Effect of Thermal Buoyancy on Fluid Flow and Heat Transfer Across a Semicircular Cylinder in Cross-Flow at Low Reynolds Numbers

The influence of superimposed thermal buoyancy on hydrodynamic and thermal transport across a semicircular cylinder is investigated through numerical simulation. The cylinder is fixed in an unconfined medium and interacted with an incompressible and uniform incoming flow. Two different orientations of the cylinder are considered: one when the curved surface is exposed to the incoming flow and the other when the flat surface is facing the flow. The flow Reynolds number is varied from 50 to 150, keeping the Prandtl number fixed (Pr = 0.71). The effect of superimposed thermal buoyancy is brought about by varying the Richardson number in the range 0 ≤ Ri ≤ 2. The unsteady two-dimensional governing equations are solved by deploying a finite volume method based on the PISO (Pressure Implicit with Splitting of Operator) algorithm. The flow and heat transfer characteristics are analyzed with the streamline and isotherm patterns at various Reynolds and Richardson numbers. The dimensionless frequency of vortex shedding (Strouhal number), drag, lift and pressure coefficients, and Nusselt numbers are presented and discussed. Substantial differences in the global flow and heat transfer quantities are observed for the two different configurations of the obstacle chosen in the study. Additionally, intriguing effects of thermal buoyancy can be witnessed. It is established that heat transfer rate differs significantly under the superimposed thermal buoyancy condition for the two different orientations of the obstacle.     

Forced Convection Heat Transfer in Power-Law Fluids Around a Semicircular Cylinder at Incidence

Two-dimensional steady flow and convective heat transfer of power-law fluids past a semicircular cylinder are investigated in the reported work. The heated semicircular cylinder is placed in an unconfined domain at different angles facing the incoming free-stream flow of power-law fluids having a generalized Prandtl number (Pr) = 100. Particular emphasis is given to studying the effect of angle of incidence (0 ≤ α ≤ 180°) on fluid dynamics and thermal transport around the semicircular object for varying Reynolds number (10 ≤ Re ≤ 40) and power-law index (0.4 ≤ n ≤ 1.8). A finite volume-based method is adopted for the numerical computation. The flow and heat transfer phenomena are visualized through the streamline and isotherm profiles at various operating conditions. Also, the pressure coefficient, drag coefficient, and Nusselt number on the surface of the object are presented and discussed.     

Steady Mixed Convection in Power-Law Fluids from a Heated Triangular Cylinder

The steady mixed convective transport from a heated triangular cylinder immersed in power-law fluids in an unconfined vertical domain is investigated numerically. Two different configurations of the cylinder are chosen; one when the base of the cylinder is facing the flow and the other when the apex of the triangle is facing the flow. The simulation is performed for: Reynolds number (1 to 35), Richardson number (0 to 2), power law index (0.4 to 1.8) and Prandtl number, 50. The flow and thermal fields are visualized through the streamlines and isotherm contours at the close proximity of the heated object for various Reynolds numbers, Richardson numbers and power law indices. The distributions of the surface pressure coefficient and local Nusselt number provide further insight of the hydrodynamic and thermal characteristics. Finally, the total drag coefficient and average Nusselt numbers on the surface of the cylinder are computed to explore the overall macroscopic behavior of the involved thermo-hydrodynamics. The flow separation is observed to be more when the apex of the cylinder is facing the flow. The average heat transfer, measured in terms of the Nusselt number, and the total drag on the cylinder are also found higher for that configuration.     

Jet impingement cooling and optimization study for a partly curved isothermal surface with CuO-water nanofluid

Numerical and optimization study of jet impingement cooling of a partly curved surface with CuO-water nanofluid was performed with Galerkin weighted residual finite element method and COBYLA (constrained optimization by linear approximation) optimization algorithm. Target surface was partly curved which has a semi-elliptic shape and kept at constant hot temperature. Simulations were performed for various values of Reynolds number and solid particle volume fraction. It was observed that effects of curved wall on the distribution of fluid flow and heat transfer characteristics are more pronounced for higher values of Reynolds number as compared to a flat wall configuration. Highest heat transfer is obtained with curved wall and significant differences are observed between the peak values of Nusselt number between a flat wall and curved wall case. The average Nusselt number is a linear increasing function of nanoparticle volume fraction and the trends in local and average heat transfer are similar for curved wall and flat wall configurations when nanoparticles are added. Average Nusselt number enhances by about 20% at the highest particle volume fraction as compared to water. A polynomial type correlation for the average Nusselt number was derived which depends on the Reynolds number and solid particle volume fraction for both configurations.     

Momentum and Heat Transfer Characteristics for the Flow of Power-Law Fluids over a Semicircular Cylinder

In this study, the two-dimensional steady flow of power-law fluids past a semicircular cylinder (flat face oriented upstream) has been investigated numerically. The governing equations (continuity, momentum, and energy) have been solved in the steady symmetric flow regime over the range of the Reynolds number (0.01 ≤ Re ≤ 25), power-law index (0.2 ≤ n ≤ 1.8), and Prandtl number (0.72 ≤ Pr ≤ 100). Extensive new results reported here endeavor to elucidate the role of power-law index (0.2 ≤ n ≤ 1.8) on the critical Reynolds number denoting the onset of flow separation (Re ^c ) and of vortex shedding (Re _c ). In shear-thinning fluids, both of these transitions are seen to be delayed than that in Newtonian and shear-thickening fluids. Furthermore, the influence of the Reynolds and Prandtl numbers, power-law index on drag phenomenon, and heat characteristics of semicircular cylinder have been studied in the steady flow regime. Finally, the present numerical values of the critical Reynolds numbers and the average Nusselt number have been correlated by simple forms which are convenient for interpolating these results for the intermediate values of the governing parameters in a new application.     

The Effects of Reynolds and Prandtl Numbers on Flow and Heat Transfer Across Tandem Square Cylinders in the Steady Flow Regime

The effects of Reynolds and Prandtl numbers on the fluid flow and heat transfer characteristics over two equal isothermal square cylinders placed in a tandem arrangement in cross flow have been investigated in this article. The spacing between the cylinders is fixed with four widths of the cylinder. The numerical results are presented for the range of conditions as 1 ≤ Re ≤ 30 and 0.7 ≤ Pr ≤ 1000 for three different blockage parameters B = 0.05, 0.25, and 0.5. Numerical simulations are performed with a finite volume code based on the PISO algorithm in a collocated grid system. The representative streamlines and isotherm patterns are presented and discussed. In addition, the overall drag coefficient and average Nusselt number are determined to elucidate the role of Reynolds and Prandtl numbers on flow and heat transfer. It is found that the flow is completely steady for the chosen ranges of the parameters.     

The Effect of Aiding/Opposing Buoyancy on Two-Dimensional Laminar Flow Across a Circular Cylinder

The effect of thermal buoyancy on the upward flow and heat transfer characteristics around a heated/cooled circular cylinder is studied. A two-dimensional finite-volume model is deployed for the analysis. The influence of aiding/opposing buoyancy is studied for the range of parameters ?0.5 ≤ Ri ≤ 0.5, 50 ≤ Re ≤ 150, and the blockage ratios of B = 0.02 and 0.25. The flow shows unsteady periodic nature in the chosen range of Reynolds numbers for the forced convective cases (Ri = 0), and the vortex shedding stops completely at some critical values of Richardson numbers.     

The Effect of a Blockage on Forced Convection Heat Transfer From a Heated Square Cylinder to Power-Law Fluids

Forced convection heat transfer characteristics of a long, heated square cylinder blocking the flow of a power-law fluid in a channel is numerically investigated in this study. In particular, the role of the power-law index n, Reynolds number Re, Prandtl number Pr, and blockage ratio β(=B/H) on the rate of heat transfer from a square cylinder in a channel has been studied over the following ranges of conditions: 0.5 ≤ n ≤ 1.8, 60 ≤ Re ≤ 160, β = 1/4, 1/2, and 0.7 ≤ Pr ≤ 50. A semi-explicit finite-volume method is used on a nonuniform collocated grid arrangement. The third-order QUICK and the second-order central difference schemes are used to discretize the convective and diffusive terms, respectively, in the momentum and energy equations. Irrespective of the type of behavior of fluid (different values of n), the average Nusselt number increases as the blockage ratio increases. Similar to the unconfined flow configuration, the average Nusselt number increases monotonically with Reynolds and Prandtl numbers for both values of the blockage ratio and for all values of power-law index considered here. Further insights into the heat transfer phenomenon are provided by presenting isotherm contours in the vicinity of the cylinder for a range of values of the Reynolds number, Prandtl number, and power-law index for the two values of β considered in this work.     

Laminar Flow and Heat Transfer Phenomena Across a Confined Semicircular Bluff Body at Low Reynolds Numbers

The present study is concerned with the simulation of incompressible Newtonian fluid flow and heat transfer over a long semicircular bluff body in a channel at low Reynolds numbers. In particular, wall effects on the forced convection from a (heated) semicircular cylinder confined in a horizontal channel are investigated for Reynolds number = 1–40 and blockage ratio = 16.67–50% for air as the working fluid. Flow and thermal fields are found steady for the preceding range of settings. The onset of flow separation increases as the wall confinement increases. The size of the recirculation zone downstream of a semicircular cylinder is seen to increase almost linearly with Reynolds number for a fixed blockage ratio, but it decreases with increasing blockage ratio for a fixed Reynolds number. As expected, total drag coefficient and its components decrease with increasing value of Reynolds number. However, with increasing blockage ratio, the values of these drag coefficients increase. On the basis of equal projected area, the total drag coefficient for the present flow system is found to be greater than the corresponding drag in the case of the unconfined semicircular cylinder. Similarly, the overall drag in the case of a confined semicircular cylinder is found to be greater than that of a confined circular cylinder for the appropriate range of dimensionless control parameters. The maximum augmentation in heat transfer for blockage ratios of 25% and 50% is found to be approximately 16% and 51% with respect to the corresponding value at the blockage ratio of 16.67% at Reynolds number = 1. Finally, the correlations of wake length, drag coefficient, and average Nusselt number are obtained.     

HEAT AND FLUID FLOW ACROSS A SQUARE CYLINDER IN THE TWO-DIMENSIONAL LAMINAR FLOW REGIME

The flow structure and heat transfer characteristics of an isolated square cylinder in cross flow are investigated numerically for both steady and unsteady periodic laminar flow in the two-dimensional regime, for Reynolds numbers of 1 to 160 and a Prandtl number of 0.7. The effect of vortex shedding on the isotherm patterns and heat transfer from the cylinder is discussed. Heat transfer correlations between Nusselt number and Reynolds number are presented for uniform heat flux and constant cylinder temperature boundary conditions.     

Heat Transfer to Power-Law Fluids from a Heated Square Cylinder

Forced-convection heat transfer to power-law fluids from a heated square cylinder has been investigated numerically for the range of conditions 1 ≤ Re ≤ 45, 0.5 ≤ n ≤ 2.0 and 1 ≤ Pr ≤ 100 (the maximum Peclet number being 4,000). In this range of Reynolds number, the flow is known to be steady and two-dimensional. The variation of the local Nusselt number on the individual surfaces of the square cylinder and the representative isotherm plots, for both the constant-temperature and uniform-heat-flux boundary conditions prescribed on the surface of the square obstacle, are presented to elucidate the role of Reynolds number, Prandtl number, and power-law index on the heat transfer characteristics. Using the present numerical data, appropriate predictive correlations are obtained for estimating the value of the mean heat transfer coefficient in a new application.     

3D Numerical study on the flow topology and heat transfer characteristics of turbulent forced convection in spirally corrugated tube

ABSTRACT

This paper presents a numerical analysis on flow configurations and heat transfer characteristics of turbulent forced convection in spirally corrugated tubes. The influences of corrugation depth (DR = 0.02–0.16), pitch ratio (PR = 0.10–1.00), and Reynolds number (Re = 5,000–20,000) on flow structure and heat transfer characteristics are described. Comparisons between the full length and periodic domains are also reported. The results show that spirally corrugated tubes induced vortex flows which helped to increase heat transfer due to enhanced fluid mixing. The maximum thermal enhancement factor of 1.16 was obtained by using the spirally corrugated tube with DR = 0.06, PR = 0.25 at Re = 5,000.     

Flow and Heat Transfer Phenomena Across Two Confined Tandem Heated Triangular Bluff Bodies

Confined flow and heat transfer phenomena across two long triangular bars in tandem arrangement in a horizontal channel have been studied for the range of Reynolds number (Re) = 1–40, Prandtl number (Pr) = 0.71–50 and gap ratio (S/B) = 1–4 for a fixed blockage ratio of 25%. The average Nusselt number of the first triangular cylinder is found to be larger than the corresponding value for the second triangular cylinder in the tandem configuration. Heat transfer correlations in terms of the Colburn j_h factor have been established in the steady regime.     

Heat Transfer and Pressure Drop Characteristics of Nanofluid Flows Inside Corrugated Tubes

An experimental investigation is carried out to study the heat transfer and pressure drop characteristics of multiwalled carbon nanotubes (MWCNTs)/heat transfer oil nanofluid flows inside horizontal corrugated tubes under uniform wall temperature condition. To provide the applied nanafluids, MWCNTs are dispersed in heat transfer oil with mass concentrations of 0.05, 0.1, and 0.2 wt%. The Reynolds number varies between 100 and 4,000. Three tubes with hydraulic diameters of 11.9, 13.2, and 15.5 mm are applied as the test section in the experimental setup. Tubes are corrugated four times on the cross section; that is, there are four different helices around the tube. Depths of the corrugations are chosen as 0.9, 1.1, and 1.3 mm, and pitch of corrugation is 14 mm. The acquired data confirm the increase of heat transfer rate as a result of utilizing nanofluids in comparison with the base fluid flow. However, corrugating the tubes decreases the heat transfer rate at low Reynolds numbers. The highest increase in heat transfer rate is observed for the Reynolds numbers for which the smooth tube is in the transition regime and the corrugated tube reaches the turbulent flow, that is, Reynolds number in the range of 1,000 to 3,000. Rough correlations are proposed to predict the Nusselt number and friction factor.     

Mixed Convection Heat Transfer from an In-Line Row of Square Cylinders in Cross-Flow at Low Reynolds Number

This article presents a two-dimensional numerical study on the unsteady laminar mixed convection heat transfer from a row of five in-line isothermal square cylinders placed in an unconfined medium and subjected to cross-flow of a Newtonian fluid at low Reynolds number (Re = 125). The hydrodynamic and thermal transport phenomena are captured for the separation ratios (spacing to cylinder size ratio, s/d) of 0.5, 1, 1.5, 2, 3, and 4. The mixed convection heat transfer is studied for Richardson numbers (Ri) ranging from 0 to 3 with a fixed Prandtl number (Pr = 0.71). Numerical calculations are performed by using a PISO algorithm-based finite volume solver in a collocated grid system. The instantaneous vorticity fields along with the isotherm patterns are systematically presented and discussed for different separation ratios and Richardson numbers. Depending on the engineering application, the temperature difference between the surface and the free stream could vary to make buoyancy of primary importance, entailing major modification of the flow field. Additionally, the instantaneous and mean drag and lift coefficients, Strouhal numbers, and mean Nusselt numbers are determined and discussed.     

Investigation of Mixed Convection in a Ventilated Cavity in the Presence of a Heat Conducting Circular Cylinder

The study is aimed to investigate the mixed convective transport within a ventilated square cavity in presence of a heat conducting circular cylinder. The fluid flow is imposed through an opening at the bottom of the left cavity wall and is taken away by a similar opening at the top of the right cavity wall. The cylinder is placed at the center of the cavity. Two cases are considered depending on the thermal conditions of the cavity walls. In the first case, the left and right vertical walls are kept isothermal with different temperatures and the top and bottom horizontal walls are considered as thermally insulated. For the second case, the top and bottom walls are maintained at different constant temperatures and the left and right walls are considered adiabatic. Heat transfer due to forced flow, thermal buoyancy, and conduction within the cylinder are taken into account. Effect of the cylinder size (0.1 ≤ D ≤ 0.5) and the solid–fluid thermal conductivity ratio (0.1 ≤ K ≤ 10) are explored for various values of Richardson number (0 ≤ Ri ≤ 5) at fixed Reynolds (Re = 100) and Prandtl (Pr = 0.71) numbers. The fluid dynamic and thermal transport phenomena are depicted through streamline and isotherm plots. Additionally, the global thermal parameters such as the average Nusselt number and average fluid temperature of the cavity are presented. It is found that the aforementioned parameters have significant influences on the fluid flow and heat transfer characteristics in the cavity.     

Heat transfer on a horizontal rotating cylinder near a flat plate in a cross‐flow

An experimental study of heat transfer on a horizontal rotating cylinder near a flat plate was performed. The cylinder and plate were set in a cross‐flow. Temperature distribution and coefficients of local heat transfer were measured by a Mach–Zehnder interferometer. Flow visualization was made using smoke. Rotating Reynolds numbers (Re_r) and cross‐flow Reynolds numbers (Re_d) were varied from 0 to 2000. The spaces between cylinder and plate were varied from 1 × 10^?3 m to 5 × 10^?3 m. The rotating direction of cylinder was changed clockwise or counterclockwise. The following results are obtained: When the space between the rotating cylinder and flat plate is the same as the displacement thickness on the plate, the heat transfer on the cylinder near the plate has the best performance. We have procured the empirical equation of heat transfer from a rotating cylinder near the flat plate in the cross‐flow. 8 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20329     

A Numerical Study of Fluid Flow and Heat Transfer around a Square Cylinder at Incidence using Unstructured Grids

A numerical investigation of flow and heat transfer around a square cylinder at incidence (α = 0° ? 45°) is presented for a range of Reynolds numbers ( Re = 60 ? 150). A finite-volume code suitable for unstructured grids has been developed to simulate the flow. The unstructured grid has been generated using the Delaunay triangulation algorithm. A modified pressure-velocity correction scheme with semi-explicit time-stepping is implemented to solve the Navier-Stokes equations. Collocated grid arrangement has been used for the dependent variables. Convective terms have been discretized using a second order upwind least squares scheme. The formation of Karman vortex street has been captured and the Strouhal number associated with the wake has been determined. The dependence of Strouhal number, force coefficients (drag and lift), moment coefficient and average Nusselt number on Reynolds number, and angle of incidence for a fixed blockage ratio has been reported and analyzed.     

Two-dimensional laminar fluid flow and heat transfer in a channel with a built-in heated square cylinder

A numerical investigation was conducted to analyze the unsteady flow field and heat transfer characteristics in a horizontal channel with a built-in heated square cylinder. Hydrodynamic behavior and heat transfer results are obtained by the solution of the complete Navier–Stokes and energy equations using a control volume finite element method (CVFEM) adapted to the staggered grid. The Computation was made for two channel blockage ratios (β=1/4 and 1/8), different Reynolds and Richardson numbers ranging from 62 to 200 and from 0 to 0.1 respectively at Pr=0.71. The flow is found to be unstable when the Richardson number crosses the critical value of 0.13. The results are presented to show the effects of the blockage ratio, the Reynolds and the Richardson numbers on the flow pattern and the heat transfer from the square cylinder. Heat transfer correlation are obtained through forced and mixed convection.     

Heat transfer by shock-wave/boundary layer interaction on a flat surface with a mounted cylinder

The detailed convective heat transfer is observed on a flat surface where the cylinder is mounted in a supersonic flow field. During the test, the thermal image of a wall temperature distribution is taken by an infra-red camera under the constant heat flux condition on the flat surface. From the measured wall temperature information, heat transfer coefficients are calculated. The shadow graph and the oil flow tests are conducted to examine the shock-wave structure and the surface shear flow around the protruding body, respectively. The entire flow also is simulated numerically. The upstream flow Mach number, total pressure and Reynolds number are about 3, 600 kPa and 2.3 × 10⁶, respectively. The swept-back effect of a cylinder to the approaching flow is considered in the range from 0° to 30°. From the results, the large increase of heat transfer is observed in a shock-wave/turbulent boundary layer interaction region and the peak heating appeared especially on a flow reattachment region. When the cylinder is swept backward to the main flow, the heat flux promotion decreases as much as its effective area. These results will provide the valuable information for the thermal analysis in a complicated shock-induced separation region.