The conjugate natural convection of a new type of hybrid nanofluid (Ag–MgO/water hybrid nanofluid) inside a square cavity is addressed. A thick layer of conductive solid is considered over the hot ...wall. The governing partial differential equations (PDEs) representing the physical model of the natural convection of the hybrid nanofluid along with the boundary conditions are reported. The thermophysical properties of the nanofluid are directly calculated using experimental data. The governing PDEs are transformed into a dimensionless form and solved by the finite element method. The effect of the variation of key parameters, such as the volume fraction of nanoparticles, Rayleigh number, and the ratio between the thermal conductivity of the wall and the thermal conductivity of the hybrid nanofluid (
R
k
), is studied. Furthermore, the effects of the key parameters are investigated on the temperature distribution, local Nusselt number, and average Nusselt number. The results of this study show that the heat transfer rate increases by adding hybrid nanoparticles for a conduction-dominant regime (low Rayleigh number). The heat transfer rate is an increasing function of both the Rayleigh number and the thermal conductivity ratio (
R
k
). In the case of a convective-dominant flow (high Rayleigh number flow) and an excellent thermally conductive wall, the local Nusselt number at the surface of the conjugate wall decreases substantially by moving from the bottom of the cavity toward the top.
In the present study, an advanced type of artificial intelligence, a deep neural network, is employed to learn the physic of conduction heat transfer in 2D geometries. A dataset containing 44,160 ...samples is produced by using the conventional finite volume method in a uniform grid of 64 × 64. The dataset includes four geometries of the square, triangular, regular hexagonal, and regular octagonal with random sizes and random Dirichlet boundary conditions. Then, the dataset of the solved problems was introduced to a convolutional Deep Neural Network (DNN) to learn the physics of 2D heat transfer without knowing the partial differential equation underlying the conduction heat transfer. Two loss functions based on the Mean Square Errors (MSE) and Mean of Maximum Square Errors (MMaSE) are introduced. The MMaSE is a new loss function, tailored for the physic of heat transfer. The 70%, 15%, and 15% of images are used for training DNN, testing DNN, and validation of the DNN during the training process, respectively. In the validation stage, the 2D domain with random boundary conditions, in which DNN has never seen them before, is introduced to DNN. Then, DNN is asked to estimate the temperature distribution. The results show that the DNNs are capable of learning physical problems without knowing the underlying fundamental governing equation. The error analysis for various training methods is reported and discussed. The outcomes reveal that DNNs are capable of learning physics, but using MMaSE as a tailored loss function could improve the training quality. A DNN trained by MMaSE provides a better temperature distribution compared to a DNN trained by MSE. As the 2D heat equation is a Laplace equation, which is practical in multiple physics, the results of the present study indicate a new direction for future computational methods and advanced modeling of physical phenomena, using a big dataset of observations.
•The melting heat transfer of an electrically conductive fluid addressed.•The melting fluid is subject to a line source magnetic field.•A moving grid method is utilized to track the phase change ...interface.•The FEM with ALE moving mesh technique is employed.•The magnetic-source location induces a notable effect in a convection-dominant regime.
Melting flow and heat transfer of electrically conductive phase change materials subjecting to a non-uniform magnetic field are addressed in a square enclosure. The top and bottom walls of the cavity are adiabatic, and the sidewalls are isothermal at different temperatures. The temperature of the hot wall is higher than the fusion temperature of PCM (Tf), and the cold wall is at the fusion temperature or lower. At the initial time, the cavity is filled with a solid saturated PCM. In the vicinity to the hot wall, there is an external line-source magnet, inducing a magnetic field. The location of the magnetic source (Y0) can be changed along the hot wall. The cavity domain is divided into two parts of the liquid domain and the solid domain. The moving grid method is utilized to track the phase change interface at the exact fusion temperature of Tf. The governing equations for continuity, flow and heat transfer associated with the Arbitrary Lagrangian–Eulerian (ALE) moving mesh technique are solved using the finite element method. The results are investigated for the melting behavior of PCM by the study of Hartmann number (0 ≤ Ha ≤ 50) and the location of the magnetic source (0 ≤ Y0 ≤ 1). Outcomes show that the effect of the magnetic field on the melting behavior of PCM is negligible at the initial stages of the melting (Fo < 1.15). However, after the initial stages of the melting, the effect of the presence of a magnetic field becomes significant. Moreover, the location of the magnetic source induces a feeble effect on the melting front at the initial melting stages, but its effect on the shape of the melting front increases by the increase of the non-dimensional time. The location of the magnetic source also significantly affects the streamlines patterns. Changing the position of the magnetic source from the bottom of the cavity (Y0 = 0.2) to the almost middle of the cavity (Y0 = 0.6) would decrease the required non-dimensional time of full melting from Fo = 10.4 to Fo = 9.0.
The free convection heat transfer of Cu-water nanofluids in a parallelogrammic enclosure filled with porous media is numerically analyzed. The bottom and top of the enclosure are insulated while the ...sidewalls are subject to limited temperature difference. The Darcy flow and the Tiwari and Das' nanofluid models are considered. The governing dimensionless partial differential equations are numerically solved using a finite difference code. The results are reported for isotherms and streamlines as well as Nusselt number as a function of the volume fraction of nanoparticles, porosity, types of the porous matrix, inclination angle, aspect ratio and different Rayleigh numbers. It is found that the presence of the nanoparticles inside the enclosure deteriorates the heat transfer rate, which is caused due to the increase of dynamic viscosity by the presence of nanoparticles. Therefore, in applications in which the nanofluids are used for their advantages, such as enhanced dielectric properties or antibacterial properties, more caution for the heat transfer design of the enclosure is necessary.
•Study on zigzag latent heat storage system during melting and solidification.•Study on the zigzag angle orientation of the system toward the optimum case.•32.6% higher heat storage rate for a higher ...angle of the zigzag wall.•Lower charging/discharging time using higher flow rate and temperature of the fluid.
Due to the remarkable energy savings, isothermal nature of the operation and low costs, energy storage with phase-change materials (PCMs) is a reliable technology for filling the gap between energy supply and demand. In this paper, an attempt has been made to modify the storage functionality of PCM in a plate type heat exchanger with zigzag configuration. A two-dimensional, time-dependent simulation model for the PCM phase transition during the charging and discharging modes has been developed and validated via earlier related findings. The effects of zigzag angle orientation, inlet flowrate and mean temperature of the heat transfer fluid (HTF) are thoroughly studied and revealed. Results show that increasing the angle of zigzag orientation has no noticeable impact on the development of phase transition during the early stages of operation. However, this effect becomes more noticeable and almost leads to faster storage/retrieval rates as time further elapses. It is found that the system with the zigzag angle of 60° augments the storage rate by 32.6% compared with the system of 30° zigzag angle. Also, higher HTF temperature and/or higher Reynold number result in faster phase-transition rates during both parts of the energy charging-discharging cycle.
•Fluid-Structure Interaction (FSI) for non-Newtonian natural convection is addressed.•There is a flexible elastic fin on the hot wall of the cavity.•The Arbitrary Lagrangian-Eulerian (ALE), along ...with the moving mesh is used.•The ALE technique is employed to track the deformation of the flexible fin.•The dilatant and pseudoplastic effects of the working fluids are investigated.
In the present study, the flow and heat transfer of a power-law non-Newtonian fluid in a cavity are addressed. The top and bottom walls of the cavity are well insulated, the left vertical wall is at a hot temperature, and the right wall is at a low temperature. A flexible elastic fin is mounted at the hot wall of the cavity. The non-Newtonian fluid circulates inside the cavity due to the buoyancy forces. Fluid-Structure Interaction (FSI) and the non-Newtonian flow within the cavity and the hot fin are coupled. The flow interaction with the fin leads to the deformation of the fin, and the change in the shape of the fin changes the flow and heat transfer. Hence, the coupling between the fluid and the structure is two ways. The Arbitrary Lagrangian-Eulerian (ALE) along the moving mesh method is employed to model the deflection of the structure inside the fluid domain. The finite element method is adopted to solve the governing equations. The results show that the deflection of the fin is higher for a dilatant non-Newtonian fluid, compared to the pseudoplastic and Newtonian fluids. The number of flow vortexes and flow hydrodynamic notably change by the variation non-Newtonian index. The variation of the non-Newtonian index produce minimal effects on the heat transfer rate. Moving from pseudoplastic effects to Newtonian and dilatant effects reduces the heat transfer rate and increases the internal stresses in the fin. Moreover, the maximum stress in stiff-fins is higher than soft-fins.
Display omitted
•Flow, heat, and mass transfer of hybrid nanofluids in a wavy chamber were addressed.•A two-phase approach, including the Brownian motion and thermophoresis forces, was ...introduced.•The drift flux of composite hybrid nanoparticles was computed.•The concentration distribution of composite nanoparticles was investigated.•The location of the solid block and undulation of surfaces are investigated.
Mixed convection flow and heat transfer within various cavities including lid-driven walls has many engineering applications. Investigation of such a problem is important in enhancing the performance of the cooling of electric, electronic and nuclear devices and controlling the fluid flow and heat exchange of the solar thermal operations and thermal storage.
The main aim of this fundamental investigation is to examine the influence of a two-phase hybrid nanofluid approach on mixed convection characteristics including the consequences of varying Richardson number, number of oscillations, nanoparticle volume fraction, and dimensionless length and dimensionless position of the solid obstacle.
The migration of composite hybrid nanoparticles due to the nano-scale forces of the Brownian motion and thermophoresis was taken into account. There is an inner block near the middle of the enclosure, which contributes toward the flow, heat, and mass transfer. The top lid cover wall of the enclosure is allowed to move which induces a mixed convection flow. The impact of the migration of hybrid nanoparticles with regard to heat transfer is also conveyed in the conservation of energy. The governing equations are molded into the non-dimensional pattern and then explained using the finite element technique. The effect of various non-dimensional parameters such as the volume fraction of nanoparticles, the wave number of walls, and the Richardson number on the heat transfer and the concentration distribution of nanoparticles are examined. Various case studies for Al2O3-Cu/water hybrid nanofluids are performed.
The results reveal that the temperature gradient could induce a notable concentration variation in the enclosure.
The location of the solid block and undulation of surfaces are valuable in the control of the heat transfer and the concentration distribution of the composite nanoparticles.
•The conjugate free convection phase change heat transfer is addressed.•The phase change materials are embedded in a metal foam.•The effect of a transient pulse heat flux is investigated.•Melting and ...solidification heat transfer during a pulse cycle are studied.
The conjugate flow and heat transfer of phase change materials (PCMs)-metal foam confined between two annuli is addressed. A pulse heat load is employed at the inner surface of annuli, while the outer surface is subject to convection cooling. (This content of this sentence is the same as that in other sentences.) The enthalpy-porosity approach is utilized to model the phase change, and the natural convection in the porous medium is taken into account using Darcy-Brinkman model. The governing equations are transformed into non-dimensional form and solved by the finite element method. The finite element method is employed to solve the governing equations in the non-dimensional form. An automatic grid adaptation technique is employed to capture the phase change interface. The results are compared with theoretical and experimental studies available in the literature and found in good agreement. The steady-state solution and transient characteristics are addressed. The results demonstrate that the heatsink filled with PCM-metal foam can enhance the heat transfer at the hot surface, particularly at low external cooling power (Biot number < 0.2). The results reveal that the fusion temperature of phase change material is the key parameter on temperature controlling of the hot surface. Using the phase change heatsink results in a cooling power four times higher than that of pure external convection during the pulse load.
The present investigation addressed the entropy generation, fluid flow, and heat transfer regarding Cu-Al 2 O 3 -water hybrid nanofluids into a complex shape enclosure containing a hot-half partition ...were addressed. The sidewalls of the enclosure are made of wavy walls including cold isothermal temperature while the upper and lower surfaces remain insulated. The governing equations toward conservation of mass, momentum, and energy were introduced into the form of partial differential equations. The second law of thermodynamic was written for the friction and thermal entropy productions as a function of velocity and temperatures. The governing equations occurred molded into a non-dimensional pattern and explained through the finite element method. Outcomes were investigated for Cu-water, Al 2 O 3 -water, and Cu-Al 2 O 3 -water nanofluids to address the effect of using composite nanoparticles toward the flow and temperature patterns and entropy generation. Findings show that using hybrid nanofluid improves the Nusselt number compared to simple nanofluids. In the case of low Rayleigh numbers, such enhancement is more evident. Changing the geometrical aspects of the cavity induces different effects toward the entropy generation and Bejan number. Generally, the global entropy generation for Cu-Al 2 O 3 -water hybrid nanofluid takes places between the entropy generation values regarding Cu-water and Al 2 O 3 -water nanofluids.
PDF
