Developed Flow Region Research Articles

Thermo-hydraulic performance of concentric tube heat exchangers with turbulent flow: Predictive correlations and iterative methods for pumping power and heat transfer

This research addresses the problem of predicting the thermo-hydraulic performance of concentric tube heat exchangers (CTHE) under turbulent flow conditions, a critical aspect in energy-efficient industrial systems such as HVAC, power generation, and chemical processing. Existing studies often lack accurate predictive methods for balancing heat transfer performance with pumping power requirements. To tackle this issue, novel correlations and an iterative Newton–Raphson method were developed for predicting pumping power and heat transfer rates. Three-dimensional CFD simulations of a water-to-water counter-flow CTHE were conducted, with Reynolds numbers ranging from 4000 to 8000 for both the hot and cold fluids. The simulations employed the Reynolds-Averaged Navier–Stokes (RANS) equations with the k−ω SST turbulence model. The results demonstrated that increasing the Reynolds number enhances both heat transfer rates and pumping power, with the cold fluid requiring consistently higher pumping power. New correlations were developed to predict pumping power, capturing the impact of both entry and fully developed flow regions. These correlations showed an average error of less than 2.33% when compared with the CFD data. The iterative Newton–Raphson method for predicting heat transfer rates demonstrated high accuracy, with an average error of 0.66% for heat transfer rate, 0.03% for hot fluid outlet temperature, and 0.01% for cold fluid outlet temperature. Additionally, we identified optimal operating conditions for efficient cooling and heating based on the heat capacity ratio (Cr). The novelty of this work lies in the development of new, highly accurate predictive correlations and iterative methods for optimizing CTHE performance, going beyond existing literature by providing comprehensive insights into the relationship between pumping power, heat transfer efficiency, and flow conditions.

THE EFFECT OF PARTIAL SLIP ON THE SURFACE PRESSURE DISTRIBUTION IN A SLIGHTLY COMPRESIBLE FLOW DEVELOPMENT REGION IN THE BOUNDARY LAYER

The study of laminar incompressible fluid flow in the boundary layer revealed, even earlier, that the condition of complete adhesion of fluid particles to the surface (non-slip condition) of the moving body (half-plane) is not met in the flow development (formation) region. The assumption of constancy of the fluid velocity on the surface of a moving body, hence non-slip, leads, in the flow development region, to the complete absence of the normal component of the velocity field. And this contradicts the very concept of the flow development region, where there should be two velocity components - longitudinal (primary) and normal (secondary) ones. In the previous works of the authors, analytical solutions were obtained for the velocity field in the region of development of incompressible fluid flow in the boundary layer. Since the use of the incompressible fluid flow model is restricted by the Mach number, to further expand the speed range, the problem of the of slightly compressible fluid flow development region in the boundary layer was considered. It is analytically proven that all considerations regarding the impossibility of complete non-slip in the flow development region can be applied to a slightly compressible flow. Slight compressibility at the same time means the subsonic nature of the flow and the neglect of temperature effects due to friction. On the basis of a critical analysis of the existing approaches, which consider the flow of a fluid around a immobile plate in the framework of non-gradient flow (which is just impossible due to the lack of a mechanism for creating the motion of the fluid), it is shown that the system of equations is actually non-closed. For the region of flow development, where the longitudinal pressure gradient is not a constant value, one equation is missing. This equation, as in previous works, is obtained from the necessary condition for the extreme of the fluid rate functional. And although the complete solution for the longitudinal component of the velocity contains four constants of integration, to obtain the asymptotics near the solid surface it is sufficient to know only two quantities - the velocity and its first derivative (gradient). These values, as it turns out from the asymptotic solution, coincide with the case of incompressible flow, which allows us to expand the scope of the previously obtained results for a wider domain of Mach numbers, for example . And such values already correspond to the speeds of modern civil aircraft. The dimensionless distribution of pressure in the slightly compressible flow development region is presented and its significant heterogeneity is shown, which, in turn, indicates the importance of the obtained results.

Impact of sandpaper grit size on drag reduction and plastron stability of super-hydrophobic surface in turbulent flows

In this work, we experimentally investigated the impact of surface roughness on drag reduction as well as the plastron stability of superhydrophobic surfaces (SHSs) in turbulent flows. A series of SHSs were fabricated by spraying hydrophobic nanoparticles on sandpapers. By changing the grit size of sandpapers from 240 to 1500, the root mean square roughness height (krms) of the SHSs varied from 4 to 14 μm. The experiments were performed in a turbulent channel flow facility, where the mean flow speed (Um) varied from 0.5 to 4.4 m/s, and the Reynolds number (Rem) based on Um and channel height changed from 3400 to 26 400. The drag reduction by SHSs was measured based on pressure drops in the fully developed flow region. The plastron status and gas fraction (φg) were simultaneously monitored by reflected-light microscopy. Our results showed a strong correlation between drag reduction and krms+ = krms/δv, where δv is the viscous length scale. For krms+ < 1, drag reduction was independent of krms+. A maximum 47% drag reduction was observed. For 1 < krms+ < 2, less drag reduction was observed due to the roughness effect. And for krms+ > 2, the SHSs caused an increase in drag. Furthermore, we found that surface roughness influenced the trend of plastron depletion in turbulent flows. As increasing Rem, φg reduced gradually for SHSs with large krms, but reduced rapidly and maintained as a constant for SHSs with small krms. Finally, we found that as increasing Rem, the slip length of SHS reduced, although φg was nearly a constant.

Flow development region in the boundary layer: two-component molecular viscosity and partial slip

The subject of this study is the flow development region of laminar incompressible fluid flow in the boundary layer. This flow is an example where a direct application of the Navier-Stokes equations of gradient-free laminar incompressible fluid flow, in which the molecular viscosity is assumed to be a constant value independent of spatial coordinates, leads to a redefinition of the mathematical model. It is about the fluid boundary layer in the region of flow establishment in the motion problem of a semi-infinite plane, where the pressure gradient is zero. There is a situation when the number of equations is equal to three (two equations of momentum conservation and the equation of continuity), and the number of unknowns is equal to two - the number of the speed component. As a logical solution to the obtained inconsistency, it is proposed, as was already done for the problem of stationary motion of a plane and the problem of acceleration of a plane, to depart from the false statement about the constancy of molecular viscosity in the gradient-free boundary layer of an incompressible flow and consider molecular viscosity as a function of spatial coordinates. The need to consider the variable nature of molecular viscosity led to the discovery of another flaw in the Navier-Stokes theory. This non-trivial flaw was discovered during the application of the original numerical analytical method for solving the flow development region problem. The Navier-Stokes equations are supplemented by boundary conditions. The most important condition is the condition of fluid non-slipping on the surface of a solid body, which, by the way, does not follow any physical law. As a result, on the surface of a half-plane (or a moving body), the component of the velocity, which coincides with the direction of motion, has a constant value equal to the velocity of the body. It immediately follows from the continuity equation that the normal derivative of the normal component of the velocity must be equal to zero along the surface of the plane (body), since the longitudinal derivative of the velocity becomes zero. However, it is quite obvious that the velocity component normal to the surface of the plane (body) changes across the boundary layer in the region of current development, which indicates the presence of a normal gradient (both components) of the velocity. The conflict or contradiction is overcome by moving away from the generally accepted condition of non-slipping to the condition of partial non-slipping, or essentially the presence of sliding. Even with the sudden braking of any vehicle, the complete stop does not occur instantly, but after some finite time and distance, so in the case of the motion of a body in a stationary fluid, there is not an instant sticking, but a gradual one - from complete sliding, when a particle of liquid has just met a moving plane (body), to complete non-slipping at the end (and further) of the flow development region. Research methods. This work uses purely theoretical methods based on the use of calculus of variations, laws of physics, and ideas from everyday life. Conclusions. An improved model of a viscous Newtonian fluid in the area of flow development in the boundary layer was derived. On the basis of assumptions about the variable nature of the molecular viscosity, which already has two components, and the departure from the non-slipping condition, analytical solutions for both components of the velocity and both components of the molecular viscosity were obtained. A comparison of the obtained results with the results of other studies is presented.

Flow velocity adjustment in a channel with a floating vegetation canopy

Floating vegetation with unanchored and connected roots can completely cover the water surface of rivers, ditches, and streams. Eichhornia crassipes is a typical macrophyte with a stable network of roots that is present in aquatic environments, forming a complicated flow velocity adjustment. This study constructed model floating canopies and real E. crassipes canopies to investigate flow velocity adjustment and verify a new proposed velocity model. Laboratory experiments showed that flow velocity was modified in both the streamwise (x) and vertical (z) directions and impacted by the mean channel velocity, canopy density, and relative flow depth. The penetration distance δe of the Kelvin–Helmholtz vortices penetrating into the floating canopy increased to its maximum beyond the flow adjustment distance XD, where XD was the distance from the canopy leading edge to the position at which the flow was fully developed. The thickness of the bed boundary layer δb was related to the vegetation drag (FD(x)), the bed shear stress (τb(x)), and the height of the free-flow region below the canopy hg. New estimators for δe and δb were proposed and validated for floating canopies. Combined with the new estimators (δe and δb), flow continuity equation, momentum equation and four-layer divided method, a new analytical model was proposed to predict vertical profiles of velocity within and below a floating canopy in both the flow adjustment region (XD > x > 0) and fully developed flow region (x > XD). Fourteen groups of velocity data from this study and published literature were used to verify the proposed model. The predicted vertical profiles of velocity in flow adjustment and fully developed flow regions agreed with measurements under a wide range of vegetation and flow conditions, suggesting that the proposed model was capable of accurately predicting velocity profiles in a channel with a floating canopy. Finally, the model was validated in a channel with a real E. crassipes canopy. A comparison between predicted and measured velocities confirmed that the new model is valid for application in a channel with real floating macrophytes.

Developed and quasi-developed macro-scale flow in micro- and mini-channels with arrays of offset strip fins

We investigate to what degree the steady laminar flow in typical micro- and mini-channels with offset strip fin arrays can be described as developed on a macro-scale level, in the presence of channel entrance and sidewall effects. Hereto, the extent of the developed and quasi-developed flow regions in such channels is determined through large-scale numerical flow simulations. It is observed that the onset point of developed flow increases linearly with the Reynolds number and channel width but remains small relative to the total channel length. Furthermore, we find that the local macro-scale pressure gradient and closure force for the (double) volume-averaged Navier–Stokes equations are adequately modeled by a developed friction factor correlation, as typical discrepancies are below 15% in both the developed and developing flow region. We show that these findings can be attributed to the eigenvalues and mode amplitudes, which characterize the quasi-developed flow in the entrance region of the channel. Finally, we discuss the influence of the channel side walls on the flow periodicity, the mass flow rate, as well as the macro-scale velocity profile, which we capture by a displacement factor and slip length coefficient. Our findings are supported by extensive numerical data for fin height-to-length ratios up to 1, fin pitch-to-length ratios up to 0.5, and channel aspect ratios between 1/5 and 1/17, covering Reynolds numbers from 28 to 1224.

Hydrodynamic modeling of coaxial confined particle-laden turbulent flow

A new particle subgrid scale model is proposed to consider the effect of gas flow on particle motions. Multiphase gas-particle turbulent flow is modeled by a second-order moment two-phase turbulence model involving a four-way coupling strategy to describe the interactions among gas-particle, particle-gas and particle-particle collisions. A large eddy simulation algorithm is developed to solve the hydrodynamic parameters of confined swirling and non-swirling particle-laden flow in coaxial chamber. Results show that predictions are well agreed with experimental data. Vortex structures and vortices distributions of gas and particle flow are quietly different. Coherent structures of swirling particle flows are not observed, and length of recirculation region is almost one quarter of non-swirling flow. Compared to developed flow region of non-swirling flow, standard deviation values of granular temperature at near entrance decreased by 5.5 times. Dominant frequencies of particle number density of non-swirling and swirling flows are 18 Hz and 10 Hz. Particle dispersions exhibit anisotropic characteristics, and their distributions are not in accordance with the normal distribution. The 2D turbulence model needs to be further improved due to the failure of describing vortex stretch in this job.

Flow periodicity analysis in an additively manufactured metal microchannel heat transfer device using micro-PIV

The flow periodicity in an additively manufactured microchannel heat transfer device is analysed using the micro-particle image velocimetry technique. A metal offset strip fin (OSF) microchannel is additively manufactured using laser powder bed fusion to overcome the limitations of conventional production techniques in manufacturing small complex features. This study demonstrates the capability of measuring the velocity field in an OSF microchannel up to 1 mm deep with a resolution of 10μm and a velocity uncertainty smaller than 0.5% for laminar flows with a Reynolds number below 10. Higher measurement uncertainties are encountered in regions close to the channel walls due to particle deposition. A methodology aiming to evaluate and minimise the uncertainties is presented. The experimentally obtained velocity fields are compared to a numerical simulation of the flow in the offset strip fin microchannel. The results verify that flow periodicity can be observed and the extent of the flow development region can be studied. Nevertheless, in regions with a large velocity gradient, a considerable uncertainty on the velocity measurements exists due to manufacturing imperfections.

ESTIMATION OF HYDRODYNAMIC ENTRY LENGTH IN MEMBRANE FLOW CHANNELS WITH PERIODIC OBSTRUCTIONS USING CFD

This paper includes analysis of the flow development region in spacer-filled membrane channels using Computational Fluid Dynamics (CFD) technique. Various spacer geometric parameters such as filament spacing, thickness, spacer placement and filament shape, and Reynolds number are investigated to determine their effect on flow pattern, shear stress, and entrance length. The CFD simulations show that when the flow is steady, the fully developed and repeating velocity profiles are achieved within 6-7 filaments. The entrance length in case of steady flow, in many spacers, is therefore found almost the same as in the empty channel. In unsteady flow, the transient effects are noticed after sufficient number of filaments. The entrance lengths in different spacers, hence, are found significant. The filament shape also has a strong influence on flow structure and shear stress. In spacer with square-shaped filament and spacing 2, the flow is steady up to Reynolds number of 500 whereas in triangular filament the critical Reynolds number is 100-300, indicating it to be more suitable for producing time-dependent fluid flow and enhancing heat and mass transfer in membrane channels.

Numerical analysis of a developing turbulent flow and conjugate heat transfer for molten salt and liquid sodium in a solar receiver

• Temperature uniformity within a solar receiver using guide vanes was investigated. • Friction coefficient and Nu number were reported for liquid sodium and molten salt. • The effect of wall heat flux on fluid flow and heat transfer was studied. A numerical analysis of the developing flow and conjugate heat transfer in a solar receiver tube with a three-blade guide vane at the tube inlet was performed to investigate the effect of guide vane and working fluid on the flow and temperature distribution in a solar receiver tube subjected to the boundary condition of the non-uniform wall heat flux. Three dimensional Navier-Stokes, energy, and Laplace equations were solved numerically using Fluent code for the molten solar salt and liquid sodium as the working fluids. The SST k-ω turbulence model was used to predict the flow behavior inside the tube. The values of the friction coefficient and Nu number predicted by the numerical analysis were compared to and validated against experimental correlations from the literature. The numerical results show that a significantly lower pressure drop, and more uniform temperature distribution in the receiver tube are achievable by using the liquid sodium, compared to the molten solar salt. Application of a three-blade guide vane improves temperature uniformity across the receiver tube cross-section, but increases pressure drop in the developing flow region and, thus the overall pressure drop in the tube. The increase in the pressure drop is attributed to the swirling flow and higher friction coefficient compared to the fully developed flow for both working fluids studied in this work.

Analytical model for predicting the lateral profiles of velocities through a partially vegetated channel

In an open channel, an emergent canopy of vegetation enhances local resistance, producing a complicated velocity distribution within and around the canopy. Laboratory experiments were performed to understand the flow velocity variations in a partially vegetated channel, revealing both streamwise and lateral velocity variations as the flow entered the canopy. An analytical model was proposed to predict the lateral velocity profiles across the vegetated region and bare channel in both the flow adjustment region and the fully developed flow region. The flow velocity variations in the streamwise and lateral directions were parameterized and included in the new proposed model, allowing the model to capture both the streamwise and the lateral velocity variations. Twenty sets of experimental data from our experiments and data from published studies were used to verify the new model. The predicted velocity profiles exhibited good agreement with the measurements under a wide range of vegetation and flow conditions, suggesting that the proposed model is capable of accurately predicting the velocity profiles in a partially vegetated channel. Finally, the proposed model was applied to evaluate the critical frontal area per canopy volume at which Kelvin–Helmholtz vortices form along the emergent canopy side edge. With the same spatially averaged velocity, the critical frontal area exhibited no dependence on stem diameter.

Mixed convection heat transfer utilizing Nanofluids, ionic Nanofluids, and hybrid nanofluids in a horizontal tube

Mixed convective heat transfer and pressure drop penalty of nanofluids flow in an isothermal horizontal tube are numerically examined in developed flow region. The study examines three types of nanofluids, simple nanofluids ([Water]/ Al2O3, TiO2, and Cu), Hybrid nanofluids ([Water]/ Al2O3 + Cu), and Ionic nanofluids ([C4mim] [NTf2]/ Al2O3). Richardson number is varied from 0.016 to 2, and Reynolds number is varied from 500 to 2000. The governing equations are solved numerically via the finite volume method by using the SIMPLER algorithm computer code. The computer code is validated by comparing the average Nusselt number with the experimental published data, a good agreement was observed. Performance evaluation criterion (λ) is introduced to evaluate the heat transfer enhancement gain of nanofluid usage to pressure drop penalty at different concentrations of nanoparticles. Results for nanofluids show that the maximum enhancement of the average Nusselt number is 15.5 % for Al2O3 with a concentration of 2% at Richardson number of 0.016. However, for hybrid nanofluids, no enhancement is noticed. Ionic nanofluid results are promising, as the Nusselt number increases significantly (by 37%) with a concentration of 2.5%. Finally, findings of various types of nanofluids investigated in the same numerical conditions are reported and compared.

Numerical analysis on particle dispersions of swirling gas-particle flow using a four-way coupled large eddy simulation

Subgrid-scale (SGS) gas flow and particle-particle collision are closely related to the particle dispersions in swirling gas-particle flow. However, investigations which consider the four-way coupled large eddy simulation (LES) are scant. The objective of the present contribution is to propose firstly a novel particle SGS kinetic turbulent energy-granular temperature (SGS-kp-θp) model to describe the interactions of gas-particle, particle-gas and particle-particle collision based on the kinetic energy of granular flow. Reynolds stresses transport equations are modeled by the second-order moment strategy. Numerical analysis on particle hydrodynamics that effected by particle diameters using LES is carried out and validations by both experiment and OpenFoam software reported are in good agreements. Results of this study showed flow structures of micro and larger size particles ranging from 12.5 μm to 105 μm significantly differ in the vortex evolutions and coherent structures. SGS particles collision incurs on the additional particle energy dissipations. Micro-particle contributes to the formation of stable vortex indicating the excellent followability and incapable of exerting counteractivity on gas flow. SGS axial interactions between gas and medium size particle of dp = 30 μm is approximately 3.5 times larger than those of largest size particle of dp = 105 μm. Moreover, maximum energy dissipation caused by largest particle collision is 1.6 times larger than that of micro particle at developing flow region.

Counterflow HE analysis of Cu and SiO2 nanofluids in the developing flow region

AbstractThree concentrations of 0.2, 0.6, and 1.0 vol.% Copper/25 nm and silica/22 nm nanofluids are prepared in a base liquid glycerol–water mixture of 30:70 ratio by volume (GW70). The thermophysical properties of Cu and SiO2 nanofluids are determined with a TPS500S hot disc thermal analyzer and Brookfield viscometer in the temperature range of 20–80°C. The maximum enhancement in Cu and SiO2 nanofluid viscosity (63.4%, 35.7%), thermal conductivity (100.4%, 71.3%), and density (7.5%, 1.5%) while specific heat (7.8%, 2.3%) determined for 1.0% concentration at 80°C compared to base liquid GW70. Heat transfer experiments are conducted in a short‐length double pipe heat exchanger. The flow rates resulted in the lamifnar entry length region. A maximum enhancement in the overall heat transfer coefficient (HTC; 25.0%, 19.7%) and convective HTC (46.2%, 34.8%), respectively for Cu and SiO2 nanofluids is estimated at 1.0% concentration compared to base liquid at a bulk temperature of 35°C.

Analysis of parallel flow heat exchanger using SiO2 nanofluids in the laminar flow region

Convective and overall heat transfer coefficients of SiO2 nanofluid flowing in a concentric DTHE are determined experimentally. The tests are carried out in the 800<Re<1900 range using SiO2/22nm nanofluids prepared in 0.2, 0.6 and 1.0% volume concentrations in 30:70 ratio glycerol-water mixture base liquid. The thermal and physical properties of silica nanofluids are determined in the range of 20-80°C. Viscosity, thermal conductivity, and density of nanofluids increased with particle concentration whereas specific heat decreased. Thermal conductivity and specific heat of nanofluids increased with temperature while viscosity and density decreased. Heat transfer experiments are conducted using nanofluids at a bulk temperature of 35°C in a laminar developing flow region. Overall heat transfer coefficient and convective HTC of 1.0% silica nanofluids are increased by 21.2 and 36.3% compared to base liquid.

Impact of an emergent model vegetation patch on flow adjustment and velocity

This study achieved three goals to clarify the impact of a vegetation patch on flow adjustment and velocity. First, a valid equation for the interior adjustment distance (Ld) inside a model patch was developed for a wide range of velocities and flow depths. Second, the minimum distance inside a patch beyond which the resuspension of fine sediment is suppressed (Lmin) was found to be related to the position at which the local velocity decreases to the threshold for generating stem-scale turbulence. Lmin primarily depends on the flow blockage (Cdab) and the stem diameter (d): a shorter Lmin is a result of a larger Cdab and a smaller d. An equation was formulated for estimating Lmin. Third, for the fully developed flow region inside a patch (L &gt; x &gt; Ld), an equation was developed to estimate the increase in the mean velocity in the bare channel relative to the overall mean channel velocity. For Cdab &lt; 2, this fraction is controlled by both the patch density (ad) and the patch blockage (b/B) whereas, for Cdab &gt; 2, this fraction is controlled by only b/B. A suggestion for choosing the patch size in future flow and sediment research projects is presented.

Thermally developing forced convection flow through porous concentric pipes annular duct

This article shows the thermally developing flow through concentric pipes annular sector duct by describing the Darcy Brinkman flow field. The cross sectional convection-diffusion terms are transformed in power law discretized form by integrating over the differential volume, whereas backward difference scheme is used in the axial direction of heat flow. With the help of semi implicit method for pressure linked equations-revised ( SIMPLE-R), we get the solution of the governing problem. The graphs of velocity profiles against R and average Nusselt number against axial distance are plotted for different values of Darcy number and geometrical configuration parameters. It has been pointed out that velocity and thermal entrance length decrease, when we decrease the value of Darcy number. By decreasing the cross section of the concentric pipes annular sector duct in the transverse direction, thermally fully developed flow region develops earlier.

Numerical investigation of nanoparticle deposition location and pattern on a sharp-bent tube wall

The characteristics of fluid flow on a sharp-bent tube under various conditions were analyzed. Numerical simulations for analyzing the particle deposition locations and patterns on a sharp-bent tube were conducted by using the modified single-particle tracking analysis based on aerosol mass flow rate. Through the numerical calculation, we showed that after the bending point in a sharp-bent tube, the faster axial velocity occurred near the outer wall, and the boundary layer at high Reynolds number became thinner. Furthermore, the faster radial velocity near the tube wall was observed at less developed-flow region at high Reynolds number owing to the stronger secondary flow. The nanoparticle deposition locations and patterns were systematically examined in various viewpoints including cumulative number of deposited particles, local deposition enhancement factor, and particle deposition pattern according to azimuthal angles. We found that most of the nanoparticles were deposited on the outer wall right after the bending point owing to outward-sloping flow. Moreover, the difference in relative deposition efficiency along the azimuthal angles at each section in the sharp-bent tube was reduced as Reynolds number increased. This is because the nanoparticles near the wall were well mixed due to the strong secondary flow at high Reynolds number.

Experimental study on transitional flow in straight channels of printed circuit heat exchanger

Experimental study on fluid flow in Printed Circuit Heat Exchanger (PCHE) with straight channels was conducted, with supercritical carbon dioxide (sCO2) and water as working fluid, respectively. The Reynolds number varies from 64.4 to 14160.9. The Fanning friction factors were obtained for laminar flow, transitional flow, hydraulically smooth region of turbulent flow, as well as the critical Reynolds numbers between different flow regions. The experimental result agrees with the theoretical study very well, with a deviation of 4.6%. The critical Reynolds numbers from laminar flow turning to transitional flow and then to hydraulically smooth region of turbulent flow are 2100 and 2700 for the semi-circular channel, respectively. While the values for circular channel are 2300 and 3980. Based on the new developed flow correlations and flow region identification method, modeling of PCHE was made. It is found that the simulated pressure drop with traditional flow correlations has an obvious deviation with the experimental result. It is recommended to use the new developed flow correlations and the identification method for the cases within the corresponding application ranges.

Numerical Investigation of a Confined Laminar Jet Impingement Cooling of Heat Sources Using Nanofluids

Abstract The thermal and fluid dynamic behavior of a confined two-dimensional steady laminar nanofluid jet impinging on a horizontal plate embedded with five discrete heating elements subjected to a constant surface heat flux has been studied for a range of Reynolds number (Re) from 100 to 400 with Prandtl number, Pr = 6.96, of the base fluid. Variation of inlet Reynolds number produces a significant change of the flow and heat transfer characteristics in the domain. Increasing the nanoparticle concentration (ϕ) from 0% to 4% exhibits discernible change in equivalent Re and Pr caused by the modification of dynamic viscosity, effective density, thermal conductivity, and specific heat of the base fluid. Considerable improvement in heat transfer from the heaters is observed as the maximum temperature of the impingement wall is diminished from 0.95 to 0.55 by increasing Re from 100 to 400; however, the result of increasing ϕ on cooling of the heaters is less appreciable. Self-similar behavior has been depicted by cross-stream variation of temperature and streamwise heat flux in the developed region along the impingement wall up to Re = 300 for ϕ=0% to 4%. But the spread of the respective quantities shows strong dependence on ϕ at Re = 300 with sudden attenuation in magnitude in the developed region of flow. Substantial influence of Re is evident on Eckert number and pumping power. Eckert number decreases, whereas pumping power increases with an increase in Re, and the respective variations exhibit correspondence with power fit correlations.