Natural Convection Heat Transfer of Copper–Water Nanofluid in a Square Cavity With Time-Periodic Boundary Temperature

This paper presents a numerical study of natural convective heat transfer of copper–water nanofluid in a square enclosure where the temperature of the left vertical sidewall is sinusoidally oscillated with a constant average temperature, the right sidewall is cooled at a relatively low temperature, and the other walls are kept adiabatic. The influence of pertinent parameters such as Rayleigh number, solid volume fraction of copper nanoparticles, and dimensionless time period on the heat transfer characteristics is studied. The results show that the heat transfer rate increases using copper nanoparticles.     

Natural Convection Heat Transfer in an Inclined Enclosure Filled with a Water-Cuo Nanofluid

This article presents the results of a numerical study on natural convection heat transfer in an inclined enclosure filled with a water-CuO nanofluid. Two opposite walls of the enclosure are insulated and the other two walls are kept at different temperatures. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influence of pertinent parameters such as Rayleigh number, inclination angle, and solid volume fraction on the heat transfer characteristics of natural convection is studied. The results indicate that adding nanoparticles into pure water improves its heat transfer performance; however, there is an optimum solid volume fraction which maximises the heat transfer rate. The results also show that the inclination angle has a significant impact on the flow and temperature fields and the heat transfer performance at high Rayleigh numbers. In fact, the heat transfer rate is maximised at a specific inclination angle depending on Rayleigh number and solid volume fraction.     

Brownian motion of nanoparticles in a triangular enclosure with natural convection

This paper presents the results of a numerical study on the natural convection in a right triangular enclosure, with a heat source on its vertical wall and filled with a water–CuO nanofluid. The effects of parameters such as Rayleigh number, solid volume fraction, heat source location, enclosure aspect ratio and Brownian motion on the flow and temperature fields as well as the heat transfer rate, are examined. The results show that when Brownian motion is considered in the analysis, the solid volume fraction, the heat source location and the enclosure aspect ratio affect the heat transfer performance differently at low and high Rayleigh numbers. At high Rayleigh numbers, an optimum value for the solid volume fraction is found which results in the maximum heat transfer rate. This is in contradiction to the results of the analysis in which Brownian motion is neglected.     

A numerical investigation of the effect of sinusoidal temperature on mixed convection flow in a cavity filled with a nanofluid with moving vertical walls

The aim of this study is to investigate numerically the effect of sinusoidal temperature on mixed convection flow in a cavity filled with nanofluid and moving vertical walls by using a new temperature function, where thermal heating takes the form of the sinusoidal temperature; and could be found in various natural processes and industries such as solar energy, and cooling of electronic components. The heating is concentrated in the center and then distributed to both ends at different values of Rayleigh numbers, Reynolds numbers, and volumetric fractions of nanoparticles ranging from 1.47 × 10³ to 1.47 × 10⁶, 1 to 100, and 0 to 0.1, respectively. The impact of nanoparticle size on thermal characteristics and hydrodynamics was considered and evaluated. From the results, the volume fraction concentration of nanoparticles affects the flow shape and thermal performance in the case of a constant Reynolds number. Moreover, the effect of nanoparticles decreases with the increase of the Reynolds number. Besides this, with increasing the volume percentage of nanoparticles, the rate of heat transmission increases. It is worth noting that the presence of nanoparticles results in height convective heat transfer coefficient. On the other hand, the thickness of thermal boundary layers decreases with increasing Rayleigh number. The current investigation found that the (sinusoidal) temperature change significantly affects heat transfer.     

Combined convection flow in triangular wavy chamber filled with water–CuO nanofluid: Effect of viscosity models

This work is focused on the numerical modeling of steady laminar combined convection flow in a vertical triangular wavy enclosure filled with water–CuO nanofluid. The left and right vertical walls of the cavity take the form of a triangular wavy pattern. The bottom and top horizontal walls are mechanically driven. The lower and upper surfaces move to the right and left direction at the same constant speed respectively. They maintain constant temperature lower than both vertical walls. Two different nanofluid models namely, the Brinkman model and the Pak and Cho correlation are employed. The developed equations are given in terms of the Navier Stokes and the energy equation and are non-dimensionalized and then solved numerically subject to appropriate boundary conditions by the Galerkin's finite-element method. Comparisons with published work are performed and found to be in good agreement. A parametric study is conducted and a selective set of graphical results is presented. The effects of the Reynolds number, Richardson number and the nanoparticles volume fraction on the flow and heat transfer characteristics in the cavity are displayed to compare the predictions obtained by the two different nanofluid models. Heat transfer enhancement can be obtained significantly due to the presence of nanoparticles. The rate of heat transfer is accentuated moderately by falling the Richardson number and rising the Reynolds number as well as the solid volume fraction.     

Thermal Enhancement of Triangular Ducts Using Compound of Vortex Generators and Nanofluids

Laminar flow and heat transfer of three different types of nanofluids; Al₂O₃, CuO, and SiO₂ suspended in ethylene glycol, in a triangular duct using delta-winglet pair of vortex generator are numerically simulated in three dimensions. The governing equations of mass, momentum and energy are solved using the finite volume method. The effects of types, concentrations, and diameter of solid nanoparticles and Reynolds number on thermal and hydraulic performance of triangular duct are examined. The range of Reynolds number, volume fraction and nanoparticles diameters is 100–1200, 1–4%, and 25–85 nm, respectively. The results indicate that the average Nusselt number increases with the particles volume fraction and Reynolds number associated with an increase in the pressure drop. The heat transfer enhancement and pressure drop penalty reduce with increasing the particles diameters. However, a reduction in the pumping power required is observed to force the nanofluids when the volume fraction increases, assuming the heat transfer coefficient remains constant.     

Buoyancy Induced Heat Transfer Flow Inside a Tilted Square Enclosure Filled with Nanofluids in the Presence of Oriented Magnetic Field

This paper analyzes heat transfer and fluid flow of natural convection in an inclined square enclosure filled with different types of nanofluids having various shapes of nanoparticles in the presence of oriented magnetic field. The Galerkin weighted residual finite element method has been employed to solve the governing non-dimensional partial differential equations. In the numerical simulations, water, ethylene glycol, and engine oil containing copper, alumina, titanium dioxide nanoparticles are considered. The effects of model parameters such as Rayleigh number, Hartmann number, nanoparticles volume fraction, magnetic field inclination angle, geometry inclination angle on the fluid flow and heat transfer are investigated. The results indicate that increment of the Rayleigh number and nanoparticle volume fraction increase the heat transfer rate in a significant way, whereas, increment of the Hartmann number decreases the overall heat transfer rate. It is also observed that a blade shape nanoparticle gives higher heat transfer rate compared to other shapes of nanoparticles. The critical geometry inclination angle at which the maximum heat transfer rate is achieved depends on the nanoparticle volume fraction as well as on the magnetic field orientation. These results are new and have direct applications in solar thermal collectors and thermal insulator of buildings.     

Jet impingement cooling and optimization study for a partly curved isothermal surface with CuO-water nanofluid

Numerical and optimization study of jet impingement cooling of a partly curved surface with CuO-water nanofluid was performed with Galerkin weighted residual finite element method and COBYLA (constrained optimization by linear approximation) optimization algorithm. Target surface was partly curved which has a semi-elliptic shape and kept at constant hot temperature. Simulations were performed for various values of Reynolds number and solid particle volume fraction. It was observed that effects of curved wall on the distribution of fluid flow and heat transfer characteristics are more pronounced for higher values of Reynolds number as compared to a flat wall configuration. Highest heat transfer is obtained with curved wall and significant differences are observed between the peak values of Nusselt number between a flat wall and curved wall case. The average Nusselt number is a linear increasing function of nanoparticle volume fraction and the trends in local and average heat transfer are similar for curved wall and flat wall configurations when nanoparticles are added. Average Nusselt number enhances by about 20% at the highest particle volume fraction as compared to water. A polynomial type correlation for the average Nusselt number was derived which depends on the Reynolds number and solid particle volume fraction for both configurations.     

A Numerical Study on the Forced Convection of Laminar Nanofluid in a Microchannel with Both Slip and No-Slip Conditions

This article provides numerically study of the thermal performance of a microchannel, cooled with either pure water or a Cu-water nanofluid, while considering the effects of both slip and no-slip boundary conditions on the flow field and heat transfer. The microchannel is partially heated at a constant temperature and cooled by forced convection of a laminar flow at a relatively lower temperature. The effects of pertinent parameters such as Reynolds number, solid volume fraction, and slip velocity coefficient on the thermal performance of the microchannel are studied. The results of the numerical simulation indicate that the heat transfer rate is significantly affected by the solid volume fraction and slip velocity coefficient at high Reynolds numbers.     

Numerical Simulation of Natural Convection in a Triangle Cavity Filled with Nanofluids Using Tiwari and Das' Model: Effects of Heat Flux

In this article, we present a fully higher‐order compact (FHOC) finite difference method to investigate the effects of heat flux on natural convection of nanofluids in a right‐angle triangle cavity, where the left vertical side is heated with constant heat flux both partially and throughout the entire wall, the inclined wall is cooled, and the rest of walls are kept adiabatic. The Darcy flow and the Tiwari and Das’ nanofluid models are considered. Investigations with four types of nanofluids were made for different values of Rayleigh numbers with the range of 100 ≤ Ra ≤ 50,000, size of heat flux as 0.1 ≤ ε ≤ 1.0, enclosure aspect ratio as 0.5 ≤ AR ≤ 2.0, and solid volume fraction parameter of nanofluids with the range of 0% ≤ ? ≤ 20%. Results show that the average heat transfer rate increases significantly as particle volume fraction and Rayleigh numbers increase, and the maximum value of average Nusselt number is obtained by decreasing the enclosure aspect ratio. The results also show that the average heat transfer decreases with an increase in the length of the heater. Furthermore, multiple correlations in terms of the Rayleigh numbers and the solid volume fraction of four types of nanoparticles have been established in a general form.     

Natural convection of water-based nanofluids in an inclined enclosure with a heat source

This study investigates natural convection heat transfer of water-based nanofluids in an inclined square enclosure where the left vertical side is heated with a constant heat flux, the right side is cooled, and the other sides are kept adiabatic. The governing equations are solved using polynomial differential quadrature (PDQ) method. Calculations were performed for inclination angles from 0° to 90°, solid volume fractions ranging from 0% to 20%, constant heat flux heaters of lengths 0.25, 0.50 and 1.0, and a Rayleigh number varying from 10⁴ to 10⁶. The ratio of the nanolayer thickness to the original particle radius is kept at a constant value of 0.1. The heat source is placed at the center of the left wall. Five types of nanoparticles are taken into consideration: Cu, Ag, CuO, Al₂O₃, and TiO₂. The results show that the average heat transfer rate increases significantly as particle volume fraction and Rayleigh number increase. The results also show that the length of the heater is also an important parameter affecting the flow and temperature fields. The average heat transfer decreases with an increase in the length of the heater. As the heater length is increased, the average heat transfer rate starts to decrease for a smaller inclination angle (it starts to decrease with inclination at 90° for ? = 0.25, 60° for ? = 0.50, 45° for ? = 1.0, respectively).     

Numerical study of natural convection cooling of horizontal heat source mounted in a square cavity filled with nanofluid

This paper presents a numerical study of natural convection cooling of a heat source horizontally attached to the left vertical wall of a cavity filled with copper-water nanofluid. The left vertical wall is kept at the constant temperature, while the other ones are kept adiabatic. The numerical approach is based on the finite volume method with a collocated grid arrangement. The SIMPLE algorithm is used for handling the pressure velocity coupling. In this study, the influence of some effective parameters such as: Rayleigh number, location and geometry of heat source and solid concentration are studied and discussed. Results are presented in the form of streamlines, isotherms, and average Nusselt number. The results show that dimension of the heat source is an important parameter affecting the flow pattern and temperature field, so that the average Nusselt number decreases with an increase in the length of the heater. It is also observed that at a given Rayleigh number and definite heat source geometry, the average Nusselt number increases linearly with the increase in the solid volume fraction of nanofluid. The increase of Rayleigh numbers strengthens the natural convection flows which leads to the decrease in heat source temperature. The algorithm and the computer code have been also compared with numerical results in order to verify and validate the model.     

Three-dimensional tilted hydromagnetic natural double-diffusive convection in a rectangular cuboid filled with nanofluids based on magnetic nanoparticles

In this article, we use magnetic nanoparticles to explore the three-dimensional natural upward force flow within a quadrangular cuboid under the influence of a sloping magnetic flux. We consider three forms of thermic conditions on the bottom surface of the cavity, such as uniform surface temperature, constant heat flux, and temperature varied parabolically in space. The Galerkin-type finite element method is used to solve the unitless leading equations of implicit physical systems. Ferrite-water nanofluid is the default, used to study the flow field, thermal field, and concentration field other than the regular Nusselt number. We examined the influence of many model parameters, especially the thermal Rayleigh number, volumetric nanoparticles fraction, the Hartmann number, nanoparticles formation, and the predisposition of magnetic flux. The influence of the position of the thermal flux on the lower surface of the thermal field cavity is also studied. The heat transfer rate of various magnetic nanofluids is compared. Our simulated data echoed nicely with the available experimental one. The results show that Mn-Zn ferrite-kerosene nanofluid exhibits advanced heat transportation more than the other nanofluids studied. For lower dimensions of aspect ratio and nanoparticle diameter, higher heat transfer is obtained. Compared with other boundary conditions studied, the uniform temperature on the bottom surface of the cuboid provides a higher heat transfer rate.     

Numerical Analysis of Turbulent Forced Convection of Nanofluid Flow over a Heated Shallow Cavity

This work presents a numerical investigation of turbulent forced convection of a nanofluid over a heated cavity in a horizontal duct. Heat transfers in separated flows are frequently encountered in engineering applications, such as: heat exchangers, axial and centrifugal compressor blades, gas turbines blades, and microelectronic circuit boards. Thus, it is very essential to understand the mechanisms of heat transfer in such regions in order to enhance heat transfer. Different volume fractions of nanoparticles are presented in the base fluid and different types of nanoparticles are used. The objective of this study is to check the effect of nanofluid on heat transfer in such a configuration. Numerical simulations are performed for pure water and four nanofluids (Cu, CuO, Ag, and Al₂O₃). The results are analyzed through the thermal and dynamical fields with a particular interest to the skin friction coefficient and Nusselt number evolutions. The average Nusselt number increases with the volume fraction of nanoparticles for the whole tested range of Reynolds number. A correlation of average Nusselt number versus Reynolds number and volume fraction of each type of nanoparticles over the cavity wall is proposed in this paper.     

Influence of Viscous Dissipation on non‐Darcy Mixed Convection Flow of Nanofluid

In this paper, the steady fully developed non‐Darcy mixed convection flow of a nanofluid in a vertical channel filled with a porous medium with different viscous dissipation models is analyzed. The Brinkman‐Forchheimer extended Darcy model is used to describe the fluid flow pattern in the channel. The transport equations for a nanofluid are solved analytically using the seminumerical‐analytical method known as differential transformation method, and numerically with the Runge‐Kutta shooting method. Finally, the influence of pertinent parameters, such as solid volume fraction, different nanoparticles, mixed convection parameter, Brinkman number, Darcy number, and inertial parameter on the velocity and temperature fields are shown graphically. The results show that velocity and temperature are enhanced when the mixed convection parameter, Brinkman number, and Darcy number increases whereas solid volume fraction and inertial parameter decreases the velocity and temperature fields. The obtained results show that the nanofluid enhances the heat transfer process significantly.     

A numerical investigation of transient natural convection heat transfer of aqueous nanofluids in a differentially heated square cavity

Transient natural convection heat transfer of aqueous nanofluids in a differentially heated square cavity is investigated numerically. The effective thermal conductivity and dynamic viscosity of nanofluids are predicted by using the proposed models that take the contribution of Brownian motion of nanoparticles into account. Three different Rayleigh numbers and five different volume fractions of nanoparticles are considered. The development of natural convection is presented through the evolutions of the average Nusselt number along the cold side wall. The predicted flow development times and time-averaged Nusselt numbers are scaled with Rayleigh number. In addition, the time-averaged Nusselt numbers are presented in terms of volume fraction of nanoparticles. It is shown that at constant Rayleigh numbers, the time-averaged Nusselt number is lowered with increasing volume fraction of nanoparticles.     

Natural convection in a parabolic enclosure with an internal vertical heat source filled with Cu–water nanofluid

The numerical investigation of the natural convection in concave and convex parabolic enclosures with a nanofluid consisting of water and copper nanoparticles is carried out by using the finite volume method. The upper and lower walls of the enclosures are adiabatic while the sidewalls are isothermal at a cold temperature. An internal heat source of constant length (ε = 0.2) and negligible thickness is placed at various vertical positions along the center of the enclosure. It was found that the increase in the location of the heat source leads to a drop in the water and nanofluid flow circulation in both types of enclosures. For both considered Cases I and II, the average Nusselt number increases when the Rayleigh number and solid volume fraction increase. Moreover, it was concluded that Case I with δ = 0.8 is the optimum case for heat transfer enhancement for Ra = 10³ and Ra = 10⁴. Case II with δ = 0.5 is optimum for Ra = 10⁵. Both cases are satisfied when the nanofluid is used with ? = 0.2.     

Modeling of conjugated heat transfer in a thick walled enclosure filled with nanofluid

The objective of this paper is to investigate the conjugated heat transfer in a thick walled cavity filled with copper-water nanofluid. The analysis uses a two-dimensional rectangular enclosure under conjugated convective-conductive heat transfer conditions and considers a range of Rayleigh numbers. The enclosure was subjected to a constant and uniform heat flux at the left thick wall generating a natural convection flow. The thicknesses of the other boundaries are assumed to be zero. The right wall is kept at a low constant temperature while the horizontal walls are assumed to be adiabatic. A moveable divider is located at the bottom wall of the cavity. The governing equations are derived based on the conceptual model in the Cartesian coordinate system. The study has been carried out for the Rayleigh number in the range of 10⁵ ≤ Ra ≤ 10⁸, and for the solid volume fraction at 0 ≤ ? ≤ 0.05. Results are presented in the form of streamlines, isotherms, average Nusselt number and input heat absorption by the nanofluid. The effects of solid volume fraction of nanofluids, the location of the divider and also the value of the ambient convective heat transfer coefficient on the hydrodynamic and thermal characteristics of flow have been analyzed. An increase in the average Nusselt number was found with the solid concentration for the whole range of Rayleigh number. In addition, results show that the position of the divider and the ambient convective heat transfer coefficient have a considerable effect on the heat transfer enhancement.     

Effect of heat generation/absorption on natural convective boundary-layer flow from a vertical cone embedded in a porous medium filled with a non-Newtonian nanofluid

This work is focused on the study of the natural convection boundary-layer flow over a downward-pointing vertical cone in a porous medium saturated with a non-Newtonian nanofluid in the presence of heat generation or absorption. The transformed boundary layer governing equations are solved numerically. The influences of pertinent parameters such as the heat generation or absorption, the solid volume fraction of nanoparticles and the type of nanofluid on the flow and heat transfer rate in terms of Nusselt number are discussed. Comparisons with previously published work on special cases of the problem are performed and found to be in excellent agreement. The generalized governing equations derived in this work can be applied to different cases of non-Newtonian fluids with different values of the power-law viscosity index. The results of this parametric study are shown graphically and the physical aspects of the problem are highlighted and discussed.     

Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field

In this paper, we examine the convective flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the presence of a magnetic field. The governing partial differential equations with the auxiliary conditions are reduced to ordinary differential equations with the appropriate corresponding conditions via scaling transformations. The analytical solutions of the resulting ODEs are obtained, and from which the analytical solutions of the original problem are presented. The influence of pertinent parameters such as the magnetic parameter, the solid volume fraction of nanoparticles and the type of nanofluid on the flow, heat transfer, Nusselt number and skin friction coefficient is discussed. Comparison with published results is presented.