Higher Values Of Re Research Articles

Exploring shape and size variations significance in hybrid nanofluid flow via rotating porous channel

AbstractThe current study investigates the thermal performance characteristics of metallic (Cu) and non‐metallic (TiO2) nanoparticles (NPs), considering variations in their shapes and sizes. Specifically, analysis is conducted for four distinct stable shapes of NPs. A hybrid model is developed to analyze the influence of rotating porous walls on the system, particularly focusing on the impact of the permeable Reynolds number and NPs within a specific range of , in conjunction with a Newtonian fluid under the influence of magnetohydrodynamics (MHDs). Additionally, we examine the phenomena of expansion/contraction in heat and mass transfer enhancement with chemical reactions. The governing partial differential equations (PDEs) are transformed into nonlinear differential equations using the help of similarity transformation. A 4th‐order Runge–Kutta method (RK), coupled with the shooting technique, is employed as a mathematical strategy to numerically solve these nonlinear differential equations. Boosting the values of 𝐾𝑐𝑟 from 2 to 10 enhances the mass transfer rate between both porous channels. Higher values of 𝑅𝑒, 𝑀, and 𝑅 lead to increasing skin friction coefficients for both porous channels. Raising the values of both NP volume fractions ( from 1% to 5% results in enhanced heat transfer rates particularly for much better in platelet‐shaped NPs as compared to other shapes such as spherical, brick, and cylinder. Larger values of 𝛼, M, and Re cause the radial velocity profile to exhibit opposite behaviors in the middle of the wall and momentum boundary layer thickness.

Fluid-structure interaction induced mixed convection characteristics in a lid-driven square cavity with non-Newtonian power law fluids

The present study aims to numerically explore Fluid-Structure Interaction (FSI) induced mixed convection characteristics in a square cavity filled with a non-Newtonian power-law fluid. The side walls of the cavity under consideration are subjected to constant low temperature having motion in opposite directions while the insulated top wall and the bottom hot wall are kept stationary. A flexible fin is mounted on the bottom wall that essentially serves as a passive flow modulator. To solve the transient flow, thermal, and stress fields, the FSI problem is presented in an arbitrary Lagrangian-Eulerian framework employing the Galerkin finite element method. Different non-Newtonian fluids are represented by the power-law index (n) varied within the range, of 0.6 ≤ n≤ 1.4. Besides, the dynamic as well as mixed convection condition of the flow is analyzed by variation of Reynolds number (100 ≤ Re ≤ 300) and Richardson number (0.1 ≤ Ri ≤ 10.0) respectively. System characteristics have been evaluated in terms of streamline and isotherm contours, spatial and time-averaged Nusselt number as well as Normalized Nusselt number in regard to the “No Fin” case. The outcome of the present study reveals that the efficacy of a flexible fin for a given system depends on both the system dynamic condition (Re) and the mixed convection regime (Ri). The presence of a flexible fin has been found to have positive impact on heat transfer performance for both the shear-thinning and shear-thickening fluids for higher values of Re and Ri. However, for lower values of Re, the inclusion of a flexible fin has been found to adversely affect the heat transfer performance for shear-thickening fluids. Moreover, the thermal field exhibits periodic oscillation properties at Ri = 10, which can be attributed to the induced motion of the flexible fin. This phenomenon has been further elucidated through Power Spectrum Analysis. Results obtained in the present study might provide valuable insights into FSI-induced mixed convection with non-Newtonian fluids having versatile industrial applications such as solar thermal collectors with strategically positioned passive flexible flow modulators.

Mixed convection within trapezoidal-wavy enclosure filled with nano-encapsulated phase change material: Effect of magnetohydrodynamics and wall waviness

The present work investigates the mixed convection of nano-encapsulated phase change material (NEPCM) inside a trapezoidal-wavy cavity subjected to a magnetic field. The mixed convection results from the movement of the upper lid of the cavity and the temperature difference between the inclined cold side walls and the hot bottom wavy wall. The main goal of this study is to address the impact of wall waviness and the magnetic field on mixed convection on a disclosure filled with NEPCM. The governing equations representing the investigated case were solved by Galerkin finite element method (GFEM). The influences of lid velocity (Re = 1–1000), bottom wall undulation number (N = 1–4), and magnetic field strength (Hartmann number (Ha) = 0–100) on the thermal behavior and the flow patterns were examined and reported. The results revealed that the mean Nusselt number is directly proportional to the lid velocity (Re), whereas it is reverse proportional to the bottom wavy undulation number (N) and the magnetic field strength (Ha). The higher values of Re (e.g., Re = 1000) could lead to a 300% enhancement in local Nu values compared to those of lower Re values (e.g., Re = 1). At Re = 1000, increasing Ha from 0 to 100 and N from 1 to 4 reduced the mean Nusselt number by 53% and 30%, respectively. According to the findings of the present study, it is recommended that heat transfer augmentation should eliminate both the waviness of the bottom wall and the magnetic field since they hinder the free and mixed convection flow.

A NUMERICAL FORMULATION FOR THE SIMULATION OF HIGHLY HETEROGENEOUS POROUS MEDIA

Although it is a tradition to investigate porous media flow with the aid of Darcy's law, there are several applications in which heterogeneity makes this approach inadequate. Carbonate reservoirs found in the pre-salt layer in Brazil are examples of highly heterogeneous naturally fractured formations, with severe variations in their petrophysical properties. Rocks submitted to acidifying treatments are another example of highly heterogeneous porous media, where, by the injection of an acid system in the rock matrix, wormholes (highly conductive channels) are created. In this work, we numerically compare the employment of Darcy's equation with a more general formulation based on the average conservation equations for highly heterogeneous porous media. The coupled continuity and momentum equations are solved employing the open source software OpenFOAM. We apply the new formulation to three cases. The first is more academic, followed by two more applied situations associated with 2D and 3D flows. Different values of the Reynolds number (Re) and different permeability ratios were tested. Since the pressure drop was imposed, an error measure based on the flow rate was computed. We show that higher values of Re and permeability ratios lead to more discrepant results between the two approaches. Analyzing the Brinkman model for one of the cases, which takes into account diffusive effects, we found that the error with respect to the complete model, which in addition considers inertial effects, decreases but is still significant. Hence, the classical extension of the Darcy model, namely Brinkman and Forchheimer, cannot handle alone the situations of high Re and/or high heterogeneity, since both effects neglected in the Darcy model are important. As a consequence, a formulation that generalizes Darcy's law is required for more accurate results in these cases.

Analytical investigation of jet impingement solar air heater with dimple-roughened absorber surface via thermal and effective analysis

In this study, the thermal and effective efficiencies (ηthe and ηeff, respectively) of a dimple-roughened jet impingement solar air heater (DRJISAH) are analytically examined. The analysis is performed based on the following conditions: Reynolds number (Re) = 3000–24000; solar irradiance (Isr) = 700–1000 W/m2; dimple height ratio (ed/Dhd) = 0.016–0.031; dimple pitch ratio (pd/Dhd) = 0.269–0.810; arc angle (αd) = 30°–75°. An enhancement in ηthe by 18%–29% is achieved, which is corresponding to the ηthe of a jet impingement solar air heater. The ηeff of a DRJISAH is greater than that of a flat-plate solar air heater (FPSAH). However, at high values of Re, the useful thermal energy gain is dominated by frictional losses in the duct; thus, the FPSAH has a higher ηeff value than the DRJISAH. The optimum ηthe and ηeff for the DRJISAH are 74% and 70%, respectively, at ed/Dhd = 0.031, pd/Dhd = 0.269, αd = 60°, and Isr = 1000 W/m2. In addition, each dimple parameter is plotted against Re to obtain the best ηeff for the specified Re.

Impacts of Heterogeneity on Aquifer Storage and Recovery in Saline Aquifers

AbstractAquifer storage and recovery (ASR) involves the injection, and later extraction, of freshwater into aquifers, which often contain saline groundwater. Mixing between the fresh injectant and native saltwater often leads to part of the injectant becoming unrecoverable, thereby impacting ASR performance. This study explores freshwater‐saltwater mixing within ASR operations arising from aquifer heterogeneity using Monte Carlo analysis of 2D‐axisymmetric, density‐dependent flow and transport models. Logarithmic hydraulic conductivity (lnK) distributions are generated using either two‐point statistics or higher‐order connectivity features. Results show that higher variance in lnK leads to stronger freshwater‐saltwater mixing, which lowers the recovery efficiency (RE; i.e., ratio of extracted to injected freshwater). On average, the lowest RE values were obtained from lnK fields with connected high‐K features, across all ASR cycles. In contrast, RE values from lnK fields with connected low‐K features were typically the highest, at least where buoyancy was considered. The impact of aquifer heterogeneity on RE reduces with subsequent ASR cycles. Buoyancy was a major factor in lowering RE regardless of the adopted heterogeneity model. Heterogeneity tended to mitigate the adverse impacts of buoyancy, leading to some heterogeneous cases having higher RE values than the corresponding homogeneous case. These results highlight the importance of understanding buoyancy effects and subsurface heterogeneity (including the connectivity of geological structures), and interrelationships thereof when assessing the feasibility of multi‐cycle ASR in heterogeneous saline aquifers.

Analysis of thermo-hydraulic characteristics for flow of MWCNT-Fe3O4/H2O hybrid nanofluid through a wavy channel under magnetic field

We investigate computationally the transport characteristics for flow of MWCNT-Fe3O4/H2O hybrid nanofluid through a wavy channel under the influence of an externally applied magnetic field. The flow and temperature fields are analyzed in terms of streamlines, isotherms, average Nusselt number ([Formula: see text]), magnetic enhancement ratio ( ERm), and magnetic performance factor ( PFm) for the following range of parameters: 100[Formula: see text]Re[Formula: see text]500, 0[Formula: see text] Ha[Formula: see text]10, and 0% [Formula: see text]0.3%. The strength of the reverse flow in the recirculatory zones decreases with Ha, and beyond a critical Ha, the flow becomes attached even in the diverging part of the channel. The hot spot intensity near the walls decreases and hence, the value of [Formula: see text] increases with the increase in volume fraction of nano-particles and Ha. The rate of increment of [Formula: see text] is steeper at lower values of Ha. It further reveals that PFm monotonically decreases with Ha for lower Re ( = 100). For higher values of Re, PFm decreases with Ha for its lower and higher values, while for the intermediate range of Ha, PFm increases with Ha.

Effect of Pin Fins on Jet Impingement Heat Transfer Over a Rotating Disk

Abstract Many engineering applications consist of rotating components that experience high-heat load. Applications like the gas turbine engine consist of rotating disks and the study of heat transfer over such rotating surfaces is of particular interest. In the case of gas turbines, the disk also needs to be protected from the ingress of hot turbine gases caused by the low-pressure region created due to the radially outward pumping of fluid close to the rotating surface. The present experimental study investigates the effects of introducing pin-fins on heat transfer over surface of a rotating gas-turbine disk. The experiments were conducted at rotational Reynolds numbers (ReR) of 5487–12,803 based on the disk diameter (D) and jet Reynolds numbers (Re) of 5000–18,000 based on the jet diameter. The effects of nozzle to target spacing (z/d=2−6), eccentricity of impingement (ε = 0−0.67), angle of impingement—both toward and away from the center (θi and θo=0 deg−20 deg), and the pin fin height (Hf=3.05 mm−19.05 mm) were studied. Steady-state temperature measurements were taken using thermocouples embedded in the disk close to the target surface, and area average Nusselt number (Nu) was calculated. The results have been compared with those for a smooth aluminum disk of equal dimensions and without any pin-fins. The average Nu was significantly enhanced by the presence of pin-fins. The enhancement was higher for lower values of Re, and the maximum enhancement was found to be 3.9 times that of a smooth disk for Re=5000. In the impingement dominant regime, the effect of disk rotation was minimal for a smooth disk, but the heat transfer increased with rotational speed in case of pin-fins. There was no impact of eccentricity on Nu for ε = 0 and 0.33. For ε = 0.67, the maximum reduction in enhancement over a smooth surface (21.95%) was observed when compared with coaxial impingement for stationary impingement for Re=18,000 and z/d=4. The effect of inclination angle was insignificant, and no clear trend could be established. Higher heat transfer rates were observed for z/d=6 with the increasing Re, and this effect diminished with the increase in the rotational speed. With the increase in pin-fin height, especially at higher values of Re, there was in increase in the value of Nu. Qualitative visualization of flow field has been performed for smooth and the pin-fin case using the commercial simulation package Ansys Fluent to further understand the flow features that result in the heat transfer enhancement.

Effect of amplitude of walls on thermal and hydrodynamic characteristics of laminar flow through an asymmetric wavy channel

In this work, we investigate the hydrothermal characteristics for laminar forced convective flow of water through sinusoidal asymmetric wavy channel of three types: linearly increasing amplitude channel (LIAC), linearly decreasing amplitude channel (LDAC) and constant amplitude channel (CAC). The computed velocity and temperature fields are analyzed by varying the Reynolds number (Re) and slope (A) of the linearly varying amplitude in the following ranges: 5 ≤Re≤ 200 and 0.02≤A≤ 0.04. The value of average Nusselt number is almost independent on the geometry of the channel at lower values of Re and A. At higher Re values, the average Nusselt number is the highest for LIAC followed by LDAC, and CAC. The combined effects of heat transfer increase in the wavy channel compared to plane channel and the associated pumping power is assessed using performance parameter (PF). For lower Re values the highest PF is obtained for CAC. For higher values of Re the PF is the largest for LDAC at A = 0.02 and 0.03, and the value of PF for A = 0.04 is the highest for CAC.

Reynolds number effect on the concentration and preferential orientation of inertial ellipsoids

Direct numerical simulations are performed to study the influence of the flow Reynolds number (Re) on the dynamics of inertial, ellipsoidal particles in a turbulent wall-bounded flow. In wall units, the time required for the particle distribution to reach a statistically steady state increases with Re. Once the distribution reached a statistically steady-state, a more uniform concentration profile is observed for higher values of Re, regardless of particle shape, but with a noticeable influence of particle inertia. Finally, in the near-wall region, preferential orientation of all ellipsoids is modified when Re increases, with a strong dependence on the ellipsoids characteristics.

Numerical Thermal Analysis of a Hot Noncircular Rotating Cylinder in the Presence of a Magnetic Field

Abstract In this paper for the first time, a Lattice Boltzmann Simulation is performed to analyze the simultaneous effects of a hot rotating elliptic cylinder and the magnetic field on the mixed convection flow in a square enclosure. Complicated flow patterns and isotherm plots are found and analyzed in the concentric annulus between the internal elliptic cylinder and the outer square enclosure. Results indicate that increasing the Reynolds number, instantaneous averaged Nusselt number of the enclosure and its oscillation amplitude increase, while decrease with increasing the Hartmann number especially at its lower values. Furthermore, response surface method is adopted to find the optimal location of the elliptic cylinder. Response surface optimization results reveal that the average Nusselt number shows a decreasing–increasing trend with increasing both nondimensional parameters of cylinder center (Xc, Yc). Finally, the optimal location of the elliptic cylinder for the maximum heat transfer rate is obtained as Xc = 0.65 and Yc = 0.35. Moreover, a comparative study is performed to evaluate the heat transfer effects of the elliptical cylinder rotation as compared to circular cylinder. It was found that the elliptical cylinder rotation has a significant effect on the heat transfer enhancement, especially at high values of Re and Ha. As an example, the heat transfer rate for the elliptical cylinder at Re = 200 is increased by 13% and 34% as compared to the circular cylinder at Ha = 50 and 100, respectively.

Heat Transfer Correlations for Star-Shaped Fins

Star-shaped fins are a newer type of fin for which correlations for heat transfer and pressure drop do not yet exist in the literature. Therefore, correlation equations for air-side heat transfer and pressure drop in a finned heat exchanger with star-shaped stainless-steel fins in staggered arrangement were developed in this work. To obtain these correlations, a numerical analysis of the basic heat exchanger geometry and another 21 variants of heat exchanger geometry was performed using computational fluid dynamics, and then the results of laboratory tests of a model of heat exchangers with star-shaped fins were used. In the numerical analysis, the fin pitch, the fin thickness, and the air velocity at the inlet to the heat exchanger were varied. The Nusselt (Nu) and Euler (Eu) numbers were determined for each variation analyzed. Initial correlations for Nu and Eu were derived using the least-squares deviation method. The correlation coefficients thus obtained were adjusted to agree with the results of the laboratory tests. The deviation of the final obtained correlation for Nu from the experimental test results was up to 10% in the range of Re < 3500, whereas for higher values of Re, the deviation was less than 2%. The Eu correlation deviated from experimental results up to 19% in the range of Re < 4000, whereas in the range of Re > 5600, the deviation was less than 1%. The correlations were valid in the range 2000 < Re < 16,000.

Entropy generation and heat transfer analysis in power-law fluid flow: Finite difference method

In this article entropy generation analysis for unsteady laminar free convection flow of power-law fluid is investigated. Fluid flow is in the presence of thermal radiation and magnetic field. The flow and heat transfer are governed by coupled system of PDE's. System of partial differential equation (PDE's) governs the continuity, momentum and energy equations. Using suitable dimensionless parameters, the system of PDE's is transformed into dimensionless form. Numerical computations made employing finite difference method (FDM). This method converts the nonlinear PDE 's to simple algebraic equations and by using variational technique the approximate solution is obtained technique. Impacts of important flow variables on velocity, skin friction and Nusselt number are shown graphically. Skin friction and Nusselt number are discussed for different pertinent flow variables. Velocity, temperature, entropy and Bejan number variations through important variables are discussed in the form of graphs. The obtained results show that velocity decays against Re, Ha and Pr. Temperature is enhanced for higher values of Re, Ec, Tr and Gr. For higher estimation of Ec entropy of the system enhance while show opposite behavior for the Bejan number. Entropy of system boosts for strong magnetic field.

Hydrothermal and entropy generation specifications of a hybrid ferronanofluid in microchannel heat sink embedded in CPUs

The objective of this numerical work is to evaluate the first law and second law performances of a hybrid nanofluid flowing through a liquid-cooled microchannel heatsink. The water-based hybrid nanofluid includes the Fe3O4 and carbon nanotubes (CNTs) nanoparticles. The heatsink includes a microchannel configuration for the flow field to gain heat from a processor placed on the bottom of the heatsink. The effects of Fe3O4 concentration (φFe3O4), CNT concentration (φCNT) and Reynolds number (Re) on the convective heat transfer coefficient, CPU surface temperature, thermal resistance, pumping power, as well as the rate of entropy generation due to the heat transfer and fluid friction is examined. The results indicated higher values of convective heat transfer coefficient, pumping power, and frictional entropy generation rate for higher values of Re, φFe3O4 and φCNT. By increasing Re, φFe3O4and φCNT, the CPU surface temperature and the thermal resistance decrease, and the temperature distribution at the CPU surface became more uniform. To achieve the maximum performance of the studied heatsink, applying the hybrid nanofluid with low φFe3O4and φCNT was suggested, while the minimum entropy generation was achieved with the application of nanofluid with high φFe3O4and φCNT.

Flow through three-dimensional self-affine fractures

We investigate through numerical simulations of the Navier-Stokes equations the influence of the surface roughness on the fluid flow through fracture joints. Using the Hurst exponent $H$ to characterize the roughness of the self-affine surfaces that constitute the fracture, our analysis reveal the important interplay between geometry and inertia on the flow. Precisely, for low values of Reynolds numbers Re, we use Darcy's law to quantify the hydraulic resistance $G$ of the fracture and show that its dependence on $H$ can be explained in terms of a simple geometrical model for the tortuosity $\tau$ of the channel. At sufficiently high values of Re, when inertial effects become relevant, our results reveal that nonlinear corrections up to third-order to Darcy's law are aproximately proportional to $H$. These results imply that the resistance $G$ to the flow follows a universal behavior by simply rescaling it in terms of the fracture resistivity and using an effective Reynolds number, namely, Re/$H$. Our results also reveal the presence of quasi-one-dimensional channeling, even considering the absence of shear displacement between upper and lower surfaces of the self-affine fracture.

Nanoparticles for improving the efficiency of heat recovery unit involving entropy generation analysis

The present article aims to suggest new thermal unit as heat recovery system to augment the available energy. Hot gas flows inside the inner pipe and the operating fluid in annulus region is nanofluid (CuO-water). Helical tape with various revolution number (N) was employed to augment the fluctuations of fluid and reduce the boundary layer thickness. Range of Reynolds number (Re=4000 to 20,000) indicates turbulent regime. To involve such range of Re, K-ɛ approach has been utilized and its validity was reported. Achieving to greater useful energy happens if the irreversibility of system minimized. This function has two terms: frictional term (Sgen,f) and thermal term (Sgen,th). The thermal term is higher than frictional term and it should be considered as main source of irreversibility. With augment of rotational speed as a result of higher values of Re and N, velocity gradient goes up but thinner boundary layer will be generated. So, with rise of such parameters, temperature gradient declines and residence time enhances which results in better mixing of fluid. So, two scrutinized factors have favorite effect on Sgen,th and considering greater values of them leads to lower thermal irreversibility. Also, growth of these factors makes Sgen,f to increase which is unfavorable effect. As N augments from 3 to 5, the value of Sgen,f enhances about 47% but Sgen,th reduces about 42.47% when Re=5000. Also, with selecting higher N from 3 to 7 when Re=2000, frictional entropy augments about 128.95% while Sgen,th reduces by 35.97%. Sgen,th faces 39.14% decrement if Re goes up when N = 3 while with same change, the value of Sgen,f augments to 7.27 times greater value.

Heat transfer and pressure drop in a sinus blowing of copper oxide- water non-Newtonian nanofluid in a sudden expansion process in the presence of variable magnetic field: a numerical solution

ABSTRACT In the current article, the effect of nanofluid blast on the forced convection heat transfer in the intra-channel turbulent flow with a sudden expansion is investigated. The different cases of Newtonian, non-Newtonian, and incompressible fluids have been studied. The effects of non-Newtonian fluid index, magnetic field, nanoparticle volume fraction and nanofluid blowing frequency parameters on the pressure drop and heat transfer in the intra-channel flow have been reviewed. The simulation was performed using finite volume method as the solution strategy. The results revealed that higher values of Re and nanoparticles volume fraction resulted in the Nusselt number increasement. Also, increasing the magnetic field and decreasing the non-Newtonian fluid index increased the forced heat transfer coefficient and subsequently the Nusselt number. The results showed that the sinus velocity caused to increase the rate of the heat transfer and slightly lower friction coefficient. However, higher frequencies caused increasing of heat transfer and friction coefficient. Finally, it was founded that higher values of the Re had the most influence on the performance of the system and the magnetic field and sinus velocity were in the next step.

Thermo-hydraulic and entropy generation analysis for magnetohydrodynamic pressure driven flow of nanofluid through an asymmetric wavy channel

PurposeThe purpose of this paper is to analyze the thermal, hydraulic and entropy generation characteristics for the magneto-hydrodynamic (MHD) pressure-driven flow of Al2O3-water nanofluid through an asymmetric wavy channel.Design/methodology/approachGalerkin finite element method is used to solve the governing transport equations numerically within the computational domain using the appropriate boundary conditions. The temperature and flow fields are computed by varying Reynolds number (Re), Hartmann number (Ha) and nano-particle volume fraction (ϕ) in the following range: 10 ≤ Re ≤ 500, 0 ≤ Ha ≤ 75 and 0 ≤ ϕ ≤ 5%.FindingsThe formation of the recirculation zones in the wavy passages, the size of it and the strength of the vortices formed can be modulated by the application of the magnetic field. The overall heat transfer rate increases with Ha for all ϕ both for a lower and higher regime of Re although the enhancement is more for lower values of Re and nanofluids as compared to base fluid and for intermediate values of Re, the effect of a magnetic field is almost insignificant. The magnetic performance factor (PFmagnetic) decreases with Ha although the rate of decrement varies with Re. The increase ϕ also enhances PFmagnetic especially at lower and higher values of Re. The addition of nano-particle enhances the entropy generation at lower values of the Re, while the opposite effect is seen for higher values of Re.Practical implicationsThe present study has enormous practical relevance for the design of heat exchanger applied for solar collectors, process plants, textile and aerospace applications.Originality/valueThe combined effects on the heat transfer rate and the associated pressure drop penalty due to the applied magnetic field for the flow of nanofluid through an asymmetric wavy channel have not been reported to date. The effect of the magnetic field on the formation of recirculation zones and hot spot intensity in the asymmetric wavy channel has been examined in detail. The PFmagnetic is investigated first time for the MHD nanofluid flow through a wavy channel.

Enhancement of the Hydrodynamic Characteristics in Shell-and-Tube Heat Exchangers by Using W-Baffle Vortex Generators

Improving the hydrodynamic characteristics of STHECs (Shell-and-Tube Heat Exchanger Channels) by using BVGs (Baffle-type Vortex Generators) is among the common passive methods due to their proved efficiency. In this computational investigation, the same method is used to enhance the hydrodynamic behavior of STHECs, by inserting W-shaped Baffle-type Vortex Generators. The numerical model represented by the computational FVM (Finite Volume Method) is used to simulate and analyzed the considered physical model. The fluid used is air, its thermal physical properties are constant, turbulent, incompressible, and its temperature is 300 K at the inlet section of the STHEC. The flow velocity ( Uin ) and atmospheric pressure ( Patm ) are considered as boundary conditions at the entrance (x = 0) and exit (x = L) of the channel, respectively. The results showed that the friction coefficients were related to the pressure, velocity, and Reynolds number values. High values of Re yielded an acceleration of the fluid, resulting thus in increased pressure on the solid walls and augmented friction values.

Analysis of mixed convective heat transfer past an isoflux/isothermal sphere: influence of Prandtl number

Numerical simulations are conducted to illustrate the influence of Prandtl number on the mixed convection heat transfer past an isoflux/isothermal sphere. A spherical geometry higher order compact scheme (SGHOCS) is applied to obtain the velocity and temperature fields. The results are demonstrated in terms of velocity, contours of vorticity, streamlines and isotherms together with drag coefficient (CD), local Nusselt number (Nu) and mean Nusselt number () on the surface of the sphere in the range of Reynolds number (Re) from 1 to 200, Prandtl number (Pr) from 0.72 to 20 and Richardson number (Ri) from 0 to 2.0. We identify the critical Richardson number (Ricr) above which the flow separation is totally suppressed. The study reveals that for a particular value of Re, Ricr increases with Pr for isoflux case, whereas the opposite trend is observed for an isothermal case. The drag coefficient decreases with Re and Pr, while the same increases with Ri. Furthermore, the drag coefficient is larger for isothermal boundary condition when compared to isoflux boundary condition. Intuitively, it is found that for higher values of Re and Pr, the variation of with Ri is non-monotonic. Moreover, as Ri increases, the decrease in is larger for isothermal boundary condition when compared to isoflux boundary condition.