Governing Conservation Equations Research Articles

Influence of Suction and Injection on Peristaltic Mechanism of a Jeffrey Nanofluid in a Vertical Channel with Complete Slip Effects

The main goal of the current study is to understand how the peristaltic system of a Jeffrey nanofluid operating in a vertical tube with complete slip properties is influenced by suction and injection. The peristaltic flow was examined by several researchers using various biological fluid types. The majority of the authors used viscous (Newtonian) fluids to illustrate the peristaltic flow mechanism. Because of its uses in industry, non-Newtonian fluids have attracted a great deal of attention. There are numerous models for non-Newtonian liquids because of the complexity of fluids. The Jeffrey fluid model is the most straightforward linear model to depict the non-Newtonian fluid characteristics for which it is reasonable to expect that accurate or analytical solutions would eventually be discovered. Nanofluids are innovative substances that have endless applications in engineering, biology, medicine and other fields. This mathematical model can be used effectively to transport cervical cancer in the tiny blood channels of the cervix. The resulting flow model is then effectively simulated with the appropriate assumptions of a small Reynolds number and long wavelength. The governing conservation equations are then established. Analytical solutions have been found for, pressure rates per wavelength, temperature, velocity and concentrations of nanoparticles in the resultant flow problem. Using the software WOLFRAM MATHEMATICA, the effects of all physical parameters on streamline, velocity, temperature, concentration fields, pressure gradient, frictional force and pressure rate are graphically analyzed. We observed in both 2D-plot and 3D-plot that we increasing the slip parameters β1 and β2 lead to increase the velocity profile. By raising the Jeffrey nanofluid parameter, the pressure rise is decreased. With frictional force, the opposite behavior is observed. The effect of suction and injection parameter k on the trapping bolus, which gets greater as k is higher.

Ternary cobalt ferrite (CoFeO4)-silver (Ag)-titanium dioxide (TiO2) hybrid nanofluid hydromagnetic nonlinear radiative-convective flow from a rotating disk with viscous dissipation, non-Darcy and non-Fourier effects: Swirl coating simulation

Magnetic nanoparticles are increasingly being deployed in smart coating systems due to their exceptional functionalities and abilities to be tuned for specific environmental conditions. Inspired by the emergence of tri-hybrid magnetic nanofluids which utilize three distinct nanoparticles in a single base fluid coating, the present article examines analytically and computationally the swirl coating of magnetic ternary hybrid nanofluid from a rotating disk, as a simulation of spin coating deposition processes in materials manufacturing. Owing to high temperature fabrication conditions, thermal radiative heat transfer is also considered and a Rossleand flux model deployed. -- hybrid nanoparticles are considered with Ethylene Glycol-Water () base fluid. A filtration medium is also featured (porous medium) adjacent to the disk and the Darcy-Forchheimer model is deployed to simulate both bulk matrix porous drag encountered at lower Reynolds numbers and inertial quadratic drag generated at higher Reynolds numbers. Thermal relaxation of the coating nanofluid is additionally addressed and a non-Fourier Cattaneo-Christov model is therefore implemented in the heat conservation equation. Viscous dissipation is also included in the model. The governing conservation equations for mass, momenta (radial, tangential and axial) and energy with prescribed boundary conditions are rendered into coupled nonlinear ordinary differential boundary layer equations via suitable scaling variables and the Von Karman transformations. The derived reduced boundary value problem is then solved with a Runge-Kutta numerical scheme and shooting scheme in MATLAB. Validation of solutions is included with previous studies. Radial and azimuthal velocities, temperature, radial skin-friction, azimuthal skin friction and local Nusselt number are computed for a range of selected parameters. A comparative assessment of mono nanofluid Hybrid - nanofluid and tri-Hybrid -- nanofluid is conducted. This combination of hybrid nanoparticles has never been examined previously in the literature and constitutes the significant novelty of the present work. Both radial and tangential velocity are depleted with increasing applied magnetic field whereas temperature and thermal boundary layer thickness are increased.

Effects of complete slip conditions on the peristaltic pumping of a Casson nanofluid with suction and injection in a vertical channel

This study investigates the effects of complete slip conditions on the peristaltic pumping of a Casson nanofluid with suction and injection in a vertical due to the crucial role that nano liquids play in a variety of technological and medical fields, particularly in peristalsis, a mechanism that transports liquids. The Casson fluid belongs to a class of non-Newtonian fluids that, through a particular stress threshold magnitude, exhibit elastic solid behavior before changing to liquid behavior. These fluids have several uses in engineering, food preparation, drilling and other fields. After establishing the governing conservation equations, the resulting flow model is effectively simulated using the realistic assumptions of a long wavelength and a low Reynolds number. The temperature distributions, velocity, pressure rate per wavelength and nanoparticle concentration of the resulting flow problem have been solved analytically. The effects of all physical factors on temperature, velocity, concentration fields, pressure rate, frictional force and pressure gradient are graphically examined using Wolfram MATHEMATICA software. There are a variety of biofluids that cannot be classified as liquids. For example, blood contains WBC, RBC and plasma. It is essential to model biofluids (blood) as nanofluids given the physical properties of these biofluids. According to reports, one of the finest yield stress models is the Casson model, and blood exhibits a similar behavior. We took these facts into consideration when thinking about Casson nanofluid flow in a vertical layer under peristalsis. Additionally, the suction and injection mechanisms can be used to represent the exchange of carbon dioxide in bold. In order to understand how blood flows through small blood vessels, this model must be examined. The obtained results show that the Newtonian case and those found in the literature have a very good agreement. Since the liquid moves faster and more effectively when the value is increased, it becomes clear that this increases the strength of the velocity. In other words, nanoperistaltic pumps can maintain a pressure differential that increases or decreases at all operating flow rates with an increasing thermophoresis effect. Furthermore, it is obvious that the pressure reduction in a Casson fluid is greater than in a Newtonian fluid.

Peristaltic motion of a Casson nanofluid in a vertical layer with suction and injection

Inquisitive researchers have studied the movement of peristaltic nanofluids due to the enlightening impact of nanoliquids in various technological and therapeutic fields, particularly in the fluids transport mechanisms known as peristalsis. The Casson fluid belongs to a group of non-Newtonian fluids that, according to a particular stress threshold, exhibit elastic solid behavior before changing to liquid behavior. These fluids are known as viscoelastic fluids and have several uses in engineering, food preparation, drilling and other fields. The Casson nanofluid model is used in this investigation. In order to better understand this, this study examines the peristaltic motion of a Casson nanofluid in a vertical layer with suction/injection. The resulting flow model is successfully simulated under the realistic assumptions of long wavelength and low Reynolds number after obtaining the governing conservation equations. By using workable transformations, the derived partial differential equations are mathematically converted into a dimensionless form. Analytical solutions have been found for the resulting flow problem’s temperature distribution, velocity, pressure rate per wavelength and concentration of nanoparticles. Using Wolfram Mathematica software, the impacts of all physical characteristics on temperature, velocity, concentration fields, pressure rate, frictional force and pressure gradient are graphically studied. The influences of thermophoresis parameter Nt raise the temperature and diminish fluid concentration. By raising the suction and injection parameter k values, the velocity in the directions of x and y is decreased. The pressure rate enhances by raising the Reynolds number and diminishes by enhancing the Grashof number.

Numerical study of dissipative SW/MWCNT-nanofluid coating flow from a stretching wall to a porous medium with shape factor effects

A mathematical model is developed for incompressible steady-state dissipative CNT-aqueous nanofluid boundary layer flow from a stretching sheet to a saturated isotropic porous medium. Three different CNT shapes (spheres, blades and platelets) are considered. Both single-walled (SWCNT) and multi-walled (MWCNT) carbon nanotubes are examined. A Darcy-Brinkman model is adopted for the porous medium and a modified viscous dissipation formulation is considered which features porous media influence in the energy conservation equation. Appropriate expressions are deployed for the CNT-modified nanofluid viscosity, density, specific heat capacity, thermal conductivity and CNT shape factor. Via similarity transformations, the governing conservation equations for mass, momentum and energy with associated boundary conditions are normalized to generate a coupled nonlinear ordinary differential boundary value problem. A numerical solution is presented with the robust MATLAB-based bvp4c method and 4th order Runge-Kutta shooting scheme. Validation with previous studies is included. Velocity, temperature, skin friction and Nusselt number are computed for a range of selected parameters. The computations show that elevation in CNT volume fraction parameter accelerates the boundary layer flow whereas increment in the Darcian (inverse permeability) parameter induces strong deceleration. MWCNTs produce higher velocities than SWCNTs. Temperature and thermal boundary layer thickness are found to be enhanced with increasing Eckert number, Darcian (inverse permeability) parameter, CNT volume fraction and CNT shape factor. Significantly greater temperatures are computed for MWCNTs.

Computation of swirling hydromagnetic nanofluid flow containing gyrotactic microorganisms from a spinning disk to a porous medium with hall current and anisotropic slip effects

AbstractPrompted by the advancements in hybrid bio‐nano‐swirling magnetic bioreactors, a mathematical model for the swirling flow from a rotating disk bioreactor to a magnetic fluid saturating a porous matrix and containing nanoparticles and gyrotactic micro‐organisms has been developed. An axial magnetic field is administered which is perpendicular to the disk and Hall currents are included. The disk is assumed to be impervious and stretches in the radial direction with a power‐law velocity. The Buongiorno nanoscale, Kuznetsov bioconvection and Darcy porous media models are deployed. Anisotropic momentum, thermal, nanoparticle concentration and motile micro‐organism slip effects are incorporated. Stefan blowing is also simulated. The governing conservation equations are transformed with appropriate variables to ordinary nonlinear differential equations. MATLAB bvp4c shooting quadrature is used to solve the emerging nonlinear, coupled ordinary differential boundary value problem under transformed boundary conditions. Verification with earlier solutions for the non‐magnetic Von Karman bioconvection nanofluid case is conducted. Further validation of the general magnetic model is conducted with the Adomian decomposition method (ADM). Extensive visualization of velocity, temperature, nanoparticle concentration and motile microorganism density number profiles is presented for the impact of various parameters including magnetic interaction parameter, Hall current parameter, Darcy number, momentum slip, thermal slip, nanoparticle slip and microorganism slip. Computations are also performed for skin friction, Nusselt number, Sherwood number and motile micro‐organism density number gradient. The simulations provide a useful benchmark for further studies.

JEFFERY-HAMEL FLOW IN CONDUCTING NANOFLUID: NON-DARCY MODEL

The Jeffery-Hamel flow of magnetized nanoparticles saturated with porous matrix is inspected. Nanotechnology has provided exciting new materials for enhancing engineering devices, including electromagnetic permeable nanofluids. The Darcy-Forchheimer model is employed to define the porous medium. The performance of both metallic and oxide nanoparticles is studied as they are dropped in water, which is a base fluid. The homogenous Tiwari-Das model is adopted. The governing conservation equations are solved using the MATLAB bvp4c shooting method. Verification of earlier solutions for the clear fluid without the porous matrix is conducted. Graphical visualization of the velocity is conferred for the impact of various parameters such as using different nanoparticles, solid volume fraction, Hartmann and Reynolds numbers, angle between the two plates, porous parameter, and inertial parameter. It is found that the silicon oxide nanoparticle produces the optimal velocity, and the silver nanoparticle gives the minimum velocity. Upon increasing the solid volume fraction, the flow is reduced, and the presence of porous matrix does not alter the flow remarkably.

Influence of variable thermal conductivity and dissipation on magnetic Carreau fluid flow along a micro-cantilever sensor in a squeezing regime

Mathematical modeling of squeezing flows finds numerous applications in biological, mechanical, and medical engineering. Sensors feature such flows and can be effectively utilized to control vibrations and regulate lubrication. Magnetic fluids are critical to modern sensor systems. Micro-cantilevers are utilized in biomedical applications as biological, physical, or chemical sensors and operate via the detection of variations in the vibrational frequency or cantilever bending. Hence, a theoretical study is conducted to explore the dissipative flow and thermal characteristics in non-Newtonian boundary layer flow along a micro-cantilever sensor surface suspended in a squeezing regime between parallel plates. To achieve a more refined simulation, the effects of variable thermal conductivity and Joule magnetic dissipation are incorporated. The governing conservation equations for unsteady magnetic Carreau squeezing flow and heat transfer are rendered dimensionless and self-similar via appropriate scaling transformations. Emerging nonlinear coupled boundary value problem is then solved by using RK-4 method. The magnifying Weissenberg parameter decays the flow field. Skin friction is elevated with increasing Carreau power-law index and Weissenberg number. The novelty of the present study is the inclusion of dissipation and thermal conductivity variation effects which extends previous investigations and provides a more accurate appraisal of thermal characteristics in sensor squeezing flows.

A critical re-examination of Reynolds analogy for micro-convective flow

The present research numerically investigates the validity of the Reynolds analogy for micro-convective water flow between Stanton number (St) and Fanning friction factor (ff), taking into account combined fluid properties variations such as temperature-dependent density, viscosity, and thermal conductivity. The Reynolds analogy is suggested to be valid when St increases for thermophysical fluid properties (TFP) with a decrease in ff. This analogy, therefore, helps to find the flow regime that increases heat transfer while shear stress decreases for TFP. Hence, the Reynolds analogy for TFP helps to design and improve the performance of the different devices, including micro-scale heat exchangers for electronics cooling, internal cooling passages of turbine airfoils, and many biomedical devices. Three modified non-dimensional parameters (ΠSρT, ΠSμT, and ΠSkT) appear from the non-dimensionalization of the governing conservation equations. Using dimensional analysis, the dependence of the friction factor on these parameters is examined.

Flow instabilities in fluid displacement through enlarged regions in annular ducts

This work presents numerical results of flow displacement and the instabilities that appear when a viscoplastic fluid is displaced by a Newtonian one in a vertical annular duct with an enlarged region. Hydrodynamic instabilities in displacement flows may be due to viscosity and density differences, inertia effects and geometry irregularities like eccentricity and variable cross sections. If one of the fluids is non-Newtonian, the situation can be more challenging due to the dependence of the rheology on the flow kinematics. The geometry analyzed is found in the well cementation process in the oil industry, where the drilling fluid (viscoplastic behavior) is displaced by a spacer fluid (Newtonian). The drilling fluid wash out must be perfect in order to guarantee the success of the cementation operation, thus preventing the collapse of the oil well. Situations with excessive wellbore enlargement can occur, hampering the removal of the drilling fluid and the establishment of a perfect zonal isolation. The numerical solution of the problem is obtained using the finite volume technique to solve the governing conservation equations of mass and momentum. The volume of fluid method is employed to deal with the multiphase problem. The aim of this study is to look at how the governing parameters affect the flow displacement pattern and efficiency inside the enlarged region, with the goal to optimize the displacement process. The results focus on real case scenario for unstable situations, and present new findings that helps understanding the role of viscous, inertia and buoyancy effects. • Instabilities in flow displacement in enlarged annular tubes. • Well cementation process in oil industry. • Viscous, inertia and buoyancy effects on the displacement efficiency. • Displacement of a yield stress fluid by a Newtonian one.

Electro-osmotic peristaltic flow and heat transfer in an ionic viscoelastic fluid through a curved micro-channel with viscous dissipation.

Emerging systems in microfluidics are embracing bio-inspired designs in which boundaries are flexible and mimic peristaltic propulsion mechanisms encountered in nature. These devices utilize electro-kinetic body forces to manipulate very precisely ionic biofluids for a range of medical applications including. Motivated by exploring in more detail electro-hemorheological micro-pumping, in the current article, a mathematical model is developed for peristalsis propulsion of a viscoelastic biofluid in a curved microchannel with electro-osmotic effect and thermal transport under static axial electrical field and with viscous heating. The third grade Reiner-Rivlin model is deployed for blood rheology. The novelty of the current work is therefore the simultaneous consideration of electrokinetics, viscoelastic behavior with the third grade Reiner-Rivlin model and coupled flow and heat transport with viscous dissipation in peristaltic pumping in a curved micro-channel. A Poisson-Boltzmann formulation is adopted to simulate the charge number density associated with the electrical potential. Asymmetric zeta potential (25 mV) is prescribed and mobilizes an electric double layer (EDL). The governing conservation equations for mass, energy, momentum and electrical potential with associated boundary conditions are simplified using lubrication approximations and rendered dimensionless via appropriate scaling transformations. Analytical solutions are derived in the form of Bessel functions and numerical evaluations are conducted via the ND solver command in MATHEMATICA symbolic software. The simulations show that with stronger viscoelastic effect, boluses are eliminated and there is relaxation in streamlines in the core and peripheral regions of the micro-channel. Increasing Brinkman number (dissipation parameter) elevates temperatures. An increase in electrical double layer thickness initially produces a contraction in the upper bolus and an expansion (lateral) in the lower bolus in the micro-channel. With modification in zeta potential ratio parameter from positive to negative values, in the lower half of the micro-channel, axial flow deceleration is generated.

The Pressure Peaking Phenomenon for Ignited Under-Expanded Hydrogen Jets in the Storage Enclosure: Experiments and Simulations for Release Rates of up to 11.5 g/s

This work focuses on the experimental and numerical investigation of maximum overpressure and pressure dynamics during ignited hydrogen releases in a storage enclosure, e.g., in marine vessel or rail carriage, with limited vent size area, i.e., the pressure peaking phenomenon (PPP) revealed theoretically at Ulster University in 2010. The CFD model previously validated against small scale experiments in a 1 m3 enclosure is employed here to simulate real-scale tests performed by the University of South-Eastern Norway (USN) in a chamber with a volume of 15 m3. The numerical study compares two approaches on how to model the ignited hydrogen release conditions for under-expanded jets: (1) notional nozzle concept model with inflow boundary condition, and (2) volumetric source model in the governing conservation equations. For the test with storage pressure of 11.78 MPa, both approaches reproduce the experimental pressure dynamics and the pressure peak with a maximum 3% deviation. However, the volumetric source approach reduces significantly the computational time by approximately 3 times (CFL = 0.75). The sensitivity analysis is performed to study the effect of CFL number, the size of the volumetric source and number of iterations per time step. An approach based on the use of a larger size volumetric source and uniform coarser grid with a mesh size of a vent of square size is demonstrated to reduce the duration of simulations by a factor of 7.5 compared to the approach with inflow boundary at the notional nozzle exit. The volumetric source model demonstrates good engineering accuracy in predicting experimental pressure peaks with deviation from −14% to +11% for various release and ventilation scenarios as well as different volumetric source sizes. After validation against experiments, the CFD model is employed to investigate the effect of cryogenic temperature in the storage on the overpressure dynamics in the enclosure. For a storage pressure equal to 11.78 MPa, it is found that a decrease of storage temperature from 277 K to 100 K causes a twice larger pressure peak in the enclosure due to the pressure peaking phenomenon.

Two-dimensional buoyant plumes in a uniform co-flow

The behaviour of turbulent, buoyant, planar plumes is fundamentally coupled to the environment within which they develop. The effect of a background stratification directly influences a plumes buoyancy and has been the subject of numerous studies. Conversely, the effect of an ambient co-flow, which directly influences the vertical momentum of a plume, has not previously been the subject of theoretical investigation. The governing conservation equations for the case of a uniform co-flow are derived and the local dynamical behaviour of the plume is shown to be characterised by the scaled source Richardson number and the relative magnitude of the co-flow and plume source velocities. For forced, pure and lazy plume release conditions the co-flow acts to narrow the plume and reduce both the dilution and the asymptotic Richardson number relative to the classic zero co-flow case. Analytical solutions are developed for pure plumes from line sources, and for highly forced and highly lazy releases from sources of finite width in a weak co-flow. Contrary to releases in quiescent surroundings, our solutions show that all classes of release can exhibit plume contraction and the associated necking. For entraining plumes, a dynamical invariance spatially only occurs for pure and forced releases and we derive the co-flow strengths that lead to this invariance.

Conjugate MHD natural convection in a square cavity with a non-uniform heat source thick solid partition

This paper aims to investigate the effect of a non-uniform internal volumetric energy generation on the conjugate MHD natural convection in a square cavity filled by an electrically conducting fluid. The uniform magnetic field is applied horizontally; the two horizontal and vertical left walls are thermally insulated, whereas the right vertical wall is kept at constant cold temperature. The governing conservation equations are solved numerically using an in house program based on the finite-volume method and the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm. The effects of internal Rayleigh, Hartmann and Prandtl numbers, thermal conductivity ratio, inclination angle of the cavity, and the thickness of heat source partition are discussed. The obtained results show that regardless of Kr , α and Δ, an almost pure conduction state is observed for low RaI without MHD and for high RaI with MHD at high magnetic field intensity.

A reactive hydrodynamic simulation of noise propagation for a concrete-confined detonation

When a point source detonation occurs, high temperature and pressure gases are released and then propagate through the open atmosphere as a blast wave. This leads to an explosive sound in the form of environmental noise, which has been known to cause hearing damage to nearby residents surrounding the explosion area. In an effort to reduce such noise levels, explosion test sites are installed with sound barriers to mitigate and minimize the noise associated with the blasts. In this study, realistic explosion pressure was calculated at an initial detonation source inside a concrete sound barrier, and a numerical prediction was made to evaluate the environmental noise propagation in an actual terrain. In particular, we applied the concrete equation of state to the governing conservation equations for a spherical detonation in a confined geometry and compared the experimental data taken within 3 m from the test site and a few kilometers away from the sound source. Moreover, the amount of noise reduction was predicted by first considering the absorbed explosion pressure by the sound barrier, which later dissipated at a far distance at which the noise propagation in an actual terrain was compared with the measurements.

Dimensionless Correlations for Natural Convection Heat Transfer from a Pair of Vertical Staggered Plates Suspended in Free Air

Buoyancy-induced convection from a pair of staggered heated vertical plates suspended in free air is studied numerically with the main scope to investigate the basic heat and momentum transfer features and to determine in what measure any independent variable affects the thermal performance of each plate and both plates. A computational code based on the SIMPLE-C algorithm for pressure-velocity coupling is used to solve the system of the governing conservation equations of mass, momentum and energy. Numerical simulations are carried out for different values of the Rayleigh number based on the plate length, as well as of the horizontal separation distance between the plates and their vertical alignment, which are both normalized by the plate length. It is observed that an optimal separation distance between the plates for the maximum heat transfer rate related to the Rayleigh number and the vertical alignment of the plates does exist. Based on the results obtained, suitable dimensionless heat transfer correlations are developed for each plate and for the entire system.

Numerical Analysis on the Storage of Nuclear Waste in Gas-Saturated Deep Coal Seam

Nuclear power has contributed humanity a lot since its successful usage in electricity power generation. According to the global statistics, nuclear power accounts for 16% of the total electricity generation in 2020. However, the rapid development of nuclear power also brings up some problems, in which the storage of nuclear waste is the thorny one. This work carries out a series of modeling and simulation analysis on the geological storage of nuclear waste in a gas-saturated deep coal seam. As the first step, a coupled heat-solid-gas model with three constitutional fields of heat transfer, coal deformation, and gas seepage that based on three governing conservation equations is proposed. The approved mechanical model covers series of interactive influences among temperature change, dual permeability of coal, thermal stress, and gas sorption. As the second step, a finite element numerical model and numerical simulation are developed to analyze the storage of nuclear waste in a gas-saturated deep coal seam based on the partial differential equations (PDE) solver of COMSOL Multiphysics with MATLAB. The numerical simulation is implemented and solved then to draw the following conclusions as the nuclear waste chamber heats up the surrounding coal seam firstly in the initial storage stage of 400 years and then be heated by the far-field reservoir. The initial velocity of gas flow decreases gradually with the increment of distance from the storage chamber. Coal gas flows outward from the central storage chamber to the outer area in the first 100 years when the gas pressure in the region nearby the central storage chamber is higher than that in the far region and flows back then while the temperature in the outer region is higher. The modeling and simulation studies are expected to provide a deep understanding on the geological storage of nuclear waste.

Modeling of Particle Deposition in a Two-Fluid Flow Environment

Particle deposition occurs in many engineering multiphase flows. A model for particle deposition in two-fluid flow is presented in this article. The two immiscible fluids with one carrying particles are model using incompressible Navier-Stokes equations. Particles are assumed to deposit onto surfaces as a first order reaction. The evolving interfaces: fluid-fluid interface and fluid-deposit front, are captured using the level-set method. A finite volume method is employed to solve the governing conservation equations. Model verifications are made against limiting cases with known solutions. The model is then used to investigate particle deposition in a stratified two-fluid flow and a cavity with a rising bubble. For a stratified two-fluid flow, deposition occurs more rapidly for a higher Damkholer number but a lower viscosity ratio (fluid without particle to that with particles). For a cavity with a rising bubble, deposition is faster for a higher Damkholer number and a higher initial particle concentration, but is less affected by viscosity ratio.

Combined close-contact and convective melting in a vertical cylindrical enclosure

The use of phase change materials (PCM) for latent heat thermal energy storage (LHTES) is receiving considerable amount of attention in recent years. Experimental findings have demonstrated that the so-called ‘close contact melting’ (CCM) enhances heat transfer during the melting process remarkably. Yet, the commercially-available numerical schemes are not suitable for the modeling of CCM. Therefore, in this study a new numerical model for combined convective and close-contact melting in an axisymmetric cylindrical geometry is devised. A full set of the governing conservation equations is solved using finite differencing framework, integrated with an advanced immersed boundary method for the fluid-solid interaction and enthalpy formulation for the phase change process into an original in-house code. First, the model is validated carefully for each physical phenomenon with known benchmarks. Then, a numerical study is conducted to elucidate the melting process in a vertical cylindrical enclosure heated isothermally from the bottom and side wall. Twelve study cases are considered in order to reveal the transient phase-change sequence dependence on the aspect ratio and the excess temperature. Detailed data on the flow and temperature fields are obtained. The overall results are generalized using a dimensional analysis, which includes the Fourier, Stefan and Archimedes numbers and the enclosure aspect ratio. A correlation for the melt fraction, suitable for all cases studied, is suggested.

Numerical analysis of mixed convection heat transfer and laminar flow in a rectangular inclined micro-channel totally filled with Water/Al2O3 Nano fluid

A numerical analysis was carried out of mixed convection heat transfer for a laminar flow in a rectangular inclined microchannel totally filled with a water/Al2O3 nanofluid. The governing conservation equations are translated into a dimensionless form using the thermal single relaxation time and they modify the lattice Boltzmann method with double distribution functions. The viscous dissipation effects are adapted to the energy equation. The effects of nanoparticle volume fractions ϕ (0 ≤ ϕ ≤ 0.04) and inclination angles γ (0° ≤ γ ≤ 60°) on the flow of the nanofluid and the heat transfer are investigated. The obtained results are presented in terms of streamlines, isotherms, slip velocity, wall temperature and Nusselt number. The results show that the higher values of the volume fraction of Al2O3 and the large values of inclination angles improve the heat transfer rate.