Heat transfer enhancement with laminar pulsating nanofluid flow in a wavy channel

In this study, the heat transfer characteristics of Al₂O₃–water based nanofluids in a wavy mini-channel under pulsating inlet flow conditions are investigated numerically. The simulations are performed for nanofluid volume fractions, pulsating frequency and amplitude while the other parameters are kept constant by using control volume based cfd solver. The flow is both thermally and hydrodynamically developing while the channel walls are kept at a constant temperature. Results indicate that there is a good potential in promoting the thermal performance enhancement by using the nanoparticles under pulsating flow. Pulsation in nanofluids is a new idea for enhancement of heat transfer. Furthermore, the pulsating flow has an advantage to prevent sedimentation of nanoparticles in the base fluid. Results show that the heat transfer performance increases significantly with increase in nanoparticle volume fraction and with the amplitude of pulsation while the pulsation frequencies have a slight effect. In the pulsating flow conditions the combined effect of pulsation and nanoparticles is favorable for the increasing Nusselt number when compared to the steady flow case. The obtained results are given as dimensionless parameters.     

Numerical investigations on the heat transfer enhancement in a wavy channel using nanofluid

In this paper, laminar copper–water nanofluid flow and heat transfer in a two-dimensional wavy channel is numerically investigated. The Reynolds number and nanoparticle volume fraction considered are in the ranges of 100–800 and 0–5% respectively. Numerical solutions are obtained by solving the governing equation of stream function, vorticity transport and energy in curvilinear coordinates using the finite difference method. The effects of nanoparticle volume fraction, the wavy channel amplitude and wavelength and the Reynolds number on the local skin-friction coefficient, local and average Nusselt number and the heat transfer enhancement are presented and discussed. Results show that the friction coefficient and Nusselt number increase as the amplitude of wavy channel increases. As the nanoparticle volume fraction increases, the Nusselt number is found to be significantly increased, accompanied by only a slight increase in the friction coefficient. In addition, it was found that the enhancement in heat transfer mainly depends on the nanoparticle volume fraction, amplitude of the wavy wall and Reynolds number rather than the wavelength.     

Finite element simulation of MHD combined convection through a triangular wavy channel

The present paper implements the analysis of magnetohydrodynamic (MHD) combined convective flow and heat transfer characteristics through a triangular wavy vertical channel using the Galerkin weighted residual finite element method. The flow enters at the bottom and exits from the top surface. The wavy vertical walls are at constant temperature and the cold flow enters the channel from the inlet. The numerical model is based on a 2D Navier–Stokes incompressible flow and energy equation. The effects of Grashof number, Reynolds number and Prandtl number on flow and thermal fields are investigated. The variation of local Nusselt number along the vertical walls for the mentioned parameters is also presented. The study reveals that the flow as well as thermal field strongly depends on the aforesaid parameters.     

Fully developed mixed convection flow of a nanofluid through an inclined channel filled with a porous medium

In this paper, the steady fully developed mixed convection flow of a nanofluid in a channel filled with a porous medium is presented. The walls of the channel are heated by a uniform heat flux and a constant flow rate is considered through the channel. The equations of the problem are made non-dimensional and are observed to depend on the dimensionless parameters, namely the mixed convection parameter λ, the Péclet number Pe, the inclination angle of the channel to the horizontal γ and the nanoparticle volume fraction ?. The effects of these parameters on the fluid and heat transfer characteristics are in detail discussed for three different nanofluids as Cu–water, Al₂O₃–water and TiO₂–water.     

Mixed convection of a nanofluid past an inclined wavy surface in the presence of gyrotactic microorganisms

The mixed convection of a nanofluid flow past an inclined wavy surface in the existence of gyrotactic microbes is considered. To convert the wavy surface to a plane surface, a transformation of coordinates is applied. The governing equations that are nonlinear and the accompanying boundary conditions are converted into a dimensionless form using pseudo-similarity variables. Using a local linearization process, the system of nonlinear partial differential equations is linearized. The resulting system is solved using the Bivariate Chebyshev pseudo-spectral collocation method. The influence of different physical and geometrical factors on the parameters of engineering importance of the flow is analyzed and illustrated graphically. It is observed that the skin friction, the density of motile microorganisms, and nanoparticle mass transfer rate are increasing with an increase in the bioconvection Peclet and Schmidt numbers whereas these quantities are decreasing with an increase in Rayleigh number. The local Nusselt number, nanoparticle Sherwood number, and density number of microbes increases with an increase in the Brownian motion and thermophoresis parameter. These physical quantities are increasing when the surface changes from horizontal to vertical.     

EHD enhanced heat transfer in wavy channel

Heat transfer enhancement with electrohydrodynamic (EHD) technique in laminar forced convection inside a wavy channel with different wire electrode arrangements is numerically investigated. The electric field is generated by the wire electrodes charged with DC high voltage. The mathematical modeling includes the interactions among electric field, flow field, and temperature field. The simulation is firstly conducted with the experimental data in case of rectangular flat channel and the results agree very well. Then the modeling is carried out in the case of wavy channel. It is found that the heat transfer coefficient with the presence of electric field increases with the supplied voltage but decreases when the Reynolds number and the distance between the wire electrodes and the wall surface are augmented. The heat transfer enhancement is also dependent on the number of the wire electrodes, the number of wave per length, and the wave aspect ratio.     

Analysis of mixed convection flow of a nanofluid in a vertical channel with the Buongiorno mathematical model

The laminar, fully developed mixed convection flow between two paralleled vertical flat plates filled by a nanofluid is investigated. By means of a new set of similarity variables, the governing equations are reduced to a set of three coupled equations with an unknown constant. The exact solutions are obtained by means of the homotopy analysis method for both the buoyancy-assisted and the buoyancy-opposing cases and their accuracies are checked in detail. The effects of the Grashof number Gr and the Prandtl number Pr on the nanofluid flows are then investigated successively. We further consider the effects of the buoyancy ratio Nr, the Brownian motion parameter Nb, the thermophoresis parameter Nt on the pressure parameter σ and the Nusselt number Nu. It is found that the heat transfer characteristic can be improved significantly as the proper nanofluids are applied.     

Entropy generation minimization and nonlinear heat transport in MHD flow of a couple stress nanofluid through an inclined permeable channel with a porous medium,thermal radiation and slip

Irreversible losses and heat transport in a magnetohydrodynamic flow of a viscous, steady, incompressible, and fully developed couple stress Al₂O₃–water nanofluid through a sloping permeable wall channel with porous medium and under the effect of radiation heat flux and slip were analyzed. The fundamental equations were solved numerically by using Runge-Kutta together with the shooting technique and the results were in qualitative agreement with an exact solution obtained for a limit case. The impacts of couple stress, Darcy number, solid nanoparticle concentrations, conduction-radiation parameter, Hartmann number and hydrodynamic slip on flow, temperature, heat transport, and entropy production were examined. It was possible to achieve values of minimum entropy production not yet reported in previous studies. In this way, optimal values of couple stress and slip were obtained. The heat transport was also explored and optimal values of slip flow and conduction-radiation parameter with maximum heat transfer were found. Finally, in addition to the alumina, the distributions of velocity, temperature, and entropy generation in TiO₂–water and Cu–water were presented for different solid nanoparticle concentrations. It was obtained that the local entropy of TiO₂–water was lower than Cu–water and Al₂O₃–water in the channel bottom region while it was greater in the upper region.     

An investigation of natural convection in a three dimensional square wavy channel

Natural convection in a three dimensional wavy channel, which is composed of numerous two dimensional cross sections, is investigated numerically. The method of elliptic partial differential equations grid generation is adopted to construct a distribution of grids on each cross section. The distributions of the whole cross sections are piled up in sequence from the inlet to outlet to form a three dimensional channel. In order to solve a low speed compressible flow problem, the compressibility and viscosity of the working fluid are taken into consideration, and the non-reflecting boundaries at the inlet and outlet of the channel are held. The Bossinesq assumption is then no longer necessary. As well, the methods of the Roe scheme, preconditioning and dual time stepping matching the implicit LUSGS algorithm (Implicit Lower Upper symmetric Gauss–Seidel algorithm) are simultaneously used to solve governing equations. Effects of the Rayleigh number and the ratio of the amplitude to wave length on heat transfer rates of the channel are examined. Results of both this study and existing studies have good agreements.     

Determination of hot spots on a heated wavy wall in channel flow

The present study deals with the effects of wall geometry on the fluid flow and heat transfer in a channel with a wavy wall heated with constant heat dissipation. The waviness is characterized by wave amplitude and period. A detailed parametric numerical investigation of the effect of waviness on the local heat transfer parameters is performed for different turbulent flow conditions and compared with the literature.The effect of flow and geometry parameters is assessed quantitatively. Generalization is done based on the Reynolds number, Re_A, which uses doubled wave amplitude, or height, A = 2a, as the characteristic length, and on the geometry parameter, A/λ, which essentially is the amplitude-to-wavelength ratio. A dimensionless location of the hottest spot on the wavy wall is shown to be dependent on these two dimensionless parameters. A correlation which encompasses the hottest spot locations for all the cases studied in the work is suggested.In order to obtain generalization for the hottest spot temperature, the Nusselt number is introduced based on the constant (uniform) heat flux and variable temperature difference, with wave amplitude as the characteristic length. It is shown that, for all cases studied herein, the hottest temperature is represented as Nu_A,min(Re_A, A/λ). Accordingly, a correlation for the minimum Nusselt number is suggested. A further generalization for the hottest spot temperature is attempted for the conjugate problem with a conducting wall. It includes wall-to-fluid thermal conductivity ratio, k_s/k_l, as the additional dimensionless parameter which determines the Nusselt number.     

Numerical simulation and optimization of turbulent nanofluids in a three-dimensional wavy channel

ABSTRACT

In this study, numerical calculations by single- and two-phase models of nanofluid turbulent forced convection in a three-dimensional wavy channel with uniform wall temperature are investigated. The numerical results for the Nusselt number ratio (Nu/Nu₀) show that the heat transfer performance of a symmetric wavy channel performs better than that of an in-line wavy channel. The multi-parameter constrained optimization procedure integrating the design of experiments (DOEs), response surface methodology (RSM), genetic algorithm (GA), and computational fluid dynamics (CFD) is proposed to design the nanofluid turbulent convection of the three-dimensional wavy channel.     

Numerical simulation and optimization of nanofluid in a C-shaped chaotic channel

ABSTRACT

In this study, numerical calculations using single- and two-phase models of CuO/water nanofluid forced convection in a three-dimensional C-shaped channel with constant heat flux are investigated. The laminar heat transfer enhancement using a nanofluid in a chaotic flow is first validated with the available data in the literature and the maximum discrepancy is within 3%; then further it is extended to design the C-shaped geometry. In addition, after comparisons of the numerical results with single- and two-phase models, the multiparameter constrained the optimization procedure integrating the design of experiments (DOE), response surface methodology (RSM), genetic algorithm (GA), and computational fluid dynamics (CFD) is proposed to design the nanofluid laminar convection of three-dimensional C-shaped channels. The thermal performance factors predicted by the regression function for the C-shaped channel case are in good agreement with the numerical results of CFD, with the difference being within 10%.     

On forced convective heat transfer for a stokes flow in a wavy channel

Study of heat transfer in a two-dimensional wavy channel due to a pressure driven Stokes flow, normal to the wall corrugation, is made. Expression for the mean Nusselt number describing the average rate of heat transfer from the warmer surface, obtained analytically, predicts a decreased heat transfer rate due to corrugations. This observation is found to be significantly opposite to the prevailing results of moderate or large Reynolds number flows.     

Toward the thermohydrodynamic behavior of a nanofluid containing C-MWCNTs flowing through a 3D annulus channel under constant imposed heat flux

The heat transport and friction factor in a three-dimensional horizontal concentric annular duct filled with nanofluids comprising clove-treated multiwalled carbon nanotubes are investigated numerically in this paper. The cylinder's outer surface is thermally insulated, while uniform heat flux is imposed on the cylinder's inner surface. The problem is formulated in dimensionless cylindrical coordinates. The numerical solutions were obtained based on the finite volume technique with second-order precision, and cover a range of the Reynolds number 1000 ≤ Re ≤ 2000 and nanoparticle weight fractions 0.075, 0.125, and 0.175 wt%. To describe the results for both heat exchange and fluid flow performance, the temperature profile, Nusselt number, heat transfer coefficient, and friction factor are represented. The findings state that heat transport increases as Reynolds is increased and nanoparticles are introduced. The friction factor was also observed to improve as the concentration of nanoparticles increased. In addition, two new Nusselt number and friction factor correlations were established.     

Mixed convection from a wavy surface embedded in a thermally stratified nanofluid saturated porous medium with non-linear Boussinesq approximation

In this article, we have made an attempt to study the convective heat transfer in the influence of non-linear Boussinesq approximation, thermal stratification and convective boundary conditions on non-Darcy nanofluid flow over a vertical wavy surface. The surface of the vertical wavy plate, put up at convective temperature and concentration. A coordinate transformation is used to transform the wavy surface into smooth surface. Using local similarity and non-similarity method the governing nondimensional equations are transformed into coupled nonlinear ordinary differential equations. Effects of thermal convective parameter, thermal stratification parameter, Lewis number, Sherwood number on the wave geometry on the heat and mass transfer characteristics have been studied. Numerical results have been obtained for various physical parameters. A comparison of the present results is made with the earlier published results and is found to be in good agreement.     

Forced convection heat and mass transfer flow of a nanofluid through a porous channel with a first order chemical reaction on the wall

This study is devoted to investigate the fully developed forced convection heat and mass transfer in a horizontal porous channel filled with a nanofluid. It is assumed that the walls of the channel are subject to a constant heat flux. It is also assumed that the first order catalytic reaction takes place on the walls and that the viscous dissipation term in the energy equation is taken into account. Brinkman model is used for the flow in the porous media and “clear fluid compatible” viscous dissipation model is considered. Thermal effect is taken also into account in the concentration equation. Closed form analytical solutions are presented for the governing dimensionless momentum, energy and concentration equations. The effects of nanoparticle volume fraction, Darcy, Brinkman, Damkohler and Soret numbers are investigated on the Nusselt number, velocity, temperature and concentration distributions.     

Mixed convection of MHD flow in nanofluid filled and partially heated wavy walled lid-driven enclosure

A computational work has been done to investigate the effects of mixed convection of MHD flow in nanofluid filled and partially heated wavy walled lid-driven enclosure. Finite difference method is used to solve governing equations of mixed convection for different parameters as Hartmann number, Richardson number, nanoparticle volume rate in partially heated and wavy walled enclosure. It is found that the rate of heat transfer decreases with increasing the Hartmann number. The rate of heat transfer can be enhanced or reduced by increasing the volume fraction of nanoparticles based on Hartmann and Richardson numbers.     

Numerical simulation of unsteady ethylene glycol/CNTs micropolar nanofluid flow through a squeezing channel: An approach to industrial applications

The impressive high thermal conductivity and low weight allow the carbon nanotubes (CNTs) to improve heat dissipation and cooling. In the present problem, we aim to analyze the CNTs embedded micropolar nanofluid flow between two parallel stretching sheets with the base fluid ethylene glycol (EG) which is effectively used as antifreeze and coolant. Both single-walled carbon nanotubes and multiwalled carbon nanotubes (MWCNTs) are considered. The fluid is influenced by the external magnetic field parallel to the microrotation along with viscous and Joule dissipations. The flow and heat equations are converted to a set of coupled ordinary differential equations with the aid of similarity transformations. Due to the nonexistence of the closed-form solution, we have developed the analytical approximate solution by homotopy analysis method using the polynomial base function. Furthermore, we have used the most efficient Runge–Kutta integration scheme of the fourth order associated with shooting technique to solve the system of equations. Results are exhibited graphically for various physical parameters and also found a good agreement with earlier work. From the results, we noticed that squeezing increases the angular velocity of the fluid particles. Also, in the case of squeezing, the volume fraction has enhanced the viscous drag and was found high for MWCNT–EG nanofluid.     

Effect of porous slab thickness and Darcy number on thermohydraulic transport characteristics of Ag–TiO2/water hybrid nanofluid flow-through partially porous wavy channels

The present article investigates the effect of varying porous slab thicknesses (S = 0–0.4) and Darcy number (Da = 10⁻⁶–10⁻²) on the thermohydraulic performance of three different corrugated channels (triangular, sinusoidal, and trapezoidal) embedded with partially filled porous media. Ag–TiO₂/water hybrid nanofluid ($\varphi$ = 0–0.04) is taken as coolant flowing at Re = 400. Results revealed that the thermal performance (average Nusselt number, Nu_avg and enhancement ratio, ER) augments with the increase in porous slab thickness and decrease in Darcy number. However, the hydraulic performance reduces (i.e., an increase in pressure drop). To check the viability of the cooling system performance factor (PF) is evaluated which demonstrates variation in thermal performance considering pressure drop penalty also. It is demonstrated that among all configurations, the trapezoidal channel with porous slab thickness (S = 0.4) and Darcy number (Da = 10⁻⁴) gives maximum enhancement thermal performance (110%) considering water as a coolant ($\varphi$ = 0). Furthermore, enhancement in thermal performance by 210% is noticed as volume concentration $\varphi$ of hybrid nanofluid varies from 0% to 4%. It is also evident that the value of PF for all corrugated channels is lower than 1 indicating the nonviable system. However, for the case of the partially porous plane channel the maximum PF = 1.07.