsating flow accrue in Newtonian fluids only. Finally, the present values of the time-average Nusselt number have been consolidated in the form of a predictive expression.

The use of orifices in measuring and regulating the discharge of Newtonian liquids from tanks has been studied extensively. For non-Newtonian liquids, this is not the case mainly due to the complex rheological properties of such liquids. To date only circular orifices have been used to measure the flow of Power-Law liquids from a tank. In this work, a range of non-Newtonian liquids flowing from a tank through different sizes of sharp crested circular, square and triangular orifices have been tested. A rectangular tank suspended from a weighbridge with a load cell was used and the orifices were fitted at the bottom of the tank for the discharge measurement. The rheological parameters of the test liquids were obtained using a concentric cylinder viscometer. The liquids tested included Newtonian, Power-law, Bingham and Herschel–Bulkley model liquids. The height-time data was transformed into discharge coefficient (Cd)-Reynolds number (Re) format for each liquid-orifice combination in all cases. The average Cd value was 0.64 in the turbulent region. Each model liquid in the laminar regime resulted in a unique relationship. Using an idea of an effective shear rate for flow through the orifice, a new Reynolds number has been defined for the different liquids to consolidate the Cd-Re relationship to the Newtonian liquid curve. A single composite model was used to predict the relationship between Cd and Re for all liquids-orifices combinations used in this work. This can be used in the engineering designs and processes.

Thermal mixing behavior of shear-thinning fluids with the specified heat flux boundary condition at mixing zone walls is studied numerically to investigate the effect of Reynolds number (10 to 50),...

Branching T-channel is a very common element of a piping system for the transportation of liquids and gases. The brachesbranches of the T-channel can be inclined at different angles which affects the flow dynamics and heat transfer characteristics significantly. Thus, the present work focuses on the flow and thermal characteristics of the laminar forced convection of power-law fluids in a rectangular branching channel which have been numerically investigated over a wide range of parameters such as Reynolds number, 50 ≤ Re ≤ 300, Prandtl number, 10 ≤ Pr ≤ 50, inclination angle, 30° ≤ α ≤ 90° and power-law index, 0.2 ≤ n ≤ 1.4 (includes shear-thinning, n 1 and Newtonian, n = 1 fluids). This is perhaps the first systematic study which examines the role of power-law fluid behaviour and of branch inclination on momentum and heat transfer characteristics. New extensive results for the flow and temperature fields are presented in terms of streamline contours and separated-flow zones, pressure coefficient, recirculation length, critical Reynolds number, isotherm contours, temperature profiles and local Nusselt number. The pressure coefficient is found to be higher for shear-thickening fluids than that for the Newtonian and shear-thinning fluids while the inclination angle has only a weak effect. The recirculation length bears a positive dependence on the Reynolds number and inclination angle while an inverse relationship is observed with power-law index in both branches. The critical Reynolds number, at which the onset of flow recirculation is observed, is found to be lower for higher inclination angles and a strong influence of the power-law index is also seen on the critical Reynolds number in both branches. Also, the local Nusselt number is seen to be higher at lower Prandtl numbers, low power-law index values and high inclination angles for both branches. Overall, the inclination angle plays a significant role in determining the heat transfer characteristics.

In this study, a rotating cylinder is placed in a stream of shear-thinning fluids, flowing with a uniform velocity. Detailed investigations are performed for the following range of conditions: Reynolds number 100≤Re≤500, power-law index 0.2≤n≤1 and rotational velocity 0≤α≤5. Flow transitions are observed from steady to unsteady at critical values of the Reynolds number, the rotational velocity, and the power-law index. Critical values of the Reynolds number Rec have been obtained for varying levels of the rotational velocity, and the power-law index. Rec varies nonmonotonically with the rotational velocity. At a particular Reynolds number, an increase of the rotational velocity acts as a vortex suppression technique. For shear-thinning fluids considered here, the vortex suppression occurs at a larger value of the critical rotational velocity αc, relative to Newtonian fluids. For the unsteady flow, the lift coefficient versus time curve exhibits oscillatory behavior, and this has been used to delineate the flow regime as steady or unsteady flow. For unsteady flow regimes, both the amplitude of the lift coefficient and the Strouhal number increase with increasing Reynolds numbers. The results presented in this work for such high Reynolds numbers elucidate the possible complex interplay between the kinematic and rheological parameters of non-Newtonian fluids. This investigation also complements the currently available low Reynolds number results up to ∼ Re=140.

The effect of pulsating laminar flow of a Bingham plastic fluid on heat transfer from a constant temperature cylinder is studied numerically over wide ranges of conditions as Reynolds number (0.1 ≤ Re ≤ 40) and Bingham number (0.01 ≤ Bn ≤ 50) based on the mean velocity, Prandtl number (10 ≤ Pr ≤ 100), pulsation frequency (0 ≤ ω* ≤ π), and amplitude (0 ≤ A ≤ 0.8). Results are visualized in terms of instantaneous streamlines, isotherms, and apparent yield surfaces at different instants of time during a pulsation cycle. The overall behavior is discussed in terms of the instantaneous and time-averaged values of the drag coefficient and Nusselt number. The size of the yielded zone is nearly in phase with the pulsating velocity, whereas the phase shift has been observed in both drag coefficient and Nusselt number. The maximum augmentation (∼30%) in Nusselt number occurs at Bn = 1, Re = 40, Pr = 100, ω* = π, and A = 0.8 with respect to that for uniform flow. However, the increasing yield stress tends to suppress the potential for heat transfer enhancement. Conversely, this technique of process intensification is best suited for Newtonian fluids in the limit of Bn → 0. Finally, a simple expression consolidates the numerical values of the time-averaged Nusselt number as a function of the pertinent dimensionless parameters, which is consistent with the widely accepted scaling of the Nusselt number with ∼Pe1/3 under these conditions.

This work aims to explore the T-channel momentum and heat transfer characteristics with the combined effect of Bingham plastic fluids (0.01 ≤ Bn ≤ 20) behavior and geometrical variation in terms of branching angle (30 deg ≤ α ≤ 90 deg). The problem has been solved over a wide range of Reynolds number (50 ≤ Re ≤ 300) and Prandtl number (10 ≤ Pr ≤ 50). For the momentum flow, qualitative and quantitative features are analyzed in terms of streamlines, structure of yielded/unyielded regions, shear rate contours, plug width and length variation, and local pressure coefficient. These features have been represented in terms of isotherm patterns, temperature profile, Nusselt number, and its asymptotic value for heat transfer characteristics. The recirculating flows have been presented here in the vicinity of T-junction, which promote mixing and heat transfer. Broadly, the size of this zone bears a positive dependence on Re and α. However, fluid yield stress tends to suppress it. The critical Reynolds and Bingham numbers were found to be strong functions of the pertinent parameters like α. The inclination angle exerts only a weak effect on the yielded/unyielded regions and on the recirculation length of main branch. Results show a strong relationship of the plug width and length with key parameters and branches. The Nusselt number exhibits a positive relationship with α, Bn, and Re but for lower Pr in the T-junction vicinity for both branches. Such length indicates the required optimum channel length for thermal mixing.

In this work, thermal mixing of shear-thinning (i.e. CMC solutions) and Newtonian fluids has been numerically investigated in a rectangular T-channel for a specified heat flux boundary condition at the mixing zone walls. The influence of the Reynolds number (10 ≤ Re ≤ 50), power-law index (0.6161 ≤ n ≤ 1), Nusselt number (a dimensionless form of convective heat transfer coefficient for external air flow, 103 ≤ Nuo ≤ 104), and ambient temperature (−2.7 ≤ θa ≤ 1.3) is studied on the mixing behaviour. The flow is assumed to be steady, laminar, and incompressible. The new results are presented in terms of isotherm contours, mixing index, and required channel length to achieve complete mixing. The mixing index decreases along channel length for both shear-thinning and Newtonian fluids. Better mixing is seen at high power-law index, ambient temperature, and Nusselt number and low Reynolds numbers. The length required to achieve the 95% of the ambient temperature or the exact ambient temperature is shorter for mildly shear-thinning fluids (high power-law index) and Nusselt number, and low Reynolds numbers. Also, for the case of heating (high ambient temperature), the complete mixing demands a shorter channel length than that in the case of cooling.

The devolatilization of polymeric systems entails the expansion of bubbles by molecular diffusion of the solvent. Boiling of non-Newtonian polymer solutions and suspensions involves the nucleation and growth/collapse of bubbles. The mass, momentum, and energy transport in the context of bubble phenomena in stagnant and/or moving liquids which exhibit complex rheological behavior is central to the understanding of the various applications. The shape of a bubble not only influences its free-rise velocity but also plays an important role in determining the rates of heat and mass transfer and coalescence. In Newtonian fluids, small bubbles are known to display solid-sphere-like behavior and the transition from a no-slip to a zero-shear condition is fairly gradual. In applications involving relative motion between gas bubbles and a stagnant/moving liquid, the residence time of the gas is a key parameter which, in turn, depends on the free-rise velocity and the height of the equipment or liquid column.

In this study, the combined influence of fluid viscoelasticity and inertia on the flow and heat transfer characteristics of a circular cylinder in the steady laminar flow regime have been studied numerically. The momentum and energy equations together with an appropriate viscoelastic constitutive equation have been solved numerically using the finite volume method over the following ranges of conditions: Reynolds number, 0.1≤Re≤20; elasticity number (= Wi/Re, where Wi is the Weissenberg number), 0≤El≤0.5; Prandtl number, 10≤Pr≤100 for Oldroyd-B and finitely extensible nonlinear elastic-Peterlin (FENE-P) (with two values of the chain extensibility parameter L2, namely 10 and 100) viscoelastic fluid models including the limiting case of Newtonian fluids (El = 0). New extensive results are presented and discussed in terms of the streamline and isotherm profiles, drag coefficient, distribution of the local and surface averaged Nusselt number. Within the range of conditions embraced here, the separation of boundary layers (momentum and thermal) is seen to be completely suppressed in an Oldroyd-B fluid whereas it is accelerated for a FENE-P fluid in comparison with that seen for a Newtonian fluid otherwise under identical conditions. At a fixed elasticity number, both the drag coefficient and average Nusselt number are seen to be independent of the Reynolds number beyond a critical value for an Oldroyd-B fluid. In contrast, the drag coefficient decreases and the average Nusselt number increases with Reynolds number for a FENE-P fluid at a constant value of the elasticity number. Finally, a simple correlation for the average Nusselt number for a FENE-P fluid is presented which facilitates the interpolation of the present results for the intermediate values of the governing parameters and/or its a priori estimation in a new application.

In this work, the effect of geometry and orientation of food cans on the heating characteristics of processed liquid foods and the resulting lethality target values as a function of the processing times have been investigated. For this purpose, the governing differential equations have been solved numerically for elliptical and cylindrical cans of varying aspect ratios in different orientations in order to delineate their effect on the heating rate (especially of the slowest heating zone [SHZ]) and lethality values over wide ranges of rheological features including shear thinning (n < 1), Newtonian (n = 1), and shear thickening (n > 1) behaviors. The flow and heat transfer characteristics were analyzed with the help of velocity vectors, isotherm contours, average Nusselt number, SHZ temperature and heat penetration parameters, and lethality target values. Also, comparisons were made in terms of the sterilization time and heat penetration parameters to identify the preferable geometries and orientations of food cans for effective heating of non-Newtonian foodstuffs. Finally, favorable conditions in terms of the shape and orientation of the can and the rheological properties have been delineated which lead to superior heating characteristics. Practical Applications Processed foodstuffs are produced in various forms ranging from that in solid, liquid, or as heterogeneous mixtures. Often such liquid and heterogeneous suspensions products are viscous non-Newtonian in character and their thermal processing (including pasteurization, sterilization, etc.) tends to be much more challenging than that of their Newtonian counterparts like air and water. This work explores heating of non-Newtonian liquid foodstuffs in cans of various shapes, geometries and in different orientations in the free convection regime. The results show that depending upon the rheological properties of the products, some orientations and/or geometries offer potential advantages in terms of shorter processing times and lethality values. This information can be of great potential in customizing the design of containers for different food products as well as of different rheological properties.

Laminar free convection in power-law fluids in a triangular duct is studied numerically to delineate the effects of the height-to-base ratio of the enclosure (0.2 to 2), power-law index (0....

I Effective Science Communication: A Practical Guide to Surviving as a Scientist, i by Sam Illingworth and Grant Allen, aims to help researchers do just that Researchers also need to communicate their findings to the public at large, as evidenced by the COVID-19 pandemic and the global spotlight it has brought to epidemiology and vaccine science Effective Science Communication: A Practical Guide to Surviving as a Scientist, Sam Illingworth and Grant Allen, IOP, 2020 (2nd ed ), $50 00 Even the most groundbreaking scientific research is of little use if it can't be communicated to the broader scientific community, and to the general public, in a cogent and timely manner [Extracted from the article] Copyright of Physics Today is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission However, users may print, download, or email articles for individual use This abstract may be abridged No warranty is given about the accuracy of the copy Users should refer to the original published version of the material for the full abstract (Copyright applies to all Abstracts )

The primary goal of the present study is to investigate the flow reversal in the side branch of a T-channel for the flow of power-law fluids. The governing equations have been solved over wide ranges of conditions as: channel Reynolds number, 20 ≤ Re ≤ 100, Prandtl number, 1 ≤ Pr ≤ 100, Richardson number, 0 ≤ Ri ≤ 10, power-law index, 0.2 ≤ n ≤ 1.4, together with the conditions of equal exit pressure (EEP) and specified flow split (SFS). The flow reversal occurs in the side branch of the T-channel at a critical value of the Richardson number for the equal exit pressure condition, and this can be eliminated by using the specified flow rates as 10 ≤ βMB (%) ≤ 99 where, βMB is the value of the specific flow rate at the main branch outlet for a particular case. The results are interpreted in terms of velocity and temperature fields, exit flow rates, the required pressure to maintain the specific flow rate, recirculation lengths and the local Nusselt number. As the power-law index and/or Reynolds number is increased, the flow reversal is encountered at lower Richardson and Prandtl numbers. The flow rate from the main branch increases with Re, n, Ri while it decreases with Pr. Furthermore, the required pressure to maintain the flow rate shows a positive dependence on n, Ri and Pr whereas it shows an inverse dependence on Re and specified flow rates (βMB). Also, the rate of heat transfer rises with an increase in Re, Ri, Pr and β while it is promoted in shear-thinning fluids and impeded in shear-thickening fluids. Furthermore, the present work also compares the critical value of Richardson number of the 2-D model with that of the 3-D model for aspect ratio as 0.5 ≤ AR ≤ 10. The results show that for AR ≥ 5, the three-dimensional effects are small. Qualitative trends of the critical Richardson number e.g., with respect to Prandtl number obtained from the 3-D model are the same as from the 2-D model irrespective of the values of the aspect ratio.

An extensive numerical investigation of the flow and heat transfer phenomena of a solid sphere translating in a cylindrical tube filled with FENE-P viscoelastic fluids is reported herein. The governing equations, namely, mass, momentum, energy, and viscoelastic constitutive equations, have been solved over the following ranges of conditions: Reynolds number, 1 ≤ R e ≤ 100 , Weissenberg number, 0 ≤ W i ≤ 10 , polymer extensibility parameter, 10 ≤ L 2 ≤ 500 and blockage ratio, 0 ≤ B R ≤ 0.7 for a fixed value of the polymer viscosity ratio β = 0.5 and Prandtl number Pr = 10. Limited simulations with the FENE-CR viscoelastic fluid model have also been carried out to make a comparison between the two viscoelastic models. At low Reynolds numbers, the velocity overshoot and/or negative wake downstream the sphere has been observed under appropriate conditions. This tendency of their appearing decreases with the increasing Reynolds number, and decreasing blockage ratio, polymer extensibility parameter and Weissenberg number. The size of the recirculation region (wake length) increases with the Weissenberg number at low values of the polymer extensibility parameter, whereas a reverse trend is seen at high values of L2. The drag coefficient decreases with the Reynolds and Weissenberg numbers, whereas it increases with the blockage ratio. On the other hand, the average Nusselt number always increases with the Reynolds number irrespective of the values of Wi, L2 and BR. However, the corresponding effect of the blockage ratio and polymer extensibility parameter is seen to be more complex, modulated by the values of Re and Wi. For instance, at high Reynolds numbers, the average Nusselt number always increases with the blockage ratio; however, at low values of it, there is a critical value of the blockage ratio present up to which the average Nusselt number increases, and beyond that, it decreases. Furthermore, the average Nusselt number always initially increases up to a certain value of the Weissenberg number, and after that, it remains almost constant or decreases depending upon the values of L2, BR and Re. Finally, simple correlations for the average Nusselt number and drag ratio are presented, which not only capture the functional dependence of the governing parameters, but also can be used for the interpolation of the present results for the intermediate values of the governing parameters in a new application.

The Poiseuille flow of power-law fluids past a heated sphere in a tapered tube is studied over the following ranges: Blockage ratio, BR (0.1 to 0.5), Separation ratio, SR (0.1 to 0.7), taper angle, α (1o to 20o), Reynolds number, Re (1 to 100), Prandtl number, Pr (10 to 100), and the power law index, n (0.2 to 1). The hydrodynamic force exerted on the sphere is expressed using the total drag coefficient and its pressure component. Both exhibit the expected inverse dependence on Re while it bears a positive dependence on n, SR and BR. The normalized drag for a confined sphere also exhibits a complex functional relationship with each of these parameters. The normalized drag is significantly influenced by the taper angle. In general, SR, BR and α delay the boundary layer separation and hence, stabilize the flow. Similarly, the heat transfer characteristics are described in terms of isotherms, local and surface average Nusselt number. The Nusselt number shows a positive relationship both with SR and BR. The taper angle exerts only a weak effect on the Nusselt number. The heat transfer coefficient is augmented up to 59% in shear-thinning fluids above that in a Newtonian fluid.

Forced convection heat transfer has been investigated numerically for a pair of identical circular cylinders in side-by-side and in tandem arrangements confined in an adiabatic square enclosure filled with a power-law fluid with single inlet and outlet ports. The governing equations for the laminar, steady, 2-D and incompressible flow have been solved using a finite-element based method, COMSOL Multiphysics (Version 4.3a) for the following ranges of parameters: 5 ≤ Re ≤ 200; 0.7 ≤ Pr ≤ 100, 0.2 ≤ n ≤ 2 and 0.1 ≤ D/L ≤ 0.3. The numerical results obtained in terms of the velocity and temperature fields have been interpreted using streamlines, isotherm contours, plots of the individual and the total drag coefficients and the local and average Nusselt number. Further insights are developed with the help of velocity vectors and shear-rate contours prevailing in the flow domain, especially adjacent to the two cylinders. Owing to the symmetry, the two cylinders in side-by-side arrangement show identical momentum and heat transfer characteristics. The corresponding values for the upstream and downstream cylinders in the tandem arrangement differ from each other depending upon the values of the Reynolds and Prandtl numbers, power-law index and the diameter of the cylinders. In both cases, an increase in heat transfer is obtained at high values of the Reynolds and Prandtl number in shear-thinning fluids. Moreover, the upstream cylinder exhibits a higher drag and heat transfer as compared to the downstream cylinder. The non-linearity in the definitions of Reynolds and Prandtl numbers due to the occurrence of the power-law index leads to non-monotonic trends in the results. The flow and heat transfer phenomena are strongly influenced by the formation of secondary flows, reverse flow and the varying level of fluid acceleration due to the space constriction in the flow domain. Thus, the overall values of the pressure drop and Nusselt number are determined by a complex interplay between the kinematic conditions, fluid properties and geometric details of the system.

Laminar natural convection has been numerically investigated from two differentially heated horizontal cylinders in a square enclosure filled with power-law fluids. Two basic configurations, namely...

Laminar natural convection in Bingham plastic fluids has been investigated from two differentially heated cylinders arranged either one above the other or along the diagonal of the square enclosure. The coupled momentum and energy equations have been solved to elucidate the effect of Rayleigh number (104–106), Prandtl number (10–100), Bingham number (0.01 to Bnmax), and the gap between the two cylinders in terms of the geometric parameters (0 to −0.25 for vertical alignment and 0.15 to 0.35 for diagonal alignment) on the detailed structure of the flow field and the overall heat transfer characteristics of the system. New extensive results are visualized in terms of streamlines, isotherm contours, and variation of the local Nusselt number along various surfaces. Additional insights are developed by examining the shear-rate contours and the yield surfaces delineating the fluid-like and solid-like regions in the flow domain. At high values of the Bingham number, the average Nusselt number reaches its asymptotic value corresponding to the conduction limit. The increasing Rayleigh number promotes fluid-like behavior which promotes heat transfer. The augmentation in heat transfer depends on the volume of fluid participating in the buoyancy-induced flow. For the vertical arrangement, the average Nusselt number (for the heated cylinder) decreases a little as these are moved slightly away from the center of the enclosure, followed by an increase as the two cylinders approach one of the sidewalls; this is so even in the conduction limit. In contrast, when the two cylinders are arranged along the diagonal, the Nusselt number progressively decreases as the gap between the two cylinders increases. Finally, predictive correlations have been developed for the average Nusselt number and the limiting Bingham number thereby enabling their estimation in a new application.

The flow past a solid sphere constitutes a primary domain in the field of fluid mechanics and has a fundamental importance in several industrially important processes. Thus, the present work endeavours to study the momentum and heat transfer characteristics from a confined sphere inside a cylindrical tube of a converging cross-section with a pressure-driven Poiseuille flow of power-law fluids (only for shear-thinning fluids), different kinematic parameters (Reynolds number, Prandtl number), and geometric parameters (separation ratio, blockage ratio, radius ratio, contraction length, etc.). To achieve this objective, a finite element based numerical approach has been employed to study the flow and thermal characteristics from an isothermal sphere. The numerical results reported herein span the following ranges of parameters: Reynolds number (1 ≤ Re ≤ 100), Prandtl number (1 ≤ Pr ≤ 100), power-law index (0.2 ≤ n ≤ 1), separation ratio (0.1 ≤ SR ≤ 0.7), and blockage ratio (0.4). It can be concluded that the hydrodynamic drag force acting on the sphere and the rate of heat transfer can be increased substantially as the sphere is located towards the exit of the tube, though the enhancement in the drag is much greater than that in heat transfer under otherwise identical conditions.

In this work, the combined influence of the power-law rheology and isothermal rotating cylinder has been investigated numerically on the flow and heat transfer characteristics in a T-channel. The cylinder placed at the T-junction imitates the functioning of a rotating valve which controls the flow rate and the enthalpy distribution of the exiting streams in two branches. The range of parameters considered in this work is as: Reynolds number, 1

In this study, laminar natural convection heat transfer to Bingham plastic fluids from two differentially heated isothermal cylinders confined in a square enclosure (with isothermal walls) has been investigated numerically. The governing partial differential equations have been solved over the ranges of the dimensionless parameters, namely, Rayleigh number, 102 to 106, Prandtl number, 10 to 100, and Bingham number, 0.01 to 100, for seven locations of inner cylinders as ±0.25, ±0.2, ±0.1 and 0. These values correspond to the range of Grashof number varying from 10 to 105. The detailed flow and temperature fields are visualized in terms of the streamlines and isotherm contours. Further insights are developed by examining the iso-shear rate contours and the yield surfaces delineating the fluid-like and solid-like regions. The corresponding heat transfer results are analyzed in terms of the distribution of the local Nusselt number along the cylinder surface together with its surface averaged value as ...

Laminar free convection heat transfer in power-law fluids from two side-by-side cylinders (one hot and one cold) confined in a square duct has been studied numerically in the two-dimensional flow regime. For a fixed value of the ratio of cylinder radius to size of the enclosure, the effect of geometrical placement of the cylinders is studied on the resulting velocity and temperature fields in the laminar free convection regime by considering six asymmetric locations of the two cylinders. In particular, extensive results reported herein span the range of conditions of Grashof number, 10 to 105; Prandtl number, 0.7 to 100, thereby yielding the range of the Rayleigh number as 7 to 107; power-law index, 0.3 to 1.8; and the relative positions (dimensionless) of the cylinders with respect to the centerline, –0.25 to 0.25. The heat transfer characteristics are analyzed in terms of the local Nusselt number along the surfaces of the two cylinders and the enclosure walls. Overall, the average Nusselt number shows a...

Combining comprehensive theoretical and empirical perspectives into a clearly organized text, Chemical Engineering Fluid Mechanics, Second Edition discusses the principal behavioral concepts of fluids and the basic methods of analysis for resolving a variety of engineering situations. Drawing on the author's 35 years of experience, the book covers real-world engineering problems and concerns of performance, equipment operation, sizing, and selection from the viewpoint of a process engineer. It supplies over 1500 end-of-chapter problems, examples, equations, literature references, illustrations, and tables to reinforce essential concepts.

This study explores the effect of Prandtl number on the laminar natural convection heat transfer to Newtonian fluids in a square enclosure consisting of one hot circular cylinder and one cold circular cylinder. The walls of the square enclosure are maintained isothermal and at the same temperature as the cold cylinder and the fluid medium. The governing partial differential equations have been solved numerically over the following ranges of conditions: Grashof number, 10 to 105; Prandtl number, 0.7 to 100 (or the range of Rayleigh numbers as 7 to 107); and relative positioning of the cylinders, −0.25 to 0.25. However, the ratio of the radius of the cylinder to the side of the enclosure is held fixed at 0.2. Extensive results on the streamline and isotherm contours, the local Nusselt number distribution, and the average Nusselt number are discussed to delineate the influence of Grashof and Prandtl numbers on them for a given location with respect to the horizontal center line. The surface-averaged Nusselt ...

Extensive results are presented on the laminar free convection heat transfer in power-law fluids from a heated hemisphere in two orientations, namely, its flat base oriented upward (inverted) or downward (upright). The coupled field equations have been numerically solved over wide ranges of conditions as follows: Grashof number (10≤Gr≤105), Prandtl number (0.72≤Pr≤100) and power-law index (0.3≤n≤1.5). Detailed flow and temperature fields are visualized in terms of the streamline and isotherm contours, respectively. At the next level, the results are analyzed in terms of the total drag coefficient and local Nusselt number variation along the surface of the hemisphere, together with its surface averaged value. The average Nusselt number increases with both the Grashof and Prandtl numbers. Furthermore, for fixed values of the Grashof and Prandtl numbers, and for a given orientation, shear-thinning behavior (n 1) impedes it with reference to th...

Extensive experimental results conducted in a 10-m flume for various types of non-Newtonian fluids spanning a range of cross-sectional open channel shapes are presented and analysed in depth in this work. Open channel flow of non-Newtonian slurries is relevant in mining and chemical engineering applications. This database coupled with the literature data is used to develop the generalised friction factor–Reynolds number correlations in a unified fashion. Much confusion still exists in the literature regarding the definition of non-Newtonian Reynolds numbers. This difficulty is circumvented by considering two widely accepted definitions of the Reynolds number, namely due to Haldenwang et al. (Hydrotransport 15: 15th international conference on the hydraulic transport of solids in pipes, Banff, pp 755–768, 2002) for open channel flow and the modified Metzner–Reed pipe flow Reynolds number adapted for open channel flow. Three different types of purely viscous non-Newtonian fluids in rectangular, trapezoidal, triangular and semi-circular channel shapes were tested. The modelling procedure of Garcia et al. (Int J Multiph Flow 29:1605–1624, 2003) used for pipe flow predictions was extended to the present work. The logistic dose curves based on the Reynolds number proposed by Haldenwang et al. [14] performed better than those based on the adapted Metzner–Reed Reynolds number. Correlations developed can be used for the design of open channels of various shapes to transport non-Newtonian fluids.