Solid Volume Fraction Of Nanoparticles Research Articles

Rheological behavior of hybrid MWCNTs-TiO2/EG nanofluid: A comprehensive modeling and experimental study

Abstract In the current paper, the rheological behavior of MWCNTs-TiO2/EG hybrid nanofluid was examined. The well-known two-step method was employed to scatter the nano-powder into the ethylene glycol (EG). The dispersed nano-powder consisted of 80 Vol% of TiO2 and 20 Vol% of MWCNTs. The viscosity measurements were performed at the temperatures ranging from 25 to 55 °C and various solid volume fractions of 0.05, 0.1, 0.125, 0.25, 0.5, 0.75, and 1%. Experimental results showed that the addition of nano-powder to EG does not alter its Newtonian behavior. Besides, it was found that the viscosity of the prepared sample was directly related to the temperature and solid volume fractions of nano-powder. The dynamic viscosity of samples enhanced by growing the solid nanoparticles volume fraction and decreasing the temperature. The dynamic viscosity increase for the nanofluid containing 1 Vol% of nanoparticles was recorded to be 194% and 323% at the temperatures of 25 and 50 °C, respectively. Therefore, at greater temperatures, the effect of nanoparticles on the viscosity became more pronounced. Additionally, Adaptive Neuro Fuzzy Inference System (ANFIS) and Support Vector Machine (SVM) methodologies were applied to estimate the nanofluid viscosity. Based on the error calculations, both techniques can forecast the rheological behavior of MWCNTs-TiO2/EG nanofluids with high accuracy. However, the accuracy of the ANFIS method outperforms the SVM approach.

Numerical study on convective heat transfer of nanofluid in a minichannel heat sink with micro-encapsulated PCM-cooled ceiling

In this work, the convective heat transfer of Al2O3-water nanofluid in a three-dimensional minichannel heat sink is exaimed numerically. The finite volume method (FOV) is applied to discrete the governing equations, and the LINE SOR and TDMA algorithms are used for solving the equations. The FORTRAN program has been developed for the numerical calculation. Ceiling of the minichannel is covered with the micro-encapsulated phase change material. The N-eicosane with the melting temperature of 34.7 °C and the latent heat of 24,300 J/kg is considered as the phase change material. The purpose of placing this material on the ceiling of the minichannel is to cool the working fluid by absorbing the heat from the fluid during melting. All simulations are performed for three values of solid volume fractions of nanoparticles including 0%, 2%, and 10%, two outer surface temperatures of ceiling including 28 °C and 30 °C, and the Reynolds number in the range of 500–2000. The effects of different parameters including the usage of the phase change material, the solid volume fractions of nanoparticles, the outer surface temperature of ceiling, and the Reynolds number on the thermal field, heat flux, melting rate of micro-encapsulated phase change material, and thermal resistance in the mini-channel heat sink are studied. The results reveal that the thermal resistance decreases about 10.88% by using the nanoparticles with solid volume fraction of 10% at Rebf = 500 and Tcw,0 = 28 °C for the case of bare celling. The heat flux received by the ceiling in heating section decreases by using the micro-encapsulated phase change material(MEPCM). In addition, the MEPCM melts faster at lower values of the Reynolds number.

MHD mixed convection of Ag–MgO/water nanofluid in a triangular shape partitioned lid-driven square cavity involving a porous compound

In the current study, magnetohydrodynamics mixed convective flow of Ag–MgO/water hybrid nanofluid in a triangular shaped partitioned cavity involving a porous layer is numerically investigated by using the finite element method. In the numerical simulation, various effects of pertinent parameters such as Richardson number (between 0.01 and 100), Hartmann number (between 0 and 60), magnetic field inclination angle (between 0 and 90), Darcy number (between $$10^{-4}$$ and $$5 \times 10^{-2}$$ ), location of the vertex of triangular porous region (between 0.2 and 0.8 H) and hybrid nanoparticle solid volume fraction ( $$\phi _1$$ between 0 and 0.01, $$\phi _2$$ between 0 and 0.01) on the fluid flow and convective heat transfer features are examined. It was observed that a large vortex is established below the main vortex near the upper wall for the lowest value Ri number. At the highest magnetic field strength, multi-recirculation flow pattern is seen in the right bottom corner. The average heat transfer enhances with higher values of permeability of the porous medium, magnetic field inclination angle, distance of the porous layer vertex from the hot wall and solid nanoparticle volume fraction of each particles in the hybrid nanofluid. The impact is reverse for higher values of Richardson number and Hartmann number. In the current work, significant changes in the average Nusselt number are obtained by varying the location of the porous medium. The triangular shaped porous compound can be used as an excellent tool for convective heat transfer control.

Pulsating Flow of CNT–Water Nanofluid Mixed Convection in a Vented Trapezoidal Cavity with an Inner Conductive T-Shaped Object and Magnetic Field Effects

Mixed convection of carbon-nanotube/water nanofluid in a vented cavity with an inner conductive T-shaped object was examined under pulsating flow conditions under magnetic field effects with finite element method. Effects of different parameters such as Richardson number (between 0.05 and 50), Hartmann number (between 0 and 30), cavity wall inclination (between 0 ∘ and 10 ∘ ), size (between 0.1 H and 0.4 H) and orientation (between −90 ∘ and 90 ∘ ) of the T-shaped object, and amplitude (between 0.5 and 0.9) and frequency (Strouhal number between 0.25 and 5) of pulsating flow on the convective flow features were studied. It was observed that the average Nusselt number enhanced with the rise of strength of magnetic field, solid nanoparticle volume fraction, and amplitude of the pulsation, while the effect was opposite for higher values of Ri number and cavity wall inclination angle. The presence of the T-shaped object and adjusting its size and orientation had significant impact on the main flow stream from inlet to outlet and recirculations around the T-shaped object and in the vicinity of hot wall of the cavity along with the magnetic field strength. Pulsating flow resulted in heat transfer enhancement as compared to steady flow case for all configurations. However, the amount of increment was different depending on the variation of the parameters of interest. Heat transfer enhancements were 41.85% and 20.81% when the size of the T-shaped object was increased from 0.1 H to 0.4 H. The T-shaped object can be utilized in the vented cavity as an excellent tool for convective heat transfer control. As highly conductive CNT particles were used in water, significant enhancements in the average Nusselt number between 97% and 108% were obtained both in steady flow and in pulsating flow cases when magnetic field was absent or present.

Impact of a rotating cone on forced convection of Ag–MgO/water hybrid nanofluid in a 3D multiple vented T-shaped cavity considering magnetic field effects

Forced convection of hybrid Ag–MgO/water nanofluid in a three-dimensional T-shaped vented cavity with multiple ports under the effects of a inner rotating cone and magnetic field is numerically studied with finite volume method. The simulation is performed for various values of parameters such as: Reynolds number (between 100 and 1000), Hartmann number (between 0 and 60), angular velocity of the rotating cone (between − 200 rad/s and 0), aspect ratio of the circular cylinders of the base of the cone (between 0.5 and 2) and nanoparticle solid volume fraction of the hybrid nanofluid ( $$\phi _1$$ between 0 and 0.01, $$\phi _2$$ between 0 and 0.01). It was observed that the average heat transfer rate rises with higher values of Reynolds number, Hartmann number above a specified value, angular rotational speed of the cone, aspect ratio of the cone for values above 1 and solid nanoparticle volume fractions of the hybrid particles. In total, 61% of average heat transfer enhancement for left horizontal upper surface is achieved with the imposed magnetic field. The enhancement in the average Nusselt numbers is 25.6% for the rotating cone at the highest angular velocity as compared to a motionless one. The average heat transfer increases almost linearly with hybrid solid nanoparticle volume fraction, while 8.96% and 15.52% enhancements are obtained for varying the solid volume fraction of the particles with the lower and higher thermal conductivity up to 0.01.

Exact solution of stagnation point flow of MHD Cu–H2O nanofluid induced by an exponential stretching sheet with thermal conductivity

This study presents the stagnation point boundary layer flow of copper–water based nanofluid subject to the applied magnetic field. The flow is caused by the presence of an exponentially stretching porous wall. Heat transfer analysis is also taken into account along with the thermal radiation and Joule heating effects. Mathematical modeling is performed to convert the physical system into a set of mathematical equations which are further simplified by using suitable variables. Exact solutions for the velocity and temperature profiles are computed and interpreted for various physical parameters of interest. It is observed that by increasing the magnitude of the solid volume fraction of nanoparticles, the velocity profile is accelerated. The results also indicate an increment in the Eckert number increases the temperature and the thermal boundary layer thickness.

Comparison of disparate solid volume fraction ratio of hybrid nanofluids flow over a permeable flat surface with aligned magnetic field and Marangoni convection

Over the past decade preparation, characterization and modeling of nanofluids plentifully deliberated to improve the heat transfer effects. Hence to gratify the advancements this paper focuses on heat transfer effects of three distinct hybrid nanoparticles and with a base fluid (water). So this work numerically investigated the influence over a permeable flat surface with aligned magnetic field in the presence of suction or injection or impermeable together with the Marangoni convection of different hybrid nanofluids. The present results are validated with previous experimental and numerical results. The effect of solid volume fraction of hybrid nanoparticles, angle of inclination, magnetic parameter and wall mass transfer parameter are deliberated and offered through graphs together with the surface velocity and rate of heat transfer is presented in tabular form. It is found that the rate of heat transfer is increased with an increment of wall mass transfer parameter and an opposite effect of the rising of magnetic parameter. Among the three hybrid nanofluids water hybrid nanofluid has higher surface velocity, water hybrid nanofluid has higher temperature profile and water hybrid nanofluid has higher heat transfer rate.

Effects of Combined Heat and Mass Transfer on Entropy Generation due to MHD Nanofluid Flow over a Rotating Frame

The current investigation aims to explore the combined effects of heat and mass transfer on free convection of Sodium alginate-Fe3O4 based Brinkmann type nanofluid flow over a vertical rotating frame. The Tiwari and Das nanofluid model is employed to examine the effects of dimensionless numbers, including Grashof, Eckert, and Schmidt numbers and governing parameters like solid volume fraction of nanoparticles, Hall current, magnetic field, viscous dissipation, and the chemical reaction on the physical quantities. The dimensionless nonlinear partial differential equations are solved using a finite difference method known as Runge-Kutta Fehlberg (RKF-45) method. The variation of dimensionless velocity, temperature, concentration, skin friction, heat, and mass transfer rate, as well as for entropy generation and Bejan number with governing parameters, are presented graphically and are provided in tabular form. The results reveal that the Nusselt number increases with an increase in the solid volume fraction of nanoparticles. Furthermore, the rate of entropy generation and Bejan number depends upon the magnetic field and the Eckert number.

Heat transfer analysis of nanofluid flow through backward facing step

This paper presents the numerical predictions of hydrodynamic and thermal characteristics of nanofluid flow through backward facing step. The governing equations are solved through the finite volume method, as described by Patankar, by taking into account the associated boundary conditions. Empirical relations were used to give the effective dynamic viscosity and the thermal conductivity of the nanofluid. Effects of different key parameters such as Reynolds number, nanoparticle solid volume fraction and nanoparticle solid diameter on the heat transfer and fluid flow are investigated. The results are discussed in terms of the average Nusselt number and streamlines.

Mixed convective hybrid nanofluid flow in lid-driven undulated cavity: effect of MHD and Joule heating

A numerical analysis has been conducted to show the effects of magnetohydrodynamic (MHD) and Joule heating on heat transfer phenomenon in a lid driven triangular cavity. The heat transfer fluid (HTF) has been considered as water based hybrid nanofluid composed of equal quantities of Cu and TiO2 nanoparticles. The bottom wall of the cavity is undulated in sinusoidal pattern and cooled isothermally. The left vertical wall of the cavity is heated while the inclined side is insulated. The two dimensional governing partial differential equations of heat transfer and fluid flow with appropriate boundary conditions have been solved by using Galerkin's finite element method built in COMSOL Multyphysics. The effects of Hartmann number, Joule heating, number of undulation and Richardson number on the flow structure and heat transfer characteristics have been studied in details. The values of Prandtl number and solid volume fraction of hybrid nanoparticles have been considered as fixed. Also, the code validation has been shown. The numerical results have been presented in terms of streamlines, isotherms and average Nusselt number of the hybrid nanofluid for different values of governing parameters. The comparison of heat transfer rate by using hybrid nanofluid, Cu-water nanofluid, TiO2 -water nanofluid and clear water has been also shown. Increasing wave number from 0 to 3 enhances the heat transfer rate by 16.89%. The enhanced rate of mean Nusselt number for hybrid nanofluid is found as 4.11% compared to base fluid.

Mixed Convective Flow of Micropolar Nanofluid across a Horizontal Cylinder in Saturated Porous Medium

The micropolar nanofluids are the potential liquids that enhance the thermophysical features and ability of heat transportation instead of base liquids. Alumina and Titania nanoparticles are mixed in a micropolar fluid. The impact of convective boundary condition is also examined with assisting and opposing flows of both nanofluids. The main objective of this study is to investigate mixed convective flow and heat transfer of micropolar nanofluids across a cylinder in a saturated porous medium. Non-similar variables are used to make the governing equations dimensionless. The local similar and non-similar solutions are obtained by using the Runge-Kutta-Fehlberg method of seventh order. The impacts of various embedded variables on the flow and heat transfer of micropolar nanofluids are investigated and interpreted graphically. It is demonstrated that the skin friction and heat transfer rates depend on solid volume fraction of nanoparticles, Biot number, mixed convection, and material parameters.

Turbulent forced convection of nanofluid in an elliptic cross-sectional pipe

In this study, numerical analysis of forced convection in a thee dimensional pipe with elliptic cross-section is considered by using CNT-water nanofluid as working fluid. Three dimensional steady flow and heat transfer equations with k- ϵ turbulence model is solved by using finite element method. Effects of aspect ratio of elliptic cross-section and solid nanoparticle volume fraction on the heat transfer performance were analyzed. An experimental validation of the numerical study was performed and comparisons were made with other existing correlations for turbulent flow in a pipe. It was observed that significant enhancements in the heat transfer rate are achieved with the use of CNT nanoparticles which are in the range of 59% to 84% depending on the mass flow rate. The average Nusselt number deteriorates for higher values of aspect ratio in turbulent three dimensional configuration while the trends are similar for fluid and nanofluid. When the aspect ratio enhances from 0.5 to 1.67, approximately 53% reduction of average Nusselt number is obtained both for water and for nanofluid. Finally, a practical modeling strategy for estimating the average Nusselt number is proposed which uses linear interpolation among polynomial model coefficients for water and for nanofluid at the highest solid particle volume fraction.

Second law analysis for nanofluid flow in mini-channel heat sink with finned surface: a study on fin geometries

In this numerical work, a second law analysis is carried out for the nanofluid flow and heat transfer in the mini-channel with finned surface. The mini-fins with various geometries, including trapezoidal, square, triangular, and sinusoidal, are located on the bottom surface of the mini-channel. The effects of mini-fins geometry, mini-fins number, Reynolds number, and solid volume fraction of nanoparticles on the temperature and velocity distributions, frictional and thermal irreversibilities, and Bejan number inside the mini-channel are studied. The numerical method is validated with the experimental data. The results show that the sinusoidal, triangular, square, and trapezoidal mini-fins generate up to 66.23%, 61.87%, 59.21%, and 57.80%, respectively, lower thermal irreversibility as compared with the smooth mini-channel. Among mini-fin geometries, the triangular mini-fins generate the maximum frictional irreversibility, while the trapezoidal mini-fins provide the minimum frictional irreversibility. The frictional irreversibility increases about 108.56%, while the thermal irreversibility decreases up to 46.33% as the mini-fin number increases from one to nine. The thermal irreversibility diminishes about 49% by boosting the Reynolds number from 100 to 500. Usage of nanofluid increases both frictional and thermal irreversibilities. Finally, the thermal irreversibility is a dominant term in the total irreversibility and the effects of frictional irreversibility can be ignored.

Viscous Flow Over a Permeable Stretching/Shrinking Surface in a Nanofluid: A Stability Analysis

This study deals with the boundary layer flow and heat transfer near the stagnation point on a permeable stretching/shrinking surface in a nanofluid. The nanoparticles considered in this study are copper and silver. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using an appropriate similarity transformation which then solved numerically to study the effect of solid volume fraction or nanoparticle volume fraction parameter Φ of the nanofluid. Multiple solutions are found for a certain range of shrinking and suction parameters, therefore, a stability analysis is performed to determine which solution is stable and physically realizable. The effects of the governing parameters on the skin friction coefficient, the local Nusselt number and the velocity and temperature profiles were presented and discussed. It was found that the nanoparticle volume fraction substantially affects the fluid flow and heat transfer characteristics.

Transportation of magnetized micropolar hybrid nanomaterial fluid flow over a Riga curface surface

We deliberated the flow of magnetized micropolar hybrid nanoparticles fluid flow over the Riga curved surface. Exponentially stretching and slip effects are also considered in this analysis. Mathematical model has been established on the base of assumptions in the form of partial differential equations. Such equations are renewed into ordinary differential equations utilizing similarity transformations. Reduced model has been elucidated by means of bvp4c scheme. Impacts of physical parameters namely as stretching parameter R0, curvature parameter K, solid nanoparticle volume fraction Φ2, micropolar parameter K1, microgyration parameter n, thermal slip parameter M, partial slip parameter γ, modified Harman number ∅ and dimensionless parameter ω. Magnetic parameter β and reciprocal magnetic Prandtl number λ are depicted by means of numerically and graphically. Our results help in the field of engineering and industrial. This model is presented in the first time through literatures. Our interest of study is to be analyzed about the heat transfer rate of magnetized micropolar hybrid nanomaterial fluid over a Riga curved surface. Comparison with the literature has been worked out and excellent agreement is found.

Heat Transfer of Hybrid-nanofluids Flow Past a Permeable Flat Surface with Different Volume Fractions

Nowadays, the preparation, characterization, and modeling of nanofluids are deliberated in plenty to improve the heat transfer effects. Therefore, this paper centers on the heat transfer effects of three separate hybrid nanoparticles such as Al2O3-SiO2, Al2O3-TiO2, and TiO2-SiO2 with a base fluid such as water to gratify the advances. Analytical investigations for the Marangoni convection of different hybrid nanofluids over the flat surface for the cases such as suction, injection and impermeable were analyzed. A validation table for the comparison between analytical and numerical studies is tabulated. The influence of the hybrid nanoparticles solid volume fraction and the wall mass transfer parameter are mentioned through graphs at the side of the heat transfer rate tabulation. The impact of solid volume fraction decelerates the velocity distribution and raises the temperature distribution for all the three hybrid nanofluids in the cases of suction, impermeable, and injection. While relating the surface velocity and heat transfer rate of the three hybrid nanofluids, Al2O3-SiO2/water has a higher surface velocity, TiO2-SiO2/water has a higher heat transfer rate and Al2O3-TiO2/water has lower surface velocity and heat transfer rate for the increment of wall mass transfer parameter.

Effects of conductive curved partition and magnetic field on natural convection and entropy generation in an inclined cavity filled with nanofluid

In this study, natural convection and entropy generation analysis of nanofluid in an inclined cavity including a curved shaped conductive partition are performed under the impact of inclined magnetic field by using Galerkin weighted residual finite element method. Numerical simulations are performed for various values of Rayleigh number (between 104 and 106), inclination angle of the cavity (between 0o and 180 o), Hartmann number (between 0 and 50), orientation angle of the magnetic field (between 0o and 90o), curvatures of the conductive partition (between 0.01 and 0.1), conductivity ratio (between 0.01 and 100) and solid nanoparticle volume fraction (between 0 and 0.03). The average Nusselt number increases with higher values of Rayleigh number, inclusion of nano sized particles whereas it is reduced with higher values of Hartmann number. When the value of Hartmann number is increased from 0 to 50, 32% and 34% of average Nusselt number reduction is obtained for water and nanofluid. The cavity inclination angle has significant effects on the convective heat transfer characteristics. When the radii of the vertical and horizontal elliptic curved partitions are increased to 0.3H, 23% and 3.8% deterioration of average Nusselt number is obtained while significant enhancement in the heat transfer is observed when the conductivity of the partition is increased. The second law analysis was included in the study and entropy generation rate was found to vary with different parameters. Contributions of solid and fluid domains to the entropy generation rate were determined.

Entropy formation analysis of MHD boundary layer flow of nanofluid over a porous shrinking wall

In the current paper, we investigate the entropy analysis of MHD boundary layer flow of copper (Cu)-water based nanofluid along with the porous shrinking wall. Heat transfer analysis is also taken into account with the thermal radiation effects. The single phase nanofluid model is used for the analysis of the effective thermal conductivity. Mathematical modeling is performed to change the physical system into a set of mathematical equations which are further simplified by using suitable variables. Exact solutions for the velocity and temperature profiles are computed and interpreted for diverse physical of interest. It is depicted that by enhancing the magnitude of solid volume fraction and velocity slip parameter of nanoparticles the velocity profile is increased. The results indicate an increment in the Hartman number increases the temperature and thermal boundary layer thickness. It is observed that the entropy generation profile is enhanced by increasing the value of Brinkman number and Reynolds number. The irreversibility parameter is decreasing function of Brinkman number.

Control of natural convection in a CNT-water nanofluid filled 3D cavity by using an inner T-shaped obstacle and thermoelectric cooler

Natural convection of CNT-water nanofluid in a 3D cavity with an inner T-shaped adiabatic obstacle is studied. The cold surface temperature of the enclosure is controlled by using a thermoelectric cooler while the hot surface of the cavity is made inclined. Numerical simulations are performed by using Galerkin weighted residual finite element method. Impact of various pertinent parameters such as current flux of the thermoelectric cooler (between 0.01 A/mm2 and 0.04 A/mm2), ambient temperature (between 298 K and 313 K), inclination of the side surface of 3D cavity (between 0 and 40∘), inclination of the T-shaped obstacle (between −90∘ and 90∘), size of the obstacle (between 0.1 H and 0.4 H) and solid nanoparticle volume fraction (between 0 and 4%) on the natural convective heat transfer features is numerically examined. It was observed the local and average heat transfer rates are enhanced with higher values of current flux of the thermoelectric element and solid nanoparticle volume fraction while the effect is reverse with higher hot side temperature of the thermoelectric element and cavity side surface inclination angle. As compared to others, size and inclination of the T-shaped obstacle have slight effects on the variation of Nusselt number and maximum deviation of 6% in the average heat transfer is obtained when the orientation of the obstacle is changed from −45∘ to −90∘. When the minimum and maximum values of cavity inclination angles are compared, 23.70% of reduction in the average Nusselt number is obtained. The heat transfer augmentation with CNT-nanoparticle inclusion is significant and 128% enhancement in the average Nusselt number is achieved at the highest solid nanoparticle volume fraction.

Cooling of an isothermal surface having a cavity component by using CuO-water nano-jet

PurposeThe purpose of this study is to numerically analyze the convective heat transfer features for cooling of an isothermal surface with a cavity-like portion by using CuO-water nano jet. Jet impingement cooling of curved surfaces plays an important role in practical applications. As compared to flat surfaces, fluid flow and convective heat transfer features with jet impingement cooling of a curved surface becomes more complex with additional formation of the vortices and their interaction in the jet wall region. As flow separation and reattachment may appear in a wide range of thermal engineering applications such as electronic cooling, combustors and solar power, jet impingement cooling of a surface which has a geometry with potential separation regions is important from the practical point of view.Design/methodology/approachNumerical simulations were performed with a finite volume-based solver. The study was performed for various values of the Reynolds number (between 100 and 400), length of the cavity (between 5 w and 40 w), height of the cavity (between w and 5w) and solid nano-particle volume fraction (between 0 and 4 per cent). Artificial neural network modeling was used to obtain a correlation for the average Nusselt number, which can be used to obtain fast and accurate predictions.FindingsIt was observed that cavity geometrical parameters of the cooling surface can be adjusted to change the flow field and convective heat transfer features. When the cavity length is low, significant contribution of the inclined wall of the cavity on the average Nusselt number is achieved. As the cavity length and height increase, the average Nusselt number, respectively, reduce and slightly enhance. At the highest value of cavity height, significant changes in the convective flow features are obtained. By using nanofluids instead of water, enhancement of average heat transfer in the range of 35-46 per cent is obtained at the highest particle volume fraction.Originality/valueIn this study, jet impingement cooling of an isothermal surface which has a cavity-like portion was considered with nanofluids. Addition of this portion to the impingement surface has the potential to produce additional vortices which affects the fluid flow and convective features in the jet impingement heat transfer. This geometry has the forward-facing step for the wall jet region with flow separation reattachment in the region. Based on the above literature survey and to the best of the authors’ knowledge, jet impingement cooling for such a geometry has never been reported in the literature despite its importance in practical thermal engineering applications. The results of this study may be useful for design and optimization of such systems and to obtain best performance in terms of fluid flow and heat transfer characteristics.