Momentum and heat transfer from a square cylinder in power-law fluids

Numerical solutions are sought, using FLUENT, to the mass, momentum and thermal energy equations for the 2-D flow of power-law fluids over a cylinder of square cross-section. The major thrust of this work is to delineate the values of the Reynolds number denoting the onset of flow separation and the limits of the steady flow regime for both shear-thinning and shear-thickening type fluids. Extensive results are reported on streamline and vorticity contours over wide ranges of power-law index (0.2–1.4) corroborating the occurrence of these two transitions. Having established the limits of the steady flow regime, drag and Nusselt number results are obtained in this regime as functions of the Reynolds number (0.1–40), of Prandtl number (0.7–100) for highly shear-thinning fluids (power-law index < 0.5) thereby extending the range of currently available results to that encountered in practical applications. The Nusselt number shows positive dependence on both the Reynolds and Prandtl numbers. Also, shear-thinning characteristics can augment the rate of heat transfer by up to 100% under appropriate conditions.     

Effect of power-law fluid behavior on momentum and heat transfer characteristics of an inclined square cylinder in steady flow regime

The governing equations describing the momentum and heat transfer phenomena of power-law non-Newtonian fluids over a heated square cylinder at 45° of incidence in the two-dimensional (2-D) steady flow regime are solved numerically. Extensive results on the detailed structure of the flow and temperature fields as well as on the gross engineering parameters are presented over the following ranges of conditions: 0.2 ? n ? 1; 0.1 ? Re ? 40 and 0.7 ? Pr ? 100. At low Reynolds numbers, the flow remains attached to the surface of the cylinder. This seems to occur for all values of power-law index, at least up to about Re = 1. On the other hand, twin standing vortices were seen to form at Re = 10 for all values of power-law index considered herein. The influence of the Reynolds number and power-law index is delineated on the detailed structure of the flow field (streamlines), wake characteristics and surface pressure distribution as well as on the value of drag coefficients. Similarly, the effect of Prandtl number is studied on forced convective heat transfer for the two commonly encountered boundary conditions, namely, constant temperature or constant heat flux prescribed on the surface of the cylinder. Using the computed numerical results, simple heat transfer correlations are obtained in terms of the Nusselt number as a function of the pertinent governing parameters thereby enabling the prediction of the rate of heat transfer between the fluid and the immersed cylinder. In addition, variation of the local Nusselt number on the surface of the inclined of square cylinder and representative isotherm plots are also presented to elucidate the effect of Reynolds number, Prandtl number and power-law index on the heat transfer phenomenon.     

Laminar free convection from a horizontal semi-circular cylinder to power-law fluids

Extensive numerical results on the flow and thermal fields are presented for free convection from a semi-circular cylinder (flat base upward) immersed in quiescent power-law fluids for the following ranges of conditions: Grashof number, 10 ? Gr ? 10⁵, Prandtl number, 0.72 ? Pr ? 100, and power-law index, 0.2 ? n ? 1.8. The heat transfer characteristics are analyzed in terms of the isotherm patterns, local and average Nusselt number as functions of the pertinent dimensionless parameters. The flow field is visualized in terms of the streamline patterns adjacent to the surface of the cylinder for a range of values of the Grashof number, Prandtl number and power-law index. A separated flow region forms at as low values of the Prandtl number as Pr = 0.72 for n ? 1 (Newtonian and shear-thickening fluids); whereas for shear-thinning fluids (n < 1), the flow remains attached to the cylinder surface over the range of conditions encompassed here. The bubble size grows with Grashof number and it shrinks with Prandtl number. In order to quantify the deviation from the Newtonian behaviour, the normalized values of average Nusselt number are analyzed as a function of the power-law index. In addition, a correlation is proposed for average Nusselt number as a function of the Grashof number, Prandtl number and power-law index. In general terms, shear-thinning fluid behaviour enhances heat transfer whereas shear-thickening has adverse influence on it.     

Two-dimensional unsteady forced convection heat transfer in power-law fluids from a cylinder

Forced convection heat transfer characteristics of a cylinder (maintained at a constant temperature) immersed in a streaming power-law fluids have been studied numerically in the two-dimensional (2-D), unsteady flow regime. The governing equations, namely, continuity, momentum and thermal energy, have been solved using a finite volume method based solver (FLUENT 6.3) over wide ranges of conditions (power law index, 0.4 ? n ? 1.8; Reynolds number, 40 ? Re ? 140; Prandtl number, 1 ? Pr ? 100). In particular, extensive numerical results elucidating the influence of Reynolds number, Prandtl number and power-law index on the isotherm patterns, local and average Nusselt numbers and their evolution with time are discussed in detail. Over the ranges of conditions considered herein, the nature of flow is fully periodic in time. The heat transfer characteristics are seen to be influenced in an intricate manner by the value of the Reynolds number (Re), Prandtl number (Pr) and the power-law index (n). Depending upon the value of the power-law index (n), though the flow transits from being steady to unsteady somewhere in the range ～33 < Re < 50, the fully periodic behavior is seen only beyond the critical value of the Reynolds number (Re). As expected, the average Nusselt number increases with an increase in the values of Reynolds and/or Prandtl numbers, irrespective of the value of the flow behavior index. A strong influence of the power-law index on both local and time-averaged Nusselt numbers was observed. Broadly, all else being equal, shear-thinning behavior (n < 1) promotes heat transfer whereas shear-thickening behavior (n > 1) impedes it. Furthermore, this effect is much more pronounced in shear-thinning fluids than that in shear-thickening fluids.     

Flow over and forced convection heat transfer in Newtonian fluids from a semi-circular cylinder

Momentum and heat transfer characteristics of a semi-circular cylinder immersed in unconfined flowing Newtonian fluids have been investigated numerically. The governing equations, namely, continuity, Navier–Stokes and energy, have been solved in the steady flow regime over wide ranges of the Reynolds number (0.01 ? Re ? 39.5) and Prandtl number (Pr ? 100). Prior to the investigation of drag and heat transfer phenomena, the critical values of the Reynolds number for wake formation (0.55 < Re^c < 0.6) and for the onset of vortex shedding (39.5 < Re_c < 40) have been identified. The corresponding values of the lift coefficient, drag coefficient, and Strouhal number are also presented. After establishing the limit of the steady flow regime, the influence of the Reynolds number (0.01 ? Re ? 39.5) and Prandtl number (Pr = 0.72, 1, 10, 50 and 100) on the global flow and heat transfer characteristics have been elucidated. Detailed kinematics of the flow is investigated in terms of the streamline and vorticity profiles and the variation of pressure coefficient in the vicinity of the cylinder. The functional dependence of the individual and total drag coefficients on the Reynolds number is explored. The Nusselt number shows an additional dependence on the Prandtl number. In addition, the isotherm profiles, local Nusselt number (Nu_L) and average Nusselt number (Nu) are also presented to analyze the heat transfer characteristic of a semi-circular cylinder in Newtonian media.     

Forced convection heat transfer from an elliptical cylinder to power-law fluids

Forced convection heat transfer to incompressible power-law fluids from a heated elliptical cylinder in the steady, laminar cross-flow regime has been studied numerically. In particular, the effects of the power-law index (0.2 ? n ? 1.8), Reynolds number (0.01 ? Re ? 40), Prandtl number (1 ? Pr ? 100) and the aspect ratio of the elliptic cylinder (0.2 ? E ? 5) on the average Nusselt number (Nu) have been studied. The average Nusselt number for an elliptic cylinder shows a dependence on the Reynolds and Prandtl numbers and power-law index, which is qualitatively similar to that for a circular cylinder. Thus, heat transfer is facilitated by the shear-thinning tendency of the fluid, while it is generally impeded in shear-thickening fluids. The average Nusselt number values have also been interpreted in terms of the usual Colburn heat transfer factor (j). The functional dependence of the average Nusselt number on the dimensionless parameters (Re, n, Pr, E) has been presented by empirically fitting the numerical results for their easy use in process design calculations.     

Flow and heat transfer across a confined square cylinder in the steady flow regime: Effect of Peclet number

The flow and heat transfer characteristics of an isolated square cylinder in crossflow placed symmetrically in a planar slit have been investigated for the range of conditions as 1 ⩽ Re ⩽ 45, 0.7 ⩽ Pr ⩽ 4000 (Pe ⩽ 4000) and β = 1/8, 1/6 and 1/4. Heat transfer correlations have been obtained in the steady flow regime for the constant temperature and constant heat flux boundary conditions on the solid square cylinder in crossflow. In addition, variation of the local Nusselt number on each face of the obstacle and representative isotherm plots are presented to elucidate the role of Prandtl number and blockage ratio on drag coefficient and heat transfer.     

Numerical prediction of flow and heat transfer of power-law fluids in a plane channel with a built-in heated square cylinder

Structure of unsteady laminar flow and heat transfer of power-law fluids in two-dimensional horizontal plane channel with a built-in heated square cylinder is studied numerically. The governing equations are solved using a control volume finite element method (CVFEM) adapted to the staggered grid. Computations are performed over a range of Reynolds and Richardson numbers from Re = 20 to 200 and from Ri = 0 to 8, respectively at fixed Prandtl number Pr = 50 and blockage ratio value β′ = 1/8. Three different values of the power-law index (n = 0.5, 1 and 1.4) are considered in this study to show its effect on the value of the critical Reynolds number defining the transition between two different flow regimes (symmetrical and periodic flows), the variations of Strouhal number, drag and lift coefficients and the heat transfer from the square cylinder as function of Reynolds number. Heat transfer correlations are obtained through forced convection. A discussion about the buoyancy effect on the flow pattern and the heat transfer for different power-law index is also presented.     

Steady forced convection heat transfer from a heated circular cylinder to power-law fluids

Forced convection heat transfer to incompressible power-law fluids from a heated circular cylinder in the steady cross-flow regime has been investigated numerically by solving the momentum and thermal energy equations using a finite volume method and the QUICK scheme on a non-uniform Cartesian grid. The dependence of the average Nusselt number on the Reynolds number (5 ⩽ Re ⩽ 40), power-law index (0.6 ⩽ n ⩽ 2) and Prandtl number (1 ⩽ Pr ⩽ 1000) has been studied in detail. The numerical results are used to develop simple correlations as functions of the pertinent dimensionless variables. In addition to the average Nusselt number, the effects of Re, Pr and n on the local Nusselt number distribution have also been studied to provide further physical insights. The role of the two types of thermal boundary conditions, namely, constant temperature and uniform heat flux on the surface of the cylinder has also been presented.     

Joule heating induced heat transfer for electroosmotic flow of power-law fluids in a microcapillary

Capillary electrophoresis systems mainly used for chemical analyses and biomedical diagnoses usually involve biofluids in electrolyte buffers which cannot be treated as Newtonian fluids. In addition, the presence of Joule heating can limit the performance of capillary electrophoresis systems. This study presents a detailed analysis of Joule heating induced heat transfer for electroosmotic flow (EOF) of power-law fluids in a microcapillary. The steady, fully developed EOF field of power-law fluids governed by the Cauchy momentum equation is solved analytically by using two approximate schemes for modified Bessel functions, I₀(x) and I₁(x). Subsequently, under the widely accepted assumption of thin electric double layer (EDL) in microfluidics, an exact solution for temperature field induced by Joule heating is analytically solved from the energy equation subject to a mixed thermal boundary condition outside the capillary. Closed form expressions are obtained for the two-dimensional temperature field, the average fluid temperature and the local Nusselt number in both thermally developing and thermally developed regions. It is found that the rheological properties of power-law fluids affect the heat transfer characteristics mainly through the thermal Peclet number.     

Momentum and heat transfer characteristics of a thin circular disk in Bingham plastic fluids

The laminar forced convection momentum and heat transfer aspects of a circular disk oriented normal to the flow and maintained at a constant flux or a constant temperature condition in a stream of a Bingham plastic fluid are studied over wide ranges of parameters as follows: Reynolds number, Re?≤?150; Prandtl number, 1 ≤Pr?≤?100; Bingham number, Bn?≤?100, and thickness-to-diameter ratio, 0.01?≤?(t/d)?≤?0.075. The new results on hydrodynamics are analyzed in terms of streamline plots, recirculation length, morphology of yielded/unyielded regions, and drag coefficient, and on heat transfer aspects in terms of isotherm contours, local and average Nusselt number. The flow domain is spanned by the simultaneous existence of the yielded and unyielded sub-regions, depending upon the relative strengths of the fluid inertia (Re) and yield stress (Bn). All else being equal, the rate of heat transfer is higher for an isothermal disk than that for the isoflux condition. Both the drag and average Nusselt number bear a positive dependence on the Bingham number. The drag is influenced only slightly (～5%) by thickness (t/d); however, the heat transfer can increase on this count by up to 15% under appropriate conditions. Finally, the present numerical results on drag and Nusselt number (in terms of j_H-factor) have been correlated via simple empirical equations using the modified definitions of the Reynolds (Re^*) and Prandtl number (Pr^*), thereby enabling a priori estimation of drag and heat transfer in a new application.     

Melting heat transfer characteristics of a horizontal ice cylinder immersed in an immiscible liquid

The melting characteristics of a horizontal ice cylinder immersed in an immiscible liquid were investigated both experimentally and analytically. A clear cylindrical ice layer formed around a horizontal cooling tube with a coaxial outer heated tube was melted in oil as the test immiscible liquid in the annulus between the ice and outer tube. Both the melting behavior of ice and the flow patterns of the immiscible liquid were observed under a variety of outer wall temperature conditions. In the analysis, two boundary layers were introduced for both the melt water film and ambient liquid, respectively. It was found from the experiments that the tendency of the mean Nusselt number changes clearly at Ra = 10⁶, which corresponds to the temperature condition T0 = 12.0 °C. This analysis might be used to estimate the melting characteristics of such a system during the initial stage of low temperature conditions. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(5): 336–352, 1998     

Melting heat transfer characteristics of a horizontal ice cylinder immersed in quiescent saline water

Experiments were performed to determine the effect of salinity level on the melting heat transfer characteristics of a horizontal ice cylinder immersed in quiescent saline water. Emphasis was placed on interpreting the heat transfer mechanism which dominates the solid-liquid interface situation. Measurements were carried out for saline water of 0.5–3.5 wt% in salinity, while the ambient temperature ranged from 1.8 to 24.0°C. Flow visualization was employed to investigate the transient flow patterns and corresponding solid-liquid interface locations. It was found that the flow patterns around the ice cylinder were a strong function of the saline water concentration, which then considerably affected the local heat transfer coefficient along the melting ice cylinder.     

Effect of temperature-dependent viscosity on forced convection heat transfer from a cylinder in crossflow of power-law fluids

The steady, two-dimensional and incompressible flow of power-law fluids across an unconfined isothermal heated circular cylinder is investigated numerically to ascertain the effect of temperature-dependent viscosity on the flow and forced convection heat transfer phenomena. Extensive numerical results elucidating the variation of the heat transfer characteristics and drag coefficient on the severity of temperature dependence of viscosity (0 ? b ? 0.5), power law index (0.6 ? n ? 1.6), Prandtl number (1 ? Pr ? 100) and Reynolds number (1 ? Re ? 30) are presented. The coupled momentum and energy equations are expressed in the stream function/vorticity formulation and solved using a second-order accurate finite difference method to determine the local and surface-averaged Nusselt numbers, the drag coefficient, and to map the flow domain in terms of the temperature and flow fields near the cylinder. The variation of viscosity with temperature is shown to have a substantial effect on both the local and surface-averaged values of the Nusselt number. As expected, the results also suggest that the rate of heat transfer shows positive dependence on the Reynolds number and Prandtl number. Furthermore, stronger the dependence of viscosity on the temperature, the greater is the enhancement in the rate of heat transfer. Finally, all else being equal, shear-thinning fluid behaviour facilitates heat transfer while the shear-thickening behaviour has deleterious effect on heat transfer.     

Momentum and heat transfer in a turbulent cylinder wake behind a streamwise oscillating cylinder

The work aims to understand the effect of an oscillating circular cylinder on momentum and heat transport in the turbulent wake of a downstream identical cylinder, which is slightly heated. The oscillating amplitude, A, was 0.79d (d is the cylinder diameter) and the frequency was 0.17f_s for L/d = 2.5 and 0.24f_s for L/d = 4, where L and f_s are the cylinder centre-to-centre spacing and the frequency of vortex shedding from the downstream cylinder, respectively, at A = 0. The velocity and temperature fields were measured using a three-wire probe at 10d behind the stationary cylinder and a Reynolds number of 5920 based on d and the free-stream velocity. It is found that the upstream cylinder oscillation modifies the frequency of vortex shedding from the stationary cylinder, which is locked on with one harmonic of the oscillating frequency. This harmonic frequency is nearest to and below the natural vortex-shedding frequency. Furthermore, the wake response to the oscillation depends on L/d in terms of the cross-stream distributions of mean velocity, Reynolds stresses, temperature variance and heat fluxes; the turbulent Prandtl number decreases at L/d = 4 but increases at L/d = 2.5. The observations are linked to whether the flow regime experiences a change under the upstream cylinder oscillation.     

Flow over and forced convection heat transfer around a semi-circular cylinder at incidence

Wake dynamics and forced convective heat transfer characteristics past a semi-circular cylinder at incidence have been investigated numerically. Utilizing air as an operating fluid computations are carried out for wide ranges of the Reynolds number (80 ? Re ? 180) and angle of incidences (0 ? α ? 180°). Angle of incidence reveals three flow separation zones. Structure properties of shear layer and vortex motions on each flow separation zones are analyzed critically. Functional dependence of drag (C_D), lift (C_L), and moment (C_M) coefficients on the angle of incidence is explored and analyzed in detail. Increase in angle of incidence increases streamline curvature. A structural similarity is observed between the contours of vorticity and the corresponding isotherms. Strouhal number shows a decreasing trend up to certain values of α and thereafter it increases marginally. A new correlation of Strouhal number as a function of Re and α has been established for the present range of Reynolds numbers. At the singularity points a sudden jump in local Nusselt number distribution is observed. The trend of variation of average Nusselt number with α is similar to that of Strouhal number variation. The average Nusselt number is found to vary as ${\mathit{Re}}^{0.529}(1+\alpha {)}^{-0.0476}$.     

滑移区气体-颗粒流动与传热特性研究

针对气体-颗粒微尺度流动与传热过程开展数值模拟研究,所构建模型中气体处理为可压缩、变物性流体,并在颗粒表面采用速度滑移和温度跳跃边界条件以考虑气体稀薄效应。在数值模拟基础上,研究分析稀薄效应对颗粒与其周围气体流动与换热的影响程度,并进一步提出新的阻力系数与传热努谢尔特数关联式。研究结果表明,气体稀薄效应将减小颗粒阻力系数,同时抑制颗粒与其周围气体的传热过程。