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Hydrodynamic and thermal features of two-dimensional, incompressible shear-thinning and shear-thickening non-Newtonian power-law liquids under forced convection across a trapezoidal cylinder are the focus of this study, carried out at Reynolds number Re = 1–40, power-law index n = 0.4–1.8 and Prandtl number Pr = 50 using ANSYS Fluent. In this steady system, the drag coefficient is found to decrease, whereas the wake size and the average Nusselt number increase with the increase in Re. However, with the increase in n value, the average Nusselt number decreases. Similar to a square cylinder, compared to Newtonian liquids, shear-thinning liquids increases heat transfer and shear-thickening reduces it. The maximum increase in heat transfer for shear-thinning liquids compared to Newtonian liquids for a trapezoidal cylinder is approximately 25%, while the average heat transfer is somewhat lower for shear-thickening liquids than for Newtonian. The average Nusselt number is smaller for the trapezoidal cylinder than for a square cylinder in the parameter domain investigated; the largest difference is around 25%. A simple relationship for the average Nusselt number as a function of Re and n has been determined.

Aiding buoyancy mixed convection features of Newtonian fluids across a periodic array of heated cylinders have been studied numerically using a commercial CFD solver ANSYS FLUENT. The governing equations have been solved for the following ranges of physical parameters: Reynolds (1 ≤ Re ≤ 40), Prandtl (0.70 ≤ Pr ≤ 50) and Richardson (0 ≤ Ri ≤ 2) numbers and fluid volume fractions of 0.70–0.99. Qualitatively, the dense and curved streamlines and isotherms were seen with the increasing inertial (Re), viscous diffusion (Pr) and buoyancy parameter (Ri) across all the fluid volume fractions. The drag coefficients were observed to be diminished with an upturn in Re and fluid volume fractions, whereas an opposite behavior was noticed with rising in Pr and buoyancy parameter. The Nusselt numbers were found to be enhanced with Re and Pr numbers and moreover with fluid volume fractions also as in contrast to forced convection (Ri = 0) cases. Aiding buoyancy enhances flow as well as heat transfer features and yields unsteady behavior also at the higher fluid volume fractions and Re for all the values of Pr and Ri numbers. Moreover, statistical correlations have been developed for the total drag coefficient and average Nusselt number to gain the more physical insight of the results. Lastly, the findings have been compared with the literature which displayed the good agreement within the ranges of parameters studied herein.

Laminar heat transfer characteristics of non-Newtonian power-law fluids from a long (heated) triangular prism in the time-periodic regime have been explored. Momentum and energy equations were solved using finite volume methodology over the range of non-dimensional control parameters: Reynolds number (Re) = 50–150, Prandtl number (Pr) = 1–50 and power-law index (n) = 0.4–1.8. For the fixed Pr, the local and the time-averaged Nusselt numbers increase with rising Re irrespective of n. However, the local and the time-averaged Nusselt numbers decrease as the fluid nature alters from pseudo-plastic (n 1) for the fixed Re and Pr. Maximum enhancements in the values of time-averaged Nusselt numbers for Pr = 10, 20 and 50 with respect to Pr = 1 are observed to be approximately 180, 273 and 438%, respectively. Further, it is observed that for the fixed n and Pr, the Colburn heat transfer factor (or the jh factor) decreases with rising Re. Finally, the various values of the jh factor at different Re, n and Pr have been correlated via a simple expression, thus enabling its estimation in a new application.

Flow around an isolated generic sharp-edged object with varying height ratio (β = 0–1) i.e. height from the rear end of the object to the front end ( β = H 2 / H 1 ) has been investigated in cross-flow configuration covering steady and periodic regimes at Reynolds number (Re) from 1 to 150 using air as a working fluid. Flow separation is delayed with a decrease in β. Wake formed is the highest for β = 1 (square object) and progressively decreases with the decrease in β. The vortex shedding effect has been demonstrated on the heat transfer phenomena around the objects. For all the cases of height ratios, as Re increases the flow undergoes supercritical Hopf bifurcation to periodic state as steady-state condition loses its stability. Stuart-Landau theory has been used to determine the value of critical Re or the onset of vortex shedding for all the cases of height ratios. As β increases from 0 to 0.7, the value of critical Re increases. Influence of surface vorticity and surface pressure on the overall drag coefficient ( C D ) has been explored. Effect of β on the Strouhal number (St) has been investigated and the findings are in agreement with previous results. Finally, correlations relating Lr, C D , Nu ‾ and St with Re and β have been developed.

A numerical analysis was carried out to examine the effect of pulsating flows around a semi-circular (heated) cylinder placed in a horizontal confined empty channel. The heat transfer induced as an outcome of non-zero mean sinusoidally varying flow past a semi-circular cylinder was investigated. For this purpose, computations are carried out for the following range of parameters: wall confinement (or blockage ratio, β) = 25%; Prandtl number (Pr) = 7 (water as a working fluid); Reynolds number (Re) = 10–100; Strouhal number (St) = 0–2; and amplitude of oscillation (A) = 0–0.6. The current situation is numerically investigated by solving the continuity, momentum and energy equations using the finite volume method—based solver Ansys Fluent. Results in terms of total drag coefficient and Nusselt number have been presented and discussed. The nature of flow for each considered case is reported. The flow (streamlines) and thermal (isothermal contours) patterns have been analyzed. The maximum augmentations of about 22 and 10% were obtained in drag coefficient and Nusselt number, respectively. It is noteworthy that amongst all the cases studied, an appreciable amount of augmentation is observed when St = 1 and A = 0.6 (with respect to the case of non-pulsating flow i.e. St = 0).

The focus of the current numerical investigation is to study the fluid flow and mixed convective (thermal cross-buoyancy) heat transfer of incompressible fluid across identical cylinders organized in a confined tandem configuration because of their enormous engineering and industrial applications such as heat exchange tubes, electronic cooling, twin chimney stacks, cooling tower, etc. The involved flow and energy equations are solved for different gap ratios (S/D = 2.5, 3, 3.5, 4, 5, and 5.5) with varying Richardson number (Ri = 0, 0.5, and 1) at Reynolds number Re = 100, Prandtl number Pr = 0.7 and wall confinement β = 25% by using a finite volume method-based commercial solver ANSYS Fluent. It is found that after a certain gap ratio there is a drastic change in the physical parameters and after that gap ratio the change is gradual; this gap ratio is termed as a critical gap ratio. The introduction of thermal cross-buoyancy (Ri > 0) plays a deep impact on the physical parameters, and it is to be noted that the critical spacing shifts towards a lower value with increasing Ri. The analysis of lift coefficients shows that the fluctuations in lift signal shift from zero average value at Ri = 0 towards the nonzero negative average value for the tandem cylinders at Ri > 0. The local Nusselt number shows the shift in the front stagnation point on both cylinders with increasing thermal cross-buoyancy. The drag coefficient and Nusselt number of the downstream cylinder are always less than the upstream cylinder, but the percentage increment in the physical parameters of the downstream cylinder after critical spacing is much more than its upstream counterpart.

This work is an attempt to simulate the effects of pulsating flow upon the thermal and hydrodynamic behavior of shear-thinning non-Newtonian fluid (approximated as power-law fluid) while it flows past a semi-circular cylinder fixed in a symmetrically confining channel and deduces the optimum oscillating frequencies and amplitude for a particular power-law index (n) and Reynolds number (Re). The semi-circular cylinder studied has a fixed temperature while the wall confinement is insulating. The ranges of control parameters varied are ${\rm Re}=10$ -100 (based on object's diameter), the amplitude of oscillation (A) = 0-0.6, the Strouhal number (St) = 0-2 and the n ranging from 0.2 to 1. The Prandtl number has been kept fixed at $({\rm Pr})=50$ (which corresponds to several fluids of industrial importance like n-butanol, etc.). The isotherms and streamlines give a qualitative insight into the heat and flow transfer behavior as various parameters are varied, while the Nusselt number, overall drag and lift coefficients have been calculated to get a quantitative insight. Further, the augmentation in heat transfer and the decline in drag upon using a pulsating non-Newtonian fluid inlet as opposed to using a steady Newtonian flow have been established. Lastly, the temporal variations and the frequency of vortex shedding have been studied using a fast Fourier transform.

Flow and heat transfer characteristics around a semi-circular cylinder placed in a confined channel are investigated in the unsteady regime. The two-dimensional simulations are carried out for varying values of control parameters: Reynolds number (Re) = 50–200 and Prandtl number (Pr) = 0.7, 10 and 100 at a fixed blockage ratio of 25% for Newtonian constant-property fluid. Continuity, Navier–Stokes and energy equations with appropriate boundary conditions are solved using the commercial computational fluid dynamics solver Ansys Fluent. The transition from steady to time-periodic flow occurs between Re = 69 and 70. The effect of Prandtl number on Nusselt number is pronounced; the ratio of Nusselt number values belonging to Pr = 100 and those belonging to Pr = 0.7 ranges from 6.3 to 6.5 over the Reynolds number domain investigated. Finally, the present numerical results are used to develop drag coefficient, Strouhal number and Nusselt number correlations.

The effects of cross-buoyancy mixed convection from a square cylinder in the proximity of a plane wall are studied for Reynolds number (Re) = 1–100, Richardson number (Ri) = 0–2, and gap ratio (G) = 0.25–1 at Prandtl number (Pr) = 0.7. The flow observed is steady for G = 0.25 and 0.5. The transition from a steady to a time-periodic system is observed for G = 1, and it is found at Re = 56, 60, and 74 for Ri = 0, 1, and 2, respectively. With increasing G and/or Ri, the drag coefficient and average Nusselt number increase for all Re values studied and the lift coefficient decreases with increasing Ri except at Re = 1. Maximum heat transfer augmentation is found about 89% at G = 0.5 (Re = 20, Pr = 0.7, Ri = 0) with respect to the corresponding value at G = 0.25 (Re = 20, Pr = 0.7, Ri = 0). Lastly, the correlations of drag coefficient and heat transfer have been obtained.

A dielectric fluid plays a significant role on the machining efficiency of Electric discharge machining (EDM). Two phase (liquid-air) dielectric medium was utilized in near-dry (EDM). It is an environmentally friendly process. The present article reports the effect of different dielectric mediums on responses of near-dry EDM. Dielectric mediums used for experimentation were water-air, EDM oil-air and glycerin-air mixtures. The process parameters selected for experimentation were current, duty factor, flushing pressure and lift. Material removal mechanism of near-dry EDM is investigated using imaging techniques. Dielectric fluid with higher viscosity and higher Prandtl number provided better results than fluids with lower viscosity. The results reveal that the Material removal rate (MRR) with glycerin-air dielectric medium is about three-times higher than other dielectric medium used with negligible recast layer. The tool wear rate is negligible in near-dry EDM in relation to all the dielectric mediums.

The influence of opposing-buoyancy mixed convection from a square cylinder in a vertical channel has been studied at Reynolds numbers (Re) = 1–100, Richardson numbers (Ri) = 0 to −1, and blockage ratios (β) = 10–50% for air as a working fluid. The onset of a steady to a time-periodic regime is found for Ri = 0 (at Re = 35, 65, 74, and 62), Ri = −0.5 (at Re = 12, 39, 48, and 54), and Ri = −1 (at Re = 9, 30, 39, and 50) for β = 10%, 25%, 30%, and 50%, respectively. The initiation of flow separation is also determined. Finally, the correlations of Strouhal number, drag coefficient, and the Colburn heat transfer factor were obtained.

In this article, investigations have been carried out to decipher the effect of thermal buoyancy in a viscosity stratified flow field for a shear-thinning fluid flowing past a pair of heated side-by-side square cylinders, which is an extension part of our recent study [Sanyal, A. and Dhiman, A., “Wake interactions in a fluid flow past a pair of side-by-side square cylinders in presence of mixed convection,” Phys. Fluids 29, 103602 (2017)]. It is found that the leading-edge flow-separations from the square cylinders influence the near-wake structures and vortex shedding patterns in the presence of shear-thinning effects, which is otherwise missing for Newtonian fluid flow at Reynolds number Re = 40 and Richardson number Ri = 1. The distribution of wall-viscosity η along the inner surfaces of the side-by-side square cylinders, at different values of transverse spacings s/d and flow-behavior indices n, hints at large dependency on the inflections in the velocity profile within the gap-flow region. Under thermal buoyancy-driven mild shear-thinning flow conditions (n = 0.6 and 0.8), the gap-flow characteristics have been classified into “pressure-driven” and “momentum-driven” flow regimes, which provides a good explanation for the aberrations noted in the distribution pattern of η. The root-mean-square fluctuations of the velocity-magnitude and vortex shedding phenomenon are found to reciprocate a consistent flow physics associated with a shear-thinning flow at near and far-field downstream. The single body deflected type flow is primarily seen under predominant shear-thinning flow conditions (n = 0.4), compared to chaotic or quasi-periodic flow under mild shear-thinning conditions. Besides, the evolution of non-linear dynamics-based flow regimes (classified with respect to s/d using power spectrum density analysis) at different values of n and s/d is thoroughly summarized. The time-variant fluctuations of lift and drag force parameters are also found to be unified through cause and effects.

The thermal characteristics of incompressible non-Newtonian power-law fluids across periodic array of circular cylinders have been examined using the finite volume-based numerical solver ANSYS-FLUENT for the following ranges of physical parameters: Reynolds number; 1 ≤ Re ≤ 40: Prandtl number; 1 ≤ Pr ≤ 100: power-law index; 0.40 ≤ n ≤ 1.8; and fluid volume fractions ranging from 0.70 to 0.99. The thermal features have been described via isotherm patterns, local and average Nusselt numbers and the Colburn heat transfer factor and found to be strongly dependent over the above physical parameters. It was observed that the dense isotherms with the increasing inertial and viscous diffusion suggest an improvement in the rate of heat transfer across the periodic cylinders. An increase in local Nusselt number was seen with the increasing values of Re and/or Pr across all the fluid volume fractions. Further, the different behavior of the average Nusselt number was noticed because of the shear-thinning and shear-thickening natures. An enhancement of about 97% was noticed in the shear-thinning region between the extreme fluid volume fractions for the highest value of Pr and the lowest values of Re and n. However, in many cases, the enhancement was noticed to be even more than 100%. An empirical correlation for the average Nusselt number and the Colburn heat transfer factor (jH) has been developed to give the additional physical insight of the results. Finally, the comparison was made with the available literature which displayed a good agreement with the present results.

The laminar flow and heat transfer across a triangular periodic array of heated cylinders are simulated computationally and analyzed. The study has been carried out at Reynolds number 10–100 for fluid volume fraction ranging from 0.7 to 0.99 and Prandtl number ranging from 0.7 to 50. The size of the wake region increases continuously with an increase in the Reynolds number for all values of fluid volume fraction. The recirculation bubble from the rear of a cylinder is reaching the front of the next cylinder in the same column of the periodic array for low values of free volume fraction, but this is not the case with the highest free volume fraction, i.e., 0.99. At high Reynolds number, the flow is separating early on the cylinder surfaces. The wake size at higher Reynolds number 75 and 100 for the lowest free volume fraction 0.7 is more in comparison with the wake size at free volume fraction 0.99, which is explained by plotting the location of flow separation against Reynolds number for both the extreme values of free volume fractions, i.e., 0.7 and 0.99. The isovorticity contours are concentrated in the vicinity of the cylinders on increasing the Reynolds number irrespective of free volume fraction and then convected downstream. On increasing free volume fraction, the friction and pressure drags in the array decrease. The increase in Reynolds number also results in the decrease in the values of the individual (friction and pressure drag coefficients) as well as total drag coefficients for all values of free volume fraction. At high values of Reynolds number, the emergence of carbuncle or thermal spike on isotherm near the cylinder’s surface is observed where the value of the local Nusselt number is observed low. The heat transfer improves and the Nusselt number increases as the Reynolds number and/or Prandtl number increases. On the contrary, heat transfer decreases as free volume fraction increases.

Extensive numerical computations for the confined flow and heat transfer of shear-thinning fluids over two long tandem triangular bluff bodies are performed for Reynolds number (Re) = 1–40, power-law index (n) = 0.2–1, and gap ratio (S/B) = 1–4 for a fixed blockage ratio and Prandtl number of 25% and 50, respectively. The values of critical Re are obtained for each of the two triangular cylinders for all S/B and n. Augmentation in heat transfer for the two tandem triangular cylinders is calculated with respect to both S/B and n.

The effects of non-Newtonian power-law fluids on the unsteady unconfined fluid flow characteristics of an equilateral triangular prism are investigated for Reynolds number (Re) ranging from 50 to 150 and power-law index (n) ranging from 0.4 to 1.8. The flow field around a triangular prism is represented by streamline contours. The output parameters such as root-mean-square values of lift and drag coefficients, time-averaged drag and lift coefficients and Strouhal number are calculated. A time-periodic behavior of the flow is observed for the entire range of control parameters studied. An increment in the time-averaged total drag coefficient is observed with the increase in Re for pseudo-plastic and Newtonian fluids. However, for dilatant fluids, a mixed trend is observed when time-averaged total drag coefficient is varied with n. There is an enhancement in the value of Strouhal number with the increase in Re for dilatant fluids, whereas a mixed trend of Strouhal number with Re is noticed for pseudo-plastic fluids.

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 proje...

A numerical analysis using Ansys Fluent was carried out to investigate the forced convection of power-law fluids (power-law index varying from 0.2 to 1.8) around a heated semi-circular cylinder with wall confinement (or blockage ratio) of 25%, Prandtl number of 50, and Reynolds numbers 1–40. Flow and thermal fields were found to be steady for Re up to 40. The shear-thickening behavior was found to have a higher value of drag coefficient, whereas the shear-thinning behavior had a smaller value of drag coefficient when compared with Newtonian fluids in the steady regime. The wake size was found shorter in shear-thickening fluids than Newtonian and shear-thinning fluids. An overall heat transfer rate was calculated and found to increase with the rise in Reynolds number. The average Nusselt numbers were observed higher for shear-thinning fluids than Newtonian and shear-thickening fluids; and the maximum enhancement in the heat transfer was achieved approximately 47% as compared to Newtonian fluids. The present results have also been correlated in terms of wake length, drag coefficient and average Nusselt number expressions for various Reynolds numbers and power-law indices studied. In addition, the effects of blockage ratios ranging from 16.67% to 50% on the engineering output parameters with varying power-law index at Re = 40 were reported.

The present study focuses on the flow across an asymmetrically confined (heated) cylinder in a channel for fluids obeying Ostwald-de Wale (power-law) equation for the settings: Reynolds number (Re) = 1–40, power-law index (n) = 1–1.8, gap ratio (γ) = 0.375–1, blockage ratio (β) = 0.2–0.5 and Prandtl number (Pr) = 1–50. Total drag coefficient and its individual components have been analyzed as a function of Re, β, γ and n. The overall drag coefficient was found to increase with blockage and behavior of fluid, while it drops gradually for increasing Re. The asymmetrical configuration is seen to mitigate the overall as well as individual drag coefficients. The surface heat transfer coefficient in the form of average Nusselt number and the Colburn heat transfer jh factor has been thoroughly discussed. Heat transfer rate is found to increase with increasing Reynolds number and wall confinement, while increasing dilatant behavior impedes the same. As expected, heat transfer results have been reconciled in a single curve by way of the Colburn jh factor. The jh factor is found higher for the symmetric case as compared to the asymmetric case.

Flow characteristics of non-Newtonian power-law fluids in a right-angled horizontal T-channel are studied in the laminar regime. In particular, the two-dimensional numerical computations are performed using Ansys Fluent for the following range of physical parameters: Reynolds number (Re) = 5–200 and power-law index (n) = 0.2–1 (covering shear-thinning, n

The present work aims at studying the laminar flow and heat transfer characteristics of a Newtonian fluid over a row of semi-circular cylinders placed in uniform cross-flow configuration. The effects of spacing to diameter (gap) ratio, varied from 1 to 10, on the flow and heat transfer patterns have been studied at a Reynolds number of 100 for air as the working fluid. There has been no significant interaction in the flow at a spacing ratio greater than 4 and each semi-circular cylinder behaved more or less like the situation of a single cylinder. At lower gap ratios, the flow becomes more complicated due to the shear layer interactions that exist in the flow. The streamline and isotherm contours have been presented and discussed in detail for various gap ratios. The variation in flow behavior is explored further by studying the drag coefficient and lift coefficient signals of various semi-circular cylinders. The presence of a secondary frequency at low gap ratios that has adverse effect on the drag coefficient has been confirmed. The variation of measured global quantities, namely the drag coefficient, the Strouhal number and the Nusselt number have been studied and discussed in detail.

Effects of cross-buoyancy mixed convection on flow and heat transfer characteristics of a long semi-circular cylinder (long in neutral direction) in a confined channel have been investigated in the laminar regime. The numerical results have been presented and discussed for the range of conditions as Reynolds number (Re) = 1–40, Richardson number (Ri) = 0–4, Prandtl number (Pr) = 0.71–50 and blockage ratio (β) = 16.67%–50%. The drag coefficient increases with increasing Richardson number and/or blockage ratio. The average Nusselt number is showing a maximum relative enhancement of approximately 45% for Ri = 4 with respect to corresponding forced convection value (Ri = 0). The average Nusselt number increases with increase in Prandtl number and shows a maximum relative enhancement of approximately 1136% for Pr = 50 with respect to corresponding value at Pr = 0.71. On the other hand, the maximum relative variation of the total drag coefficient is found to be approximately 55% for Ri = 4 with respect to corresponding value at Ri = 0. Finally, the simple heat transfer correlation is obtained for the proceeding range of control parameters.

Two-dimensional numerical simulations are carried out to understand the effects of cross-buoyancy on the confined flow and heat transfer characteristics over an equilateral triangular bluff body at low and intermediate Reynolds numbers (Re). For a fixed Richardson number (Ri), an average cylinder Nusselt number increases with increasing Re. However, the average Nusselt number shows a soft response toward increasing Ri. The critical Re for the onset of periodic unsteady flow increases with increasing cross-buoyancy (Ri). A simple heat transfer correlation is also obtained to relate the values of average cylinder Nusselt number, Re, and Ri.

The effects of wall confinements (β) and of Prandtl numbers (Pr) on the laminar flow around a heated trapezoidal prism are investigated numerically for Pr = 0.71–100 and β = 12.5–50 % at low Reynolds numbers (Re). The critical value of the Reynolds number (i.e., the transition from a steady to a time-periodic regime) is calculated and it exists between Re = (36 and 37), (60 and 61) and (91 and 92) for the blockage ratios of 12.5, 25 and 50 %, respectively. The average Nusselt number increases with increasing Re and/or Pr and/or blockage ratio. The variation of local Nusselt number on each surface of the obstacle and the representative isotherm contours are presented to elucidate the role of Pr and blockage ratio on the heat transfer from the trapezoidal prism. The maximum heat transfer enhancement with respect to a square prism on the basis of equal projected area is found to be approximately 31 and 45 % for the blockage ratios of 12.5 and 25 %, respectively, for Pr = 0.71 and Re = 1. The Colburn heat transfer factor correlations are also obtained for the preceding range of settings. Finally, the influence of Richardson number (Ri = 0–1) on the flow and heat transfer characteristics has been studied for air as working fluid.

This study involves the numerical solution of the laminar heat transfer in a separating and reattaching flow by simulating the flow and heat transfer downstream of a backward-facing step. The in-house finite volume code has been implemented employing a hybrid differencing scheme and the SIMPLE algorithm for the pressure–velocity coupling. Three principal parameters governing heat transfer in this geometry, that is channel expansion ratio (ER), Reynolds number (Re), and Prandtl number (Pr), are systematically varied in the range ER = 1.111 to 2, Re = 1 to 200, and Pr = 0.71 to 100, and the simple correlations between these parameters have been elucidated. A series of important findings have been established by analyzing the results some of which are: (1) there is an associated shifting of the point of maximum heat transfer with respect to the flow-reattachment point with gradually decreasing the values of ER and (2) the heat transfer enhancement increases with the increase in Pr number as a result of the compression of the thermal boundary layer and the maximum Nusselt number varies as .

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 jh factor have been established in the steady regime.

Power-law shear-thinning fluid flow over a heated square bluff body is numerically investigated under aiding buoyancy mixed convection at low Reynolds numbers. Semi-explicit finite volume code is developed to solve the governing equations along with the appropriate boundary conditions. Both aiding buoyancy and shear-thinning natures are found to augment the heat transfer rate from the surface of the long square bar. In aiding buoyancy, the total drag coefficient is found to be more for the square cylinder than that of the circular cylinder, whereas the average cylinder Nusselt number for the square cylinder is found to be lower than the circular one on equal side/diameter basis. Maximum augmentation in heat transfer is found to be approximately 20% with respect to forced convection. Finally, a heat transfer correlation is established by using the Colburn heat transfer factor.

Effects of wall confinements on the laminar flow and heat transfer around a heated tapered trapezoidal bluff body are investigated numerically in the confined domain (Reynolds number, Re = 1 to 40; blockage ratio = 0.125 to 0.5; and Prandtl number, Pr = 0.71). The onset of flow separation is found between Re = 4 and 5 for the blockage ratio of 0.125 and between Re = 5 and 6 for the blockage ratios of 0.25 and 0.5. If compared with a long circular obstacle on the basis of equal projected area, the total drag coefficient of the trapezoidal cylinder is found to be larger than the circular one, but an opposite trend is observed for the heat transfer. The augmentation in heat transfer for trapezoidal and circular cylinders is found to be approximately 46, 72, 74, and 65 percent for Re = 1, 5, 10, and 40, respectively for the blockage ratio of 0.25. The maximum enhancement in heat transfer for a tapered trapezoidal bluff body with respect to a square bluff body is found to be approximately 104 percent and 101 percent for blockage ratios of 0.25 and 0.5, respectively. Finally, simple correlations of wake length, drag, and average cylinder Nusselt number are established.

The present study focuses on momentum and heat transfer characteristics of the laminar flow of power-law fluids in a vertical channel with a built-in square cylinder under the influence of aiding buoyancy. The simulations are carried out at low Reynolds numbers (1–40) for the range of settings as power-law index = 0.4–1, Richardson number = 0–1, blockage ratio = 25%–50%, and Prandtl number = 50. It is found that the drag coefficient and the Nusselt number increase with the aiding buoyancy, while the shear-thinning behavior reduces the drag coefficient and increases the heat transfer rate.

A numerical investigation is conducted to analyze the steady and unsteady laminar flow and heat transfer in a channel with two square bars (of equal diameters) arranged side-by-side. The analysis is carried out for Reynolds number = 10–100, Prandtl number = 0.7–50, for transverse separation distance between the bars (i.e., gap ratio) of 1.5, 2, 2.5, 5, and 10 at the blockage ratio of 1/18. The results found here are in good agreement with previously published data. The effects of gap ratio, Reynolds number, and Prandtl number on the detailed kinematics of the flow and the heat transfer are presented. The engineering parameters such as total drag coefficient, average Nusselt number, and Strouhal number are calculated for the preceding range of conditions. It is observed that the overall drag coefficient decreases with increasing Reynolds number, whereas the average Nusselt number for the square cylinders increases with increasing Reynolds number and/or Prandtl number for all the values of gap ratios studie...

Flow and heat transfer of non-Newtonian power-law fluids over an inclined square cylinder placed inside a channel are studied numerically at low Reynolds numbers. In particular, calculations are carried out for Reynolds number (Re) = 1–40; power-law index (n) = 0.4–1 and blockage ratio (β) = 12.5–50% at a Prandtl number (Pr) = 50. An increase in blockage ratio results in an increase in the total drag coefficient and decrease in the wake length. The Strouhal number and the root mean square value of the lift coefficient increase with the increasing Reynolds number for the fixed values of blockage ratio and power-law index. The average Nusselt number increases with power-law index and/or blockage ratio. The maximum enhancement in heat transfer is approximately 49, 41, and 35% for the values of blockages of 50, 25, and 12.5%, respectively, as compared to the corresponding Newtonian value. The average Nusselt number for the inclined square cylinder (at α = 45°) is always greater than the average Nusselt number for the regular square cylinder (at α = 0). Finally, simple expressions of drag and Nusselt number have been established for the above range of settings. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 167-196, 2014; Published online 20 June 2013 in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21071

Steady and unsteady forced convection flow and heat transfer past a long expanded trapezoidal bluff body are investigated for the air as working fluid for Re = 1–150. The wake length increases as the Reynolds number increases in the steady flow regime (1 ⩽ Re ⩽ 47). The transition from steady regime to unsteady regime occurs between Re = 47 and 48. The total drag coefficient decreases with the increasing value of the Reynolds number up to Re = 90 and thereafter it increases with Reynolds number. However, heat transfer as well as Strouhal number increase with the increasing value of the Reynolds number. The maximum augmentation in heat transfer for the expanded trapezoidal cylinder with respect to the tapered trapezoidal cylinder is found to be approximately 146%. On the other hand, pressure drop shows an enhancement of approximately 97% for the expanded trapezoidal cylinder when compared with the tapered one. Simple correlations of wake length, drag, average Nusselt number and Strouhal number with Reynolds number have also been established.

This study focuses on the confined upward flow and heat transfer around a square cylinder under the effect of aiding buoyancy (Richardson number, Ri=0–1) in the vertical channel for Reynolds number (Re)=1–40 and blockage ratio (BR)=25–50% for the air as working fluid. Flow is found to be steady and symmetric for the range of settings. For Re≤2, no separation zone occurs for BR=25% and 30%. However, for BR=50%, no wakes are observed for Re≤3. The onset of flow separation takes place between Re=2 and 3 for BR=25% and 30%; whereas, for BR=50%, it exists between Re=3 and 4, irrespective of the value of Ri. Heat transfer correlations have also been obtained at different values of Re, BR and Ri.

Wall effects on the flow of incompressible non-Newtonian power-law fluids across an equilateral triangular cylinder confined in a horizontal plane channel have been investigated for the range of conditions: Reynolds number, Re=1–40, power-law index, n=0.4–1.8 (covering shear-thinning, Newtonian and shear-thickening behaviors) and blockage ratio=0.125–0.5. Extensive numerical results on flow pattern, wake/recirculation length, individual and overall drag coefficients, variation of pressure coefficient on the surface of the triangular cylinder and so forth are reported to elucidate the combined effect of power-law index, blockage ratio and Reynolds number. The size of vortices decreases with an increase in the value of the blockage ratio and/or power-law index. For a fixed value of the Reynolds number, individual and overall drags decrease with decrease in power-law index and/or blockage ratio in steady confined flow regime. Simple correlations of wake length and drag are also obtained for the range of settings considered.

The two-dimensional numerical simulations of Newtonian fluid stream about a square bluff body have been studied in an unconfined configuration in addition in the propinquity of a plane wall. The comparison of flow and heat transfer constraints is done with the pure unconfined flow about a square obstacle. The set of physical constraints considered as Reynolds numbers (Re) = 100, 120 and Prandtl number (Pr) = 0.7 (air) at varying values of gap ratios (g). The values of drag and lift coefficients, and average Nusselt number are computed. The present study shows that on increasing the gap ratio, the drag coefficient is acquired to be the highest for the gap ratio of unity and it is observed the lowest for the unconfined case. Lift coefficient decreases and average Nusselt number increases with increasing gap ratio, but opposite effects are observed for the unconfined case. The flow becomes steady at low gap ratio, but on increasing gap ratio the flow behavior changes to periodic unsteady. The augmentation in heat transfer is found about 35 % for g = 1, with respect to the corresponding value for the unconfined case.

Flow and heat transfer of non-Newtonian power-law fluids across a pair of identical circular cylinders in side-by-side arrangement are investigated numerically by solving the continuity, momentum and energy equations along with the appropriate boundary conditions. The numerical calculations are performed in an unconfined computational domain for the following range of physical parameters: Reynolds number, Re = 1–40 and power-law index, n = 0.4–1.8 (covering shear-thinning, n n = 1 and shear-thickening, n > 1 behaviors) for gap ratio, T / D = 1.5–4.0 at a constant Prandtl number of 50. The global characteristics such as drag coefficients and average Nusselt number, etc. are calculated and the representative streamline and isotherm contours are presented for the above range of conditions. It has been found that the individual and overall drag coefficients decrease and the average Nusselt number increases with Reynolds number for all T / D and n considered here. The heat transfer is found higher in shear-thinning fluids than Newtonian fluids and followed by shear-thickening fluids for 1.5 ⩽ T / D ⩽ 4.0 and 1 ⩽ Re ⩽ 40.

Two-dimensional unconfined flow and heat transfer across a long tapered trapezoidal bluff body are investigated for the range Re = 1 to 150 (thereby covering both steady and unsteady periodic regimes) and Pr = 0.7 (air). A number of engineering parameters, e.g. drag and lift coefficients, Strouhal and Nusselt numbers, and others, is calculated for the above range of conditions. No flow separation occurs from the surface of the trapezoidal cylinder for the range Re ≤ 5; however, flow starts to separate from the rear surface of the cylinder at Re = 6. Therefore, the onset of flow separation exits between Re = 5 and 6. The critical value of the Reynolds number (i.e. transition from steady to unsteady) exists between Re = 46 and 47. The drag coefficient decreases with increasing Reynolds number in the steady regime; however, the drag increases with Reynolds number in the unsteady regime. The Strouhal number and the average Nusselt number increase with increasing value of the Reynolds number. Finally, the simple correlation for the average Nusselt number is obtained in the steady flow regime. © 2012 Curtin University of Technology and John Wiley & Sons, Ltd.

Flow of non-Newtonian power-law fluids across a long circular bluff body confined symmetrically between infinitely long two parallel plane walls is investigated numerically by solving the continuity and momentum equations using the finite volume method–based solver Fluent. The numerical calculations are performed in the full computational domain for the following ranges: Reynolds number = 50–150 and power-law index = 0.4–1.8 (covering shear-thinning, Newtonian, and shear-thickening behaviors) for the blockage ratio of 0.25. Global characteristics such as drag and lift coefficients, and Strouhal number and derived variables such as stream function are calculated for the above range of conditions. It is observed that the shear-thinning behavior yields a lower value of the time-averaged drag coefficient than the corresponding Newtonian value; however, an opposite trend is observed in the shear-thickening behavior. The Strouhal number increases with increasing Reynolds number for the fixed value of the power-...

The effects of blockage ratio on the combined free and forced convection from a long heated square obstacle confined in a horizontal channel are investigated in this work. The numerical computations are performed in the steady regime for Reynolds number = 1 - 30, Richardson number = 0 - 1 for blockage ratios of 0.125 and 0.25 for the fixed Prandtl number of 0.7 (air). The governing equations, along with appropriate boundary conditions, are solved by using a semi-explicit finite volume method implemented on the collocated grid arrangement. The total drag and lift coefficients, local and average Nusselt numbers and the representative streamline, vorticity and isotherm patterns are presented to elucidate the role of blockage ratio on the cross-buoyancy across a confined square cylinder. The asymmetry in the flow and temperature fields decreases with increasing value of the blockage ratio. Similar to forced convection, the total drag coefficient increases with increasing value of the blockage ratio for the fixed values of the Reynolds and Richardson numbers.

In this paper, mixed convection flow and heat transfer around a long cylinder of square cross-section under the influence of aiding buoyancy are investigated in the vertical unconfined configuration (Reynolds number, Re = 1–40 and Richardson number, Ri = 0–1). The semi-explicit finite volume method implemented on the collocated grid arrangement is used to solve the governing equations along with the appropriate boundary conditions. The onset of flow separation occurs between Re = 1–2, between Re = 2–3 and between Re = 3–4 for Ri = 0, 0.5 and 1, respectively. The flow is found to be steady for the range of conditions studied here. The friction, pressure and total drag coefficients are found to increase with Richardson number, i.e., as the influence of aiding buoyancy increases drag coefficients increase at the constant value of the Reynolds number. The temperature field around the obstacle is presented by isotherm contours at the Prandtl number of 0.7 (air). The local and average Nusselt numbers are calculated to give a detailed study of heat transfer over each surface of the square cylinder and an overall heat transfer rate and it is found that heat transfer increases with increase in Reynolds number and/or Richardson number. The simple expressions for the wake length and average cylinder Nusselt number are obtained for the range of conditions covered in this work.

The current study investigates the augmentation in the laminar forced convection characteristics of the backward-facing step flow in a two-dimensional channel by means of introducing an adiabatic circular cylinder in the domain. The effects of various cross-stream positions (i.e., yc = 0–1.5) of the circular cylinder on the flow and heat transfer characteristics of the backward-facing step flow has been numerically explored for the Reynolds number range 1–200 and Prandtl number of 0.71 (air). The governing continuity, Navier–Stokes and energy equations along with appropriate boundary conditions are solved by using FLUENT. The flow and thermal fields have been explained by streamline and isotherm profiles, respectively; however, no temperature dependency effects are considered for the flow viscosity and thermal conductivity. The engineering parameters like wake/recirculation length, total drag coefficient and average Nusselt number, etc. are calculated for the above range of conditions. The present results show an enhancement in the peak Nusselt value of up to 155% using a circular cylinder as compared to the unobstructed case (i.e., without cylinder). Finally, simple correlations for total drag coefficient and peak Nusselt number are obtained for the above range of conditions.

In this work, effects of Prandtl number on the heat transfer characteristics of an unconfined rotating circular cylinder are investigated for varying rotation rate (? = 0 - 5) in the Reynolds number range 1 - 35 and Prandtl numbers range 0.7 - 100 in the steady flow regime. The numerical calculations are carried out by using a finite volume method based commercial CFD solver FLUENT. The isotherm patterns are presented for varying values of Prandtl number and rotation rate in the steady regime. The variation of the local and the average Nusselt numbers with Reynolds number, Prandtl number and rotation rate are presented for the above range of conditions. The average Nusselt number is found to decrease with increasing value of the rotation rate for the fixed value of the Reynolds and Prandtl numbers. With increasing value of the Prandtl number, the average Nusselt number increases for the fixed value of the rotation rate and the Reynolds number; however, the larger values of the Prandtl numbers show a large reduction in the value of the average Nusselt number with increasing rotation rate.

Effects of Reynolds number on the heat transfer characteristics of a long (heated) equilateral triangular cylinder are investigated for the range of conditions Re = 50–150 (in the steps of 10) and Prandtl number = 0.71 (air) in the unconfined unsteady cross-flow regime. In order to simulate the present situation, the computational grid is created by using commercial grid generator GAMBIT and the numerical computations are carried out by using FLUENT (6.3). The SIMPLE method is used to solve continuity, Navier-Stokes and energy equations along with the appropriate boundary conditions. The second order upwind scheme is used to discretize the convective terms, while the central difference scheme is used to discretize the diffusive terms in the governing equations. The present results are in an excellent agreement with the literature values. The temperature isotherms and temporal history of Nusselt number are presented in detail. The local as well as time-averaged Nusselt numbers are calculated. The time-averaged Nusselt number increases with increasing Reynolds number for the fixed value of the Prandtl number. Finally, the present numerical results are used to develop the simple heat transfer correlation for the range of conditions covered here.

In this paper, fluid flow and heat transfer across a long equilateral triangular cylinder placed in a horizontal channel is studied for Reynolds number range 1–80 (in the steps of 5) and Prandtl number of 0.71 for a fixed blockage ratio of 0.25. The governing Navier-Stokes and energy equations along with appropriate boundary conditions are solved by using a commercial CFD solver FLUENT (6.3). The computational grid is created in a commercial grid generator GAMBIT. The flow and temperature fields are presented by stream-line and isotherm profiles, respectively. The wake/recirculation length, mean drag coefficient and average Nusselt number, etc. are calculated for the above range of conditions studied here. The critical value of the Reynolds number (i.e., transition to transient) is found to lie between Re = 58 and Re = 59. The average Nusselt number and the wake length increase with increasing value of the Reynolds number; however, the mean drag coefficient decreases with increasing value of the Reynolds number. Finally, simple correlations for wake length, mean drag coefficient and average Nusselt number are obtained for the range of conditions studied here.

In this study, heat transfer to power-law dilatant fluids from a long square cylinder (heated) confined in a channel in the steady flow regime is investigated. The effects of Reynolds number, Prandtl number and flow behavior index on the heat transfer characteristics of a cylinder is examined for the range of conditions 1 ⩽ Re ⩽ 45 , 1 ⩽ n ⩽ 2.0 and 1 ⩽ Pr ⩽ 100 (the maximum Peclet number being 4000) for a fixed blockage ratio, β = 1 / 8 . The variation of the local Nusselt number on the individual surfaces of the square obstacle for the constant wall temperature (CWT) and uniform heat flux (UHF) boundary conditions prescribed on the surface of the square obstacle are presented. Likewise, the representative isotherm plots for the two classical thermal boundary conditions are shown. The average Nusselt number and the heat transfer factor ( j h ) have also been calculated. Irrespective of the value of the flow behavior index, the value of the local Nusselt number at each corner of the square cylinder increases with an increase in the Reynolds and/or Prandtl number. The average Nusselt number increases monotonically with an increase in the Reynolds and/or the Prandtl number. Finally, simple heat transfer correlations have been provided for the range of conditions covered here.

The effect of blockage ratio on the flow characteristics of power-law fluids across a square cylinder confined in a channel has been investigated for the range of conditions 1 ≤ Re ≤ 45, 0.5 ≤n ≤ 2.0 and β = 1/8, 1/6 and 1/4. Extensive numerical results on the individual and total drag coefficients, wake length, stream function, vorticity and power-law viscosity on the surface of the square cylinder are reported to determine the combined effects of the flow behavior index, blockage ratio and Reynolds number. The size of the wake region is influenced more by blockage than by power-law index. Similarly, drag is also seen to be more influenced by blockage ratio and the Reynolds number than that by the power-law index.

The effects of cross-buoyancy and of Prandtl number on the flow and heat transfer characteristics of an isothermal square cylinder confined in a channel has been investigated here. The numerical results have been presented for the range of conditions as: 1 ≤ Re ≤ 30, 0.7 ≤ Pr ≤ 100 (the maximum value of Peclet number being 3000) and 0 ≤ Ri ≤ 1for a fixed blockage ratio of 0.125. The overall drag and lift coefficients, local and average Nusselt numbers and the representative streamline and isotherm plots are presented to elucidate the role of Reynolds number, Prandtl number and Richardson number. The drag coefficient is found to be less sensitive to the Richardson number than the lift coefficient.