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Applying nanofluids with modification in the structure have engrossed in fluid mechanics. This utilization has demonstrated significant enhancement in heat exchangers performance. In this work, a double pipe heat exchanger with loaded Al2O3-TiO2 hybrid nanofluid in turbulent flow regimes is studied and evaluated through exergy analysis. Praised equations are employed to verify the resulted information. In order to obtain the exergy efficiency of the nanofluid-loaded double pipe heat exchanger a complete factorial experimental design approach was employed. Nanofluid concentration in the range of 0.2 to 1.5, Reynolds number from 3000 to 12000, and twist ratio between 2 to 8 are considered as the test's variables. Statistical analysis including the Student’s t-test, variance analysis, F-test, and lack of fit is performed to determine the most significant parameters on the exergy efficiency. It is concluded that applying nanocomposites and twisted tapes boost up the exergy efficiency in comparison to utilizing conventional water as a heat transfer fluid. Moreover, raising the nanoparticles volume concentration and the Reynolds number, simultaneous to decreasing the twist ratio can result in higher exergy efficiency.

The aim of the present study is to analyze the entropy generation and convective heat transfer in a bottom-heated wavy porous cavity containing a solid rotating cylinder. An isothermal heater of length h is placed on the bottom wall of the cavity, while both the left and right vertical wavy walls are maintained at a constant cold temperature Tc. The remainder parts of the bottom wall and the top wall are kept adiabatic. The Forchheimer-Brinkman-extended Darcy model is assumed to hold. The dimensionless governing equations subject to the selective boundary conditions are solved numerically using the Galerkin weighted residual finite element method. The governing parameters of this study are the Rayleigh number (Ra = 105 and 106), angular rotational velocity (− 1000 ≤Ω≤ 1000), Darcy number (10−6 ≤ Da ≤ 10−2), number of oscillations (1 ≤ N ≤ 4) and porosity of the medium (0.2 ≤ e ≤ 0.8). The developed computational code is validated comprehensively using the grid independence test and numerical data of other authors. The obtained results reveal that the flow control can be accomplished by the angular rotational velocity or direction of the cylinder rotation, which have important design implications in practical applications. In addition, an augmenting in the porosity of the medium causes an increase in heat transfer from the wall to the fluid and therefore an increase in the convective flow and consequently a decrease in the Bejan number.

Local thermal non-equilibrium effects on heat natural convection features in a horizontal confocal elliptical annulus with the inner cylinder covered with a nanofluid-saturated porous sleeve is investigated in this study. The steady and laminar natural convective flow is incited by the thermal buoyancy resulting from the differential heating between the inner and outer annulus' surfaces. The nanofluid phase and the solid phase of the porous sleeve are hors local thermal equilibrium situation. The heat and the hydrodynamics equations in their dimensionless form under Darcy-Brinkman Forchheimer model for the porous region were computationally solved by the finite volume technique using the standard SIMPLER algorithm. The results were analyzed according to different porous materials characteristics under LTNE condition. The standard 0.05 significance level was employed to determine the local thermal equilibrium situation in the porous sleeve. For the first time, contours of the spatial distribution of the LTNE sources within the porous sleeve region were represented.

Numerical study of mixed convection in a lid-driven 3D flexible walled trapezoidal cavity with nanofluids was performed by using Galerkin weighted residual finite element method. Effects of various pertinent parameters such as Richardson number (between 0.05 and 50), elastic modulus of the side surfaces (between 1000 and 10 5 ), side wall inclination angle (between 0° and 20°) and solid particle volume fraction (between 0 and 0.04) on the fluid flow and heat transfer characteristics in a 3D lid-driven-trapezoidal cavity were numerically examined. It was observed that these characteristics are influenced when the pertinent parameters change. Flexible side surface can be used as control element for heat transfer rate. Increment and reduction in the space which are provided by the flexible side walls result in heat transfer enhancement and deterioration for side wall inclination angle of 0° and 10°. Average Nusselt number enhances by about 9.80 % when the value of the elastic modulus is increased from 1000 to 10 5 for side wall inclination angles of θ = 0°. Adding nanoparticles to the base fluid results in linear increment of heat transfer and at the highest volume fraction, 25.30 % of heat transfer enhancement is obtained. A polynomial type correlation for the average Nusselt number along the hot wall was proposed and it has a fourth order polynomial dependence upon the Richardson number and first order dependence upon the solid particle volume fraction.

This study aims to explain the impact of the presence of a solid conductive partition on the thermal-free convective motion mechanism and heat transmission process within a concentric circular annulus filled with a water-based hybrid nanoliquid containing Copper (Cu) and Alumina (Al2O3) nanoparticles. The thermal natural convective flow is formed within the annulus due to the temperature difference which is externally imposed between the internal heated cylinder and the external cooled one and internally generated by the interior heat generation/absorption (IHG/A) phenomenon. The technique of finite volume is applied to discretize and approximately solve the non-dimensional conservation equations. The influence of selected factors such as the nanoparticles concentration, Rayleigh number, fluid/solid heat conductivity ratio, and the IHG/A parameter on the thermo-hydrodynamic behavior and heat exchange rate is interpreted. The findings show that, in the presence of a conductive solid partition, the combined effects of the IHG/A phenomenon and the combined nanoparticles considerably modify the flow and heat exchange behaviors within the annulus. We also employed a new correlation to predict the mean heat exchange rate in the defined input parameter range.

The magnetohydrodynamic conjugate heat transfer characteristics of a ferrofluid-filled porous inclined enclosure heated differentially have been investigated numerically in the present work. Two-conducting fins are attached to the hot wall of the cavity and the horizontal walls are insulated. The ranges of dimensionless flow controlling parameters are taken as: modified Rayleigh number (10 ≤ Ra⁎ ≤ 104), length of the fins (a = 0.3, 0.5, 0.7), gap between the two fins (b = 0.3, 0.5, 0.7), and Darcy number (10−5 ≤ Da ≤ 10−2), volume fractions of nanoparticles (0 ≤ ϕ ≤ 0.06), Hartmann number (0 ≤ Ha ≤ 50), and the cavity inclination angles (0 ≤ γ ≤ 90o). The finite element method has been used to solve the governing equations and the present code have been validated with previously published work. The results show that the average Nusselt number increases by increasing the modified Rayleigh number, Darcy number, fins length while it decreases by increasing the Hartmann number. For any range of modified Rayleigh numbers, the highest fin length and the widest gap between the fins can be a superior heating strategy. At a fixed fin length, the lower gap between the fins is of a better choice to boost heat transfer when the cavity inclination angle increases up to 30o.

Convective heat transfer is a major phenomenon in different technical and natural systems. This process can be found in enclosures under the different temperature distributions at bounded walls. In this research, the thermogravitation energy transport of a non-constant viscosity medium inside a 3D region under the non-uniform or uniform temperature profile at one of the vertical walls is addressed. The opposite border is at a low constant temperature, and the remaining borders are well insulated. The control equations with the border restrictions are reduced into a non-dimensional form and then integrated by the finite difference procedures. The control characteristics are the Rayleigh number and viscosity changeable magnitude. The impacts of these characteristics on the energy transference and flow structures are studied.

The purpose of this paper is to assess thermal management and optimization of several parameters such as: materials, size and thickness of all subcomponents of single-chip Light Emitting Diode (LED) in order to minimize its junction temperature and thereby maximizing light output and device reliability. For this, we developed a three-dimensional code using Comsol Multiphysics that solves the systems of equations for the mass, momentum and energy. After validation of this numerical 3D code, the thermal Characterization of Subcomponents of LED system is studied numerically. This system is divided into 6 parts such as: metallization, die, die-attach, substrate, Thermal Interface Material and heat sink. Several materials which can be used in each part of the LED package from metallization to the heat sink are studied. By moving to one part to another, it was selected the best materials always allowing a minimum junction temperature.

A confined slot jet impinging into an open trapezoidal cavity containing a porous layer is investigated. To make the study accounts for a practical problem, constant heat flux is applied at the bottom of the cavity which is covered by a thin porous layer subjected to a cold impingement air jet. Darcy-Forchheimer model is used for the porous layer and its porosity range was taken to ensure thermal equilibrium between the fluid and the porous matrix. Finite element method is adopted for the numerical solution. Results show that the best thickness of the porous layer should be as minimal as possible, where increasing the porous layer thickness from 0.1 to 0.3 reduces the average Nusselt number by 17% when Darcy number is 10−3. It is found also that the trapezoidal cavity serves in attaining the fully developed condition early.

This paper intends to analyze computationally the rarefied gaseous flow and performance of heat transfer for a steady-state laminar 2D free convection within tilted enclosures where the sided walls are of wavy shape. Low-pressure or rarefied flows are flows with Knudsen number greater than zero. These kinds of flows are of incredible significance in different applications. Boussinesq estimation is adopted to represent the buoyancy effects. Grid independence tests are carried out to ensure accuracy. Moreover, the current code is verified with numerical and experimental results existing in the literature. Flow and thermal fields for simulated cases are presented. The outcome of this research indicates that there is a direct relationship between the average Nusselt number and the Rayleigh number, and a converse relationship between the average Nusselt number and Knudsen number. Additionally, the numerical simulations reveal that increasing the amplitude of the two-sided wavy walls of the enclosure slightly mends the transfer of heat. Besides, it is determined that the tilt angle slightly affects the heat transfer performance of such flows; and it is evident from the simulations that horizontal or nearly horizontal orientations of such cavities give the maximum transfer of heat. Finally, a correlation representing the relationship of the average Nusselt number in terms of all the examined parameters is introduced.

The unsteady thermal flow and heat transfer adjacent to the sidewall of a differentially heated cavity with single and multiple nonconductive fins are investigated utilizing the finite element method. The transition to the unsteady flow, as well as flow oscillations, is described for the water-filled cavity and Rayleigh numbers ranging from 1 × 107 to 1 × 1010, including the critical Rayleigh number. Characteristics of unsteady flows are investigated for early, transitional, and quasi-steady stages. For all cases, heat transfer from the finned sidewall to the interior fluid is quantified and compared with the cavity without the fin. Results show that the volumetric flow rate along the vertical axis in the middle of the cavity rises by increasing the number of fins (up to 13.41% for the cavity with two fins for Ra = 1.84 × 109) in transitional and quasi-steady stages. Moreover, the increment of fin number and Ra leads to a higher enhancement factor (e) that shows the heat transfer enhancement or depression. For Ra = 1.84 × 109, the maximum e for the cavity with one and three fins is calculated about 17.5% and 34% respectively.

We investigated the Hall and ion slip effects on the MHD convective flow of elastico-viscous fluid through porous medium between two rigidly rotating parallel plates with time fluctuating sinusoidal pressure gradient in this paper. In an initially undisturbed state both the fluid and the plates are in rigid rotation with the uniform angular velocity Ω about the normal to the plates. At t > 0 the fluid is driven by a fluctuating pressure gradient parallel to the channel walls. Analytical solutions for the velocity, temperature and concentration are evaluated and discussed computationally with the help of graphical profiles. For engineering interest, we obtained skin friction, Nusselt number, Sherwood number and volumetric flow rate and discussed numerically. Elasticity and magnetic field resist the fluid motion gets thinner boundary layer. Lesser frequency of oscillating pressure gradient frightens the reverse flow. The similar variation of skin friction should be circumvented with less significant time span and strength of the magnetic field.

In this work, the role of various configurations of wavy circular heater and nanoparticles on convective heat transfer inside an enclosure having a wavy circular heater is explored. Various configurations of the inner wavy heater are considered. Numerical solutions of dimensionless governing equations are obtained via a hybrid method called Control Volume Finite Element Method (CVFEM). The influence of active parameters e.g. undulation number, wavy contraction ratio and so on is perused on convective heat transfer. According to the outcomes, it was found that the configuration of the wavy heater plays a crucial role in controlling the convective flow characteristic and the heat transfer rate within the enclosure. Hence, the present study can be a useful source for the manufactures of heated elements.

Transient natural convection of an alumina-water nanofluid saturated in non-Darcy porous media is investigated in this paper. The domain of the nanofluid is an annulus composed from a square cavity confining a solid conductive body. The nanoparticles are assumed to be slipping in the base fluid according to Buongiorno model. The Brinkman-Forchheimer-extended Darcy formulation has been adopted for the porous medium. The dimensionless governing equations are solved by implementing the finite difference method. In this study, a special focus is given on the following model parameters; porosity of the porous medium, Darcy number and the nanoparticles average volume fraction. The results show that the nanoparticles possess high uniformity in the base fluid and the Nusselt number augments with increasing values of the Darcy number. The porosity increases the average Nusselt number at a higher Darcy number while its influence remains negligible at a low Darcy number. For the given porosity, there is a critical value of the nanoparticles volume fraction when the average Nusselt number is maximal.

This work is focused on the numerical modeling of steady laminar mixed convection flow in a lid-driven cavity with a wavy wall filled with a water–CuO nanofluid. The left and right walls of the enclosure are kept insulated while the bottom and top walls are maintained at constant temperatures with the top surface being the heated lid wall and moving at a constant speed. The governing equations for this investigation are given in terms of the stream function–vorticity formulation and are non-dimensionalized and then solved numerically subject to appropriate boundary conditions by a second-order accurate finite-volume method. Various comparisons with previously published work are performed and the results are found to be in good agreement. A parametric study of the governing parameters such as the Richardson number, bottom wall geometry ratio (B/H) and the nanoparticles volume fraction is conducted and a representative set of graphical results is presented and discussed to illustrate the effects of these parameters on the flow and heat transfer characteristics. It is found that the presence of nanoparticles causes significant heat transfer augmentation for all values of Richardson numbers and bottom wall geometry ratios.

A study of natural convective flow, heat transfer and entropy generation in an odd-shaped geometry is presented here. The geometry considered is a combination of the horizontal and vertical enclosure shapes. The cavity is filled with Cu–water nanofluid. The numerical study focuses specifically on the effect of natural convection parameter and solid volume fraction of nanoparticle on the average Nusselt number, total entropy generation and Bejan number. Also isotherms, stream function and entropy generation due to heat transfer are presented for various Rayleigh number and solid volume fraction. The governing equations are solved by using penalty finite element method with Galerkins weighted residual technique. The results reveal that increasing Rayleigh number causes increase of the average Nusselt number as well as the heat transfer term of entropy generation and decrease of the viscous term. The proper choice of Rayleigh number could be able to maximize heat transfer rate simultaneously minimizing entropy generation.

article i nfo This paper presents a numerical study of a double diffusive convection in a cubic cavity filled with a binary mixture. The verticalwalls are given differenttemperaturesand concentrations. The potential-vorticity formulation in three-dimensional configuration using the finite volume method is utilized in this study. The results are given for Rayleigh number Ra = 10 5 , Prandtl number Pr = 10 and Lewis number Le = 10, characterizing the case of aqueous solutions. The influence of the magnetic field on the structure of the three-dimensional flow, the distribution of temperature and concentration and the different characteristics of heat and mass transfer of the thermal and solutal dominated region are presented.

The flow, heat and nanoparticle mass transfer characteristics in the free convection from a vertical plate in a thermally linearly stratified nanofluid saturated non-Darcy porous medium under convective boundary condition is investigated. In addition, the magnetic field effect under convective boundary condition is incorporated in the nanofluid model. The transformed non-similar non-linear coupled partial differential equations representing the transport of mass, momentum, thermal energy, and the nanoparticles volume fraction are solved numerically by the Blottner [18] scheme, which is modified to accommodate the effect of the convective boundary condition. The accuracy of the numerical results is validated by a quantitative comparison of the heat transfer rates with previously published results for a special case and the results are found to be in good agreement. It is observed that the thermal transport is significantly affected due to the stratification of the medium and it is more significant with varying values of the parameters related to the nanofluid in the medium as well as the Biot number due to the convective boundary condition. The effects of thermal stratification, non-Darcy, convection and magnetic field parameters on the velocity, temperature, nanoparticle volume fraction, heat and nanoparticle mass transfer rates are illustrated graphically.

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.

Mixed convection flows in a lid-driven square cavity filled with porous medium are studied numerically using penalty finite element analysis for uniform and non-uniform heating of bottom wall. The relevant parameters in the present study are Darcy number (Da = 10− 5− 10− 5), Grashof number (Gr = 103− 105), Prandtl number (Pr = 0.026−10) and Reynolds number (Re = 1−102). The influence of convection is analyzed with Peclet number (Pe = Re.Pr). It is observed that the temperature profiles are symmetric for low values of Pe or Pr even in the presence of asymmetric flow fields irrespective of Da. The flow distribution affects significantly temperature distributions at high Pe irrespective of Da. Effect of Peclet numbers have been further investigated for both natural convection and forced convection dominant regimes at high Da. Strong coupling between flow fields and temperature are observed at high Pe. It is interesting to observe that large isothermal mixing zone at Pr = 10 reduces the overall flow strength compared to Pr = 0.026 case. Local Nusselt numbers show almost uniform and low values for low Peclet numbers and localized enhanced heat transfer rates are observed for high Peclet numbers at Da = 10− 3.