Search

Homogeneous fruit juice in a sealed container available in the commercial market exhibits some degree of non-Newtonian behavior with a wide viscosity range. During thermal processing, it is necessary to understand the effect of viscosity on thermal behavior, which may guide insight into the choice of physics involved in the conservation law equations. In this context, the present study considered the Carboxyl Methyl Cellulose (CMC) solutions (a viscosity-enhancing agent) as model foodstuffs to understand the effect of viscosity on the heat transfer mechanism in the thermal treatment of canned liquid products. Computational Fluid Dynamics (CFD) was employed to analyze the thermal behavior of different concentrations of CMC solutions, estimated based on averaged wall heat flux, averaged heat transfer coefficient, volume-averaged temperature, and minimum temperature. The effect of the CMC solutions' rheological properties on the thermal behavior was evaluated by comparing it with the pure conduction simulations. The time–temperature history obtained from the simulations was coupled with the kinetic parameter of microbial destruction to predict the heating time. When the viscosity increases due to increasing the concentration of CMC solution, the natural convection is suppressed, which leads to the heat transfer in almost pure conduction mode.

High Explosive Anti-Tank (HEAT) warheads and ammunitions are frequently produced by explosive casting inside an axis-symmetric mold with an inverted conical geometry in the basis. In order to prevent manufacturing defects, the solidification process must be controlled. In this study, a dimensionless solidification model has been proposed to investigate the heat transfer considering the natural convection inside the liquid explosive and the numerical simulations were performed by using COMSOL Multiphysics and Modeling Software, employing trinitrotoluene (TNT) thermophysical properties. The effect of three different boundary conditions on the top of the mold have been evaluated: convection, adiabatic and isothermal. It has been observed that solidification process was faster for convection case and slower for isothermal case, while an intermediary total solidification time value was found for adiabatic case. Moreover, liquid explosive was completely surrounded by solid explosive during the solidification process for convection case and also for adiabatic case through the end of the process. Otherwise, it was not observed for isothermal case. The natural convection effects promoted a vortex inside the liquid explosive, accelerating the heat transfer process. It has been concluded that isothermal mold top boundary condition should be preferred to prevent manufacturing defects, avoiding high thermal stress.

Flow and heat transfer dynamics are considered quite complex phenomenon in different enclosures. Heat transport mechanism and its improvement due to the presence of nanoscale particles is vital topic of research. Owing to the widespread importance of free convection through fluids with nanoparticle in various configuration and constraint, we have addressed in this article the natural convection nanofluid flow in a hexagon shaped enclosure with heated cylinder. Simulation has been performed in the influence of porous medium and inclined magnetic field. The physical model is translated in terms of differential systems. For solutions purpose, the finite element method is utilized. The quantities of interest include the fluid flow and heat transfer aspects. The obtained results against flow controlling parameters are offered by means of contour plots and line graphs. It is noticed that the at lower Darcy number the heat transfer rates has diminishing behavior because of the higher porosity of medium. At higher Hartman number the velocity profile tends to decrease due to resistive nature of Lorentz forces. At maximum radius of heat source, the Nusselt number and velocity profile has higher values.

Understanding fluid flow, heat, and mass transfer over a stretching cylinder is essential in ascertaining the quality of wire coating and coper thinning. This study looks at the influence of the heat source, thermal radiation, chemical reaction, and natural convection of Carreau fluid flows over a vertical stretching cylinder immersed in a porous medium. Suitable similarity variables are applied to convert the partial governing equations arising in fluid flows, heat, and mass transfer into ordinary differential equations. The optimal homotopy analysis method is then utilized to solve the transformed highly nonlinear governing equations. The impacts of the relevant parameters such as the Weissenberg number, porosity, heat source parameter, radiative number, chemical reaction parameter, mixed convection parameter, and curvature parameter on the dimensionless velocity, temperature, and concentration distribution as well as for the skin friction, Nusselt number, and Sherwood number are discussed through graphs and tables. It is observed that the velocity shows an opposite behavior as compared to temperature, and concentration in shear-thinning, n 1 , and shear-thickening, n ≥ 1 , fluid for an increment of the Weissenberg number. Additionally, the thickness of the momentum, thermal, and concentration boundary layer is enhanced by the curvature of the cylinder.

The proposed study focuses on the effect of double diffusive convection on the flow structures of power-law fluids between two coaxial cylinders of finite aspect ratios with end caps. We adopted a ...

In this investigation, a comprehensive and accurate numerical analysis of the local thermal non-equilibrium effects on the natural convection characteristics in a horizontal elliptical porous annulus saturated with nanofluid has been carried out using finite volume technique. The internal surface is isothermally heated while the external one is fixed at uniform lower temperature. The nanofluid phase and the solid phase of the porous structure are hors local thermal equilibrium situation. The heat and the hydrodynamics equations in their dimensionless form under Darcy-Brinkman Forchheimer model were solved computationally by the finite volume technique using the standard SIMPLER algorithm. The results have been examined for various porous medium properties under the LTNE condition. The standard 0.05 significance level was used to identify the local thermal equilibrium within the system. According to the obtained results, the higher the Darcy number and the smaller the non-dimensional heat transfer coefficient for the solid/nanofluid interface, the modified thermal conductivity ratio and the media’s porosity, the higher are the LTNE effects. In addition, the spatial distribution contours of the LTNE sources within the porous annulus were schematized.

In this paper, improvements in the basic physical laws of natural convection heat transfer were implemented in two major respects by incorporating recent research findings in this field. A preferred transition criterion was adopted in this paper to correlate all of the experimental data. Since transition correlations are primarily flow stability problems, the Grashof number, instead of the Rayleigh number, was found to be the preferred criterion. Furthermore, in the case of natural convection heat transfer from a horizontal cylinder, a series of experimental data in the high-Rayleigh-number regions recently became available. These data made it possible to establish new reliable correlations and also to test the validity of previous correlations. It is concluded that the previous correlation for a horizontal cylinder in high-Rayleigh-number regions was based on unreliable experimental results. The transition correlation for a horizontal cylinder occurred at much higher values of Rayleigh number than the previous recommendation. In the case of natural convection heat transfer from a vertical plate, more accurate property values for air under pressurized conditions are now available. This made it possible to replot the reliable data of Saunders. From this result and the experimental result of Warner and Arpaci, a new set of basic correlations in natural convection heat transfer for laminar, transitional, and turbulent regimes are recommended. These recommendations reflect a better understanding of the basic physical laws in the field of heat convection. © 2001 Scripta Technica, Heat Trans Asian Res, 30(4): 293–300, 2001

This is a review of a new class of fundamental results concerning the optimal spacing of parallel heat generating boards arranged in a stack of fixed volume. The cooling is by single-phase laminar flow, in natural convection or forced convection. Several board models will be considered: smooth boards with uniform temperature or uniform heat flux, flush mounted heat sources, protruding heat sources, and a board cooled in its own (insulated) parallel plate channel.

Natural convective flow and heat transfer of a hybrid nanofluid contained in an enclosure with multiple heat sources at the bottom wall are investigated in the presence of magnetic field applied to an angle with the horizontal axis. The system of equations is formulated systematically using dimensionless variables and parameters as well as defining stream function in terms velocity components. Solutions obtained by the finite difference method are then validated with experimental and numerical results which provides a good agreement. A grid independent test is also performed. Results reveal that flow pattern is substantially changed with the change of the magnetic field parameter, angle of magnetic field, number and breadth of heat sources and Rayleigh number. The intensity of the stream function is stronger for higher Rayleigh number and smaller magnetic field parameter. When the volume fraction of Cu nanoparticles is more than 6% the streamlines and isotherms demonstrate distinct pattern from those for its lower value. Moreover, symmetric pattern of streamlines is observed for angle of magnetic field equal to 0 and π/2. Due to the increase of the number of heat sources, angle of magnetic field and Rayleigh number, average Nusselt number is found to increase.

Numerical investigation on natural convection heat transfer of Tiwari - Das model nanofluid inside a square cavity with thermal radiation and magnetic field is carried out in this analysis. Ethylene Glycol E G is considered as base fluid and T i O 2 (Titanium Oxide) considered as nanoparticles for the present investigation. The side horizontal walls of cavity are assumed to be adiabatic and isothermal conditions on both sides walls are considered in this analysis. The finite difference method is implemented to solve the governing non-linear partial differential equations representing momentum and temperature equations. The sway of volume fraction parameter ( 0.01 ≤ ϕ ≤ 0.09 ) , magnetic field parameter ( 1.0 ≤ M ≤ 3.0 ) , Rayleigh number ( 100 ≤ R a ≤ 1000 ) , radiation parameter ( 0.1 ≤ R ≤ 0.9 ) , Reynolds number ( 0 . 1 ≤ R e ≤ 0 . 5 ) and Prandtl number ( 5.2 ≤ P r ≤ 7.2 ) on T i O 2 - E G nanofluid flow and heat transfer is illustrated through graphs. Furthermore, the codes of average Nusselt number with dissimilar values of pertinent parameters are also calculated and results are depicted through graphs. The result shows that, temperature of T i O 2 - E G nanofluid escalates inside the cavity with higher values of (M). Higher heat can be transferred from hot wall to cold wall when radiation parameter (R) intensifies.

Batch-type solar collector is a tilt-able water-heating solar-thermal system comprising an isosceles-trapezoidal enclosure housing a circular-cylinder absorber at the bottom wall, insulated side-walls, and flat-top glazing. Free convection of air inside such trapezoidal enclosure is studied numerically by varying the tilt angle of the whole enclosure from 0o-70o. The influence of tilt on the flow field has been demonstrated by plotting the streamlines and isotherms. The present study successfully identifies the importance of enclosure-tilt in quantifying heat-loss between absorber and glazing by developing a computational correlation between Nusselt and Rayleigh as a function of tilt. The correlation trend is non-monotonic over the range of angular Rayleigh numbers numerically experimented with having a peak around angular Rayleigh number 3×105 corresponding to the tilt-angle 30 degrees. The irregular-shaped cavity implies that the heat-transfer correlations already existing for regular-shaped cavities may not be used otherwise they will draw implausible conclusions and this argument identifies the novelty of the present study.

In this paper, we present a numerical study of turbulent natural convection in a square cavity differentially heated and filled with nanofluid and subjected to an inclined magnetic field. The standard k-e model was used as the turbulence model. The transport equations were discretized by the finite volume method using the SIMPLE algorithm. The influence of the Rayleigh number, the Hartmann number, the orientation angle of the applied magnetic field, the type of nanoparticles as well as the volume fraction of nanoparticles, on the hydrodynamic and thermal characteristics of the nanofluid was illustrated and discussed in terms of streamlines, isotherms and mean Nusselt number. The results obtained show that the heat transfer rate increases with increasing Rayleigh number and orientation angle of the magnetic field but it decreases with increasing Hartmann number. In addition, heat transfer improves with increasing volume fraction and with the use of Al2O3 nanoparticles.

The effect of nanoparticle shape on the natural convection heat transfer of Cu-Al2O3/water hybrid nanofluid inside a U-shaped enclosure is presented in this paper. The governing equations are transformed into the dimensionless form using dimensionless variables. A three-node triangular finite element method is used with the Newton-Raphson method to solve the problem numerically. The streamlines and isotherms as well as the local and average Nusselt numbers are presented for the fluid flow with Rayleigh number of 104 to 106.It is found that blade nanoparticle shape produces the highest heat transfer rate while sphere is the lowest.

We report the complex evaporation kinetics of saline sessile droplets on surfaces with elevated temperatures. Our previous studies show that on non-heated substrates, saline sessile droplets evaporate faster compared to the water counterparts. In the present study, we discover that on heated surfaces, the saline droplets evaporate slower than the water counterpart, thereby posing a counter-intuitive phenomenon. The reduction in the evaporation rates is directly dependent on the salt concentration and the surface wettability. Natural convection around the droplet and thermal modulation of surface tension is found to be inadequate to explain the mechanisms. Flow visualizations using particle image velocimetry (PIV) reveal that the morphed advection within the saline droplets is a probable reason behind the arrested evaporation. Infrared thermography is employed to map the thermal state of the droplets. A thermo-solutal Marangoni based scaling analysis is put forward and the major governing non-dimensional numbers have been accounted for in the analysis. It is observed that the Marangoni flow and internal advection borne of thermal and solutal gradients are competitive, thereby leading to the overall decay of internal circulation velocity compared to the equivalent pure water case, which reduces the evaporation rates. The theoretically proposed advection velocities conform to the experimental results. This study sheds rich insight on a novel species transport behaviour in saline droplets.

The unsteady natural-convection of Al2O3-water nanofluid form heated open T-pipe inside a cavity has been investigated by incompressible smoothed particle hydrodynamic (ISPH) method using non-homogenous two-phase Buongiorno?s model. Different lengths and heights of T-pipe shape are considered. The side walls of the cavity are kept at cool temperature Tc and the horizontal walls are thermally insulated. The Lagrangian description of the controlling governing equations is discretized and solved using improved ISPH method. In this study, ISPH method is improved using kernel renormalization function for boundary treatment plus modification in the source term of pressure Poisson equation. The source term of pressure Poisson equation contains the velocity divergence plus density invariance multiply by relaxation coefficient. The calculations are performed for variable lengths of T-open pipe (0.2 ? Lb ? 0.6), variable widths of T-open pipe (0.02 ? Wb ? 0.16), (0.02 ? Wt ? 0.16), and variable concentration of nanoparticles volume fraction (1% ? ?avg ? 10%). The obtained results showed that the maximum values of the stream function are reduced by 80.8% when ?avg is increased from 1-10%. Additionally, as lengths and widths of the T-pipe are raised, the average Nusselt numbers at the vertical walls are enhanced.

The paper addresses numerically a study on thermal management of a cavity-shaped thermal system providing localized heating at the bottom. For this fundamental study, different fluids namely air, water, ethylene glycol (EG), and nanofluid are considered in a square cavity from the application point of view. The upper halves of the sidewalls, and top wall act as the isothermal heat sink. The heater acts as an isothermal heat source. Four different configurations are studied in this work: (a) Case-1: central heating with one heater (b) Case-2: corner heating with one heater (c) Case-3: corner heating with two heaters of equal length (d) Case-4: central heating with two heaters of equal length. For all the configurations, the total length of heaters is fixed. The other walls are maintained in an adiabatic condition. The finite volume approach is employed to solve the governing differential equations numerically. The simulation is executed for a spectrum of Prandtl numbers covering the most commonly used working fluids, keeping the Rayleigh number and the volumetric concentration of nanoparticles fixed. The streamlines and isotherms are employed for the visualization of flow and thermal field. The transmission of heat by free convection is characterized by the Nusselt number. The irreversibility in the flow domain is studied using the contours of the entropy generation rate. The aim of this work is to find out the heater location and fluid for which the rate of heat transmission is maximum. The results reveal that the maximum heat removal rate occurs for central heating with a double heater (Case-4) and the minimum heat removal rate takes place for corner heating with a double heater (Case-3). It is noted that the heat transmission rate is maximum for nanofluid.

In this study, heat transfer utilizing non-Newtonian fluids with a power-law model in a rectangular enclosure containing a hot obstacle was verified experimentally. The impact of aspect proportion (AR) on fluid flow characteristics and heat transfer, obstacle shapes, and various amounts of carboxymethylcellulose was explored with distilled water which in turn controls the index of powers-law (n). The findings show that the increases in the Number of Rayleigh, lead to the greater the Number of Nusselt, and the greater the non-Newtonian behavior, increased the heat transfer. There is also a noticeable impact when changing the shape of an obstacle on heat transfer as the cylindrical shape enhances heat transfer greater than the cuboid shape. As for aspect proportion, it also affects heat transfer inversely.

This paper reports a numerical study of double-diffusive natural convection through an annular space delimited by a square cylinder on the outside and a cylindrical cylinder on the inside covered by a porous layer. The Darcy-Brinkmann-Forchheimer is used for modeling flow in both fluid and porous areas. The annular space is partially or completely filled with an isotropic porous medium. A finite volume method, using the Patankar-Spalding technique is used for solving the discretization of the dimensionless equations governing the problem. The effects of simultaneously applied thermal and solutal buoyancy forces on heat and mass transfer are shown in the results for a large range of buoyancy ratios N, Rayleigh number, and thermal conductivity. Streamlines, isotherms, and iso-concentrations are presented to analyze the flow structure transition from mass species dominated to thermal dominated flow. Results show that the buoyancy ratio can change the flow pattern and the increased thermal conductivity ratio can improve heat and mass transfer. A good agreement was obtained between the present results and those published were found.

Flow and heat transfer components of buoyancy driven convection in a hybrid nanofluid filled wavy-walled cavity are numerically investigated in this study. A cylindrical heat generating blockage is placed at the center of the cavity. The cavity is partially heated from its bottom wall and cooled from wavy-walls while the remaining walls are adiabatic. The cavity is permeated by a transverse magnetic field. Thermal conductivity model of hybrid nanofluid is developed comprising Brownian motions of different nanoparticles. The non dimensional governing equations are solved by implementing finite element method. Obtained results demonstrate the intensification of fluid flow circulation for increasing Rayleigh number and heater length. The heat transfer rate is expeditiously augmented for increase in Rayleigh number and hybrid nanoparticles volume fraction but reverse trend is observed for higher Hartmann number. The flow circulation and temperature distribution are influenced with the presence of heat generating cylinder and roughness of the cavity walls. In addition, strength of fluid motion becomes higher for wavy cavity containing heat generating obstacle compared to smooth cavity without blockage. Maximum heat transfer is ensured at lower heater length and radius of the heat generating cylinder. Heat transfer rate also increases with the roughness of the cavity.

The study of mass transfer in the non-Newtonian fluid is essential in understanding the engine lubrication, the cooling system of electronic devices, and the manufacturing process of the chemical industry. Optimal performance of the practical applications requires the appropriate conditions. The unsteady transient free convective flow of second-grade fluid with mass transfer and wall transpiration is concerned in the present communication. The behavior of the second-grade fluid under the influence of injection or suction is discussed. Suitable non-dimensional variables are utilized to transform the governing equations into non-dimensional governing equations. A Maple solver “pdsolve” that is using the centered implicit scheme of a finite difference method is utilized to solve the dimensionless governing equations numerically. The effects of wall injection or suction parameter, second-grade fluid viscoelastic parameter, Schmidt number, and modified Grashof number on the velocity and concentration profiles are graphically displayed and analyzed. The results show that with increasing wall suction, viscoelastic parameter, and Schmidt number, the velocity and concentration profiles decrease. Whereas, the velocity profiles show an opposite tendency in situations of wall injection. The wall suction has increased the skin friction and also the rate of mass diffusion in the second-grade fluid.

This numerical study is intended for the analysis of thermal convection induced by buoyancy forces generated within a conical annular porous gap. The annulus was vertically positioned, it contains a discrete heat source and is filled with a Single-Walled Carbon Nanotubes-Water (SWCNT- H 2 O) nanoliquid exposed to a Lorentz force. To describe the porous medium in question, we have adopted the Darcy–Forchheimer model. Galerkin Finite Element Method (GFEM) has been used in this study to predict both thermal and hydrodynamic fields in the physical model. An extensive range of parameters are explored, i.e., the Rayleigh number (103 to 106), Hartman number Ha (1 to 100), and the volume fraction of nanoparticles (0 ≤ ϕ ≤ 0.08). For the purpose of exterminating the effects of heat source location on thermal and hydrodynamic fields, three locations (bottom, middle and upper) have been considered. Findings include current lines, isotherms, and Nusselt number evolution according to the previously stated variables. Predictably, our findings prove that heat transfer rate exhibits a decreasing function of Ha and an increasing function of Da and ϕ . Also, it was revealed that the convective regime is preponderant when the heat source was located in the bottom wall.

Background The exploration of natural convection which is one the substantial types of convective heat transmission in various applications for instance heat exchangers and geothermal systems along with nanofluids (Nanofluids have greater thermal conductivity in comparison to the conventional fluids) engrossed all researchers’ attention. Methods This study is dedicated to the inspection of the free convection of nanofluid as well as entropy generation inside a porous cavity loaded with nano-encapsulated phase change materials (NEPCMs). The wavy bottom section of the enclosure may be subject to a constant heat flux due to the transmitted sunlight comes from a parabolic trough solar collector. The volumetric heat source/sink is comprised in the governing equation. The robust finite element method (FEM) is deployed to handle the transformed governing equations. Findings The numerical simulation of the streamlines and isotherms associated with velocity distribution for diverse factors are displayed. Further, the significant behavior of the contributing parameters on the Nusselt and Bejan numbers are represented. The results demonstrate that the various profiles of wavy bottom section could affect the heat transmission features as well as fluid flow remarkably. Furthermore, it is noteworthy that all the profiles of entropy enhance with increasing the amplitude with respect to the increasing undulation number for the existence of various Rayleigh number.

Recent advancements in nanotechnology research have introduced hybrid nanofluids which are sophisticated classes of fluids with enhanced thermal properties that outperform conventional nanofluids. The objective of current communication is to illustrate the comparative mathematical model of MHD hybrid nanofluid and mono-nanofluid flows with heat flux condition through a stretching sheet. Impact of melting phenomenon, heat generation/absorption and natural convection is considered. The thermal radiation, viscous dissipation and temperature-dependent viscosity are also considered. In current model, two different nanoparticles namely zinc oxide ( ZnO ) and zirconium dioxide ( ZrO 2 ) are dispersed in kerosene oil ( C 10 H 22 ) base fluid to form a hybrid nanofluid. Similarity transformations are utilized to renovate the governing PDEs structure system into ordinary ones. The numerical computations of current mathematical model are computed through bvp4c built-in function in MATLAB with shooting scheme. The fluctuations of velocity and temperature distributions are analyzed with physical impacts for different flow parameters. It is visualized that the growing amount of convection parameter corresponds to increment in velocity profile. The velocity of hybrid nanofluid reduces as the magnetic parameter increases. It is analyzed that the thermal field of hybrid nanofluid is an increasing function of thermal radiation parameter. Furthermore, the thermal profile is a reducing function of melting and Prandtl numbers.

An exhaustive numerical investigation is carried out to analyze the role of an isothermal heated thin fin on fluid flow and temperature distribution visualization in an enclosure. Natural convection within square enclosures finds remarkable pragmatic applications. In the present study, a finite difference approach is performed on two-dimensional laminar flow inside an enclosure with cold side walls and adiabatic horizontal walls. The fluid flow equations are reconstructed into vorticity - stream function formulation and these equations are employed utilizing the finite-difference strategy with incremental time steps. The parametric study includes a wide scope of Rayleigh number, Ra, and inclination angle ϴ of the thin fin. The effect of different Rayleigh numbers ranging Ra = 104-106 with Pr=0.71 for all the inclination angles from 0°-360° with uniform rotational length of angle 450 of an inclined heated fin on fluid flow and heat transfer have been investigated. The heat transfer rate within the enclosure is measured by means of local and average Nusselt numbers. Regardless of inclination angles of the thin fin, a slight enhancement in the average Nusselt number is observed when Rayleigh number increased for both the cases of the horizontal and vertical position of the thin fin. When the fin has inclined no change in average Nusselt number is noticed for distinct Rayleigh numbers.

The present article analyzes the effect of viscous dissipations on natural convection heat transfer. The power law model for non-Newtonian fluid with heat generation or absorption effect along a sinusoidal wavy surface with isothermal boundary condition is investigated. A simple coordinate transform is employed to map the wavy surface into a flat surface, and also, the fully implicit finite difference method is incorporated for the numerical solution. The findings of this study can help better understand the effect of parameters such as the Brinkman number, heat generation/absorption, wave amplitude magnitude, and generalized Prandtl number on convective heat transfer in dilatant and pseudoplastic non-Newtonian. Results show that as the Brinkman number increases, the amount of heat transfer decreases. This is physically justifiable considering that the fluid becomes warmer due to the viscous dissipation, decreasing its temperature difference with the constant temperature surface. Also, the effect of the power law viscosity index is surveyed. It is demonstrated that the magnitude of the local Nusselt number in the plane leading edge has the smallest quantity for pseudoplastic fluids compared to dilatant Newtonian fluids. Additionally, as the distance from the plane leading edge increases, the heat transfer declines.

An investigative approach on study of a laminar natural heat convection on different geometric annuluses under impact of a constant magnetic field, using Ferro-Nano has been carried out. The three ...

Laminar convective heat transfer for the thermally developing flow in elliptical minichannels is numerically investigated under constant heat flux with high thermal conductivity materials (H1) and ...

This study deals with the influence of a rotating cylinder inside the square cavity and multiwalled carbon nanotube–iron oxide (Fe3O4) hybrid nanofluid with water. A two-dimensional system of parti...

Using boundary-layer theory, natural convection heat transfer formulas which are accurate over a wide range of Rayleigh numbers ($Ra$) were developed in the 1970s and 1980s for vertical and downward-facing plates. A comprehensive formula for upward-facing plates remained unsolved because they do not form conventional boundary-layers. From the thermodynamic constraints on heat-engine efficiency, the novel approach presented here derives formulas for natural convection heat transfer from isothermal plates. The union of four peer-reviewed data-sets spanning $1, Comment: 26 pages; 12 figures; 13 tables; 17 references. Improved Abstract, Introduction, and Conclusion sections

The prolonged heat and mass transfer can be enhanced by orders of magnitude that originate from the natural convection. This work examines the mass transfer enhancement in the fluid motion inside a...

In this paper, we made elaborate investigation of the Hall current and radiation effects on MHD heat absorbing unsteady natural convection flow of a viscous incompressible electrically conducting f...

Concentrated Solar Power (CSP) technology stands out among other renewable energy sources not only because of its ability to address current energy security and environmental challenges but because its energy can be stored for future use. To ensure optimum performance in this system, the heat losses need to be evaluated for better design. This work studies the natural convection in the receiver absorber tube of a CSP plant taking into consideration the influence of neighboring absorbers. A 2-Dimensional model was adopted in this study. Initially, a single absorber tube was considered, it was subjected to heat flux at the top wall, the bottom wall was insulated and a temperature differential was set up at the lateral walls. The dimensionless forms of Navier-Stokes and energy equations were solved using the finite element formulation of COMSOL Multiphysics software. The result obtained for a single absorber tube showed good agreement with existing research works. This validated model was then extended to multiple absorber tubes (two to six absorber tubes). On the basis of the study, there is an observed increase in the intensity and dominance of convective heat transfer with an increase in the number of absorber tubes. This is occasioned by an increase in the average surface temperature as well as average Nusselt number. For the Rayleigh number of 104, 105 and 106, the average Nusselt number increases with the number of absorber tubes by 13.87 %, 6.26 %, and 1.55 %, respectively. This increment suggests effect of thermal interactions among the neighboring absorber tubes

The current study is to explore the phenomena of the hydromagnetic free convective flow of an electrically conducting and incompressible viscous fluid through an impermeable vertical cylinder, with the point heat source under the influence of the transversely applied magnetic field of uniform strength in the radial direction. The free convection phenomenon in the working fluid occurs due to the presence of the point/line heat source as it appears in many real-world mechanisms. The main motive of this analytical study is thus to examine the effect of point and line heat source on this buoyancy-dominated developing flow. The governing equations thus framed for the prescribed flow namely energy and momentum, simplify to steady linear differential equations in the physical setup assumed in this investigation. These equations, in non-dimensional forms, have been solved, in turn, employed simultaneous ordinary differential equations (ODEs) theory. The resulting closed form solutions for the physical variables, namely fluid temperature and fluid velocity have been presented in terms of Bessel, modified Bessel, and Regularized Hypergeometric functions. Additionally, skin friction coefficient, Nusselt number, and mass flow rate are numerically discussed for the involved parameters. There arises a number of pertinent physical parameters in our analysis: Heat source, Hartman number, and point heat source whose influence on the developing velocity and some temperature profiles have been illustrated through a number of plots. Major outcomes show that the enhancement in Hartmann number motivates a reduction in the velocity profile for the point and line heat source cases. In addition, the fluid motion rises due to the line and point heat source, and the velocity and temperature profiles have a higher value in the case of the line heat source as compared to the point heat source.

The present investigation centers around a numerical study of the impact of the presence of phototactic microorganisms on the thermo-bioconvection inside a wavy-walled horizontal porous annulus that is saturated with a Newtonian fluid. Consequently, an equation describing the movement of the microorganism cells is added to the mathematical model of natural convection. The thermal equilibrium, Oberbeck–Boussinesq approximations and Darcy law are taken into consideration. The transformed dimensionless partial differential equations with the temperature-concentration-stream function formulation are discretized applying the alternate direction implicit finite difference scheme. Results confirm that in the absence of microorganisms the Nusselt number decreases with the increase of the amplitude of wall waviness. It was also observed that the wall waviness influence the thermo-bioconvective instabilities and the flow regime structure.

This problem considers the instabilities, which can occur when a horizontal sparsely filled nanofluid porous layer is saturated with a binary mixture with fast chemical reaction. The upper and lower plates are heated isothermally. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The modified Darcy equation that includes the time derivative term is used to model the momentum equation. The energy equation includes cross and regular diffusion conditions. In conjunction with the Brownian motion, the nanoparticle fraction becomes stratified; hence the viscosity and the conductivity are stratified. The nanofluid is assumed to be diluted and this enables the porous medium to be treated as a weakly heterogeneous medium with variation, in the vertical direction, of conductivity and viscosity. The oscillatory and stationary convection are evaluated analytically. The reaction rate is supposed to be greater than the diffusion rate. We find that both a stationary instability and an oscillatory instability can occur as the first bifurcation, depending on the sign and the value of the heat of reaction. The execution of the porous parameter, Prandtl number, Soret parameter, Dufour parameter, Lewis number, solutal Rayleigh number, chemical reaction and the modified diffusivity ratio parameters is implemented pictorially. It is found that the presence of nanoparticles the critical Rayleigh number is increased and helps to stabilize the system. The presence of chemical reaction parameter destabilizes the system. The results of previously-published work are also obtained as special cases of the general solution.

We have studied the buoyancy-driven convection enhancement and entropy production in a Cu–TiO2/water (water with copper and titanium dioxide nanoparticles) hybrid nanofluid filled curved enclosure subjected to a uniform magnetic field. The enclosure has a sinusoidally heated right wall, cold left wall, uniformly heated bottom wall, and thermally insulated upper curved wall. The effect of different amplitudes (concave, square, and convex) of the upper curved wall is considered. The non-linear governing equations are non-dimensionalized and written in stream function-velocity formulation. Bi Conjugate Gradient Stabilized (BiCGStab) method is employed followed by a Tri-diagonal matrix algorithm (TDMA) for the numerical simulation. The considered parameters are as follows: Rayleigh number (Ra), Hartmann number (Ha), phase angle (ε), the amplitude of the curved wall (a), and nanoparticle volume fraction (Φ). The influence of the model parameters on entropy production, fluid flow, and heat transfer phenomenon has been investigated, and the simulated results are displayed in terms of flow fields and temperature fields. According to the studies, increasing the Rayleigh number and volume percentage of nanoparticles has a significant impact on heat transmission and hence dominates the convection effect, whereas increasing the Hartmann number has the opposite effect.

Unsteady flow of Casson fluid past through a vertical channel has been studied by some researchers due to its importance of applications in science and technology. Therefore, the main purpose of this paper is to obtain exact solutions for unsteady free convection flows of Casson fluid with effects of magnetohydrodynamics (MHD) past through vertical channel. This paper is continued study from published article [18] with additional effects of magnetohydrodynamics (MHD). Dimensional governing equations are converted into dimensionless forms by using appropriate dimensionless variables. Dimensionless parameters are obtained through dimensionless process such as Casson fluid, time, Prandtl number, Grashof number and magnetic field. Laplace transform method is used to solve the dimensionless equations with associated initial and boundary conditions. Solutions for velocity and temperature profiles are obtained. Skin friction and Nusselt number are also calculated. The obtained analytical results for velocity and temperature are plotted graphically to discuss the influence of dimensionless parameters on profiles. It is observed that fluid velocity increases with increases of Grashof number, Gr and time, t whereas it decreases with increases of Casson parameter, γ, magnetic field parameter, M and Prandtl number, Pr. Besides that, it is found that temperature profiles decrease with high value of Prandtl number, Pr while increases with high value of time, t. In order to validate the results, the obtained results in limiting cases are compared with the published results and it is found to be in a mutual agreement.

The problem of unsteady magnetohydrodynamics (MHD) free convection flow of nano-fluid past an oscillation moving vertical semi-infinite permeable flat plate with constant heat source and vertical variable thermal boundary condition in a rotating frame of reference is studied theoretically. The boundary layer has the oscillatory type of solution because slip velocity is assumed to oscillate in time with constant frequency. The governing equations are solved using small perturbation approximation. For this investigation, we use two types of nano-particles in base fluid, namely Cu (copper) and Al2O3 (aluminium oxide). The effect of various types of suspended metallic nano-particles and non-dimensional physical parameters on the fluid flow and heat transfer rate are presented and discussed through the graphs.

This paper proposes and analyzes a novel heating coil bundle with the tubes arranged in a multi- level manner. The bundle generates a heated cargo large-scale circulation that enables a superposition of the circulation-driven forced convection on the buoyancy-driven natural convection, providing a more efficient mixed convection heat transfer mechanism. A simulation based comparison of the proposed design and the conventional design is provided. The test case comprising an actual tank heating of an RMH 45 residual fuel oil by an 8-bar steam is simulated by a finite volume method and an OpenFOAM computational fluid dynamics software. The simulation results reveal that a 47.1% higher average heat transfer coefficient may be achieved, allowing a 32.0% reduction of the required heating coil area.

The previous studies related to the thermal-driven flow within enclosures had been summarized in the present work. Various geometries of enclosures like square, rectangular and triangular had been summarized. Besides, enclosures filled with different fluids had been taken into consideration like traditional and nanofluids as well as porous medium, Newtonian and non-Newtonian fluids and multilayer systems. The governing equations of heat transfer and fluid flows had been presented for different cases. Different numerical models like homogeneous, inhomogeneous and thermal non-equilibrium model, Darcy, Darcy extended–Forchheimer model, etc., had been summarized. The influence of various dimensionless parameters like Rayleigh, Darcy, Bejan and Hartmann number, nanofluid loading, diverse thermal cases of the applied boundary conditions, angle of inclination, the number for undulations, the existence of inner body and many others parameters acting and influencing hardly up on both of the entropy generation and the heat transfer was illustrated. The present review illustrates the physical mechanism behind the buoyancy thermally driven flow in terms of figures of contours as well as the Nusselt numbers profiles.

Natural convection flow and heat transfer characteristics of Buongiorno's mathematical model nanofluid flow inside square cavity with isothermal conditions on both side walls and adiabatic conditions on top and bottom walls is studied numerically in this analysis. Finite difference method is employed to solve the governing partial differential equations formulated in stream function, nanoparticle volume fraction and temperature numerically. The results are presented in the form of streamlines, isotherms, isoconcentrations, local Nusselt number and Sherwood number for various values of influenced parameters, such as, Rayleigh number (100 ≤ Ra ≤ 300), buoyancy ratio parameter (0.1 ≤ Nr ≤ 0.9), Lewis number (1.0 ≤ Le ≤ 10), thermophoresis number (0.1 ≤ Nt ≤ 0.5), Brownian motion number (0.1 ≤ Nb ≤ 0.9) and radiation number (0.1 ≤ R ≤ 0.9) and are represented through graphs. It is detected that the values of rate of heat transfer elevates with rising values of Rayleigh number (Ra).

The oily water from various sources in combined cycle power plants is collected in oil/water separator in which the oil separates from water due to the density difference. The idea of the presented geometry is taken from conventional oil/water separators. This paper studies the natural convection of the CuO-water nanoliquid in a rectangular cavity with fins attached to the insulated wall and porous media. Discretion of Navier-Stokes equations is done by Finite Element Method and assumptions are laminar, steady and incompressible flow. Heat transfer performance and entropy generation are investigated for distinct Rayleigh numbers (103–105), Darcy numbers (10−2–10−4), and Hartmann numbers (0, 10, 20). Different sizes of the fins are also studied to show consequences of fin size on heat transfer in cavity. This is the first time that these parameters and their impacts on Nusselt number and entropy generation are studied for a conventional oil/water separator cavity. Corollaries demonstrate that increasing Rayleigh number and Darcy number improves heat transfer performance and average Nusselt number. Nevertheless, Hartmann number has a reverse effect with average Nusselt number. Finally, a new equation for average Nusselt number is developed with regard to Rayleigh number, Hartmann number, and Darcy number.

The cornerstone of a new method to modeling nanofluids is particle movement. There are three primary forms of nanofluid simulation. The single-phase modeling with nanofluid properties (SPU), the multiphase fluid with discrete particle (MDP) and the discrete element method with particle (DEMP). In this study, by comparing three approaches to modeling the natural convection heat transfer in nanofluid, this method's (discrete element method with particle) ability was examined to predict properties and processes, such as heat transfer and friction factor. With a high range of Rayleigh numbers (0 ≤ Ra ≤ 100, 000), this method tries to model the natural convection process in a conical cavity filled with Al2O3 nanofluid and nanoparticles. For modeling the MDP and thermophoresis effect (DEMP), a unique code with a novel grid generation algorithm was developed. The results demonstrated that the initial conditions determined the accuracy of the three methods for modeling the final parameters of natural convection within the conical cavity, the accuracy of the used equations, the procedure through which the boundary conditions were applied and the Rayleigh number. Accordingly, the DEMP and MDP methods were recommended for low Rayleigh numbers and those beyond 5500, respectively.

In this numerical contribution, hybrid nanofluid flow behavior, thermal characteristics, and entropy generation analysis through a porous enclosure containing three circular cylinders with magnetic field effects were investigated using finite element approach. The cylinders are arranged in horizontal arrangement in the middle of cavity height, and the active hot central cylinder can move along the vertical central axis while other cold cylinders are considered fixed. The cylinders are enclosed by an adiabatic wavy cavity loaded with Cu-Al2O3-water. The results are discussed for the scrutinized parameters e.g., Rayleigh number (Ra), Darcy number (Da), Hartmann number (Ha), relative position of the hot cylinder (δ), and concentration in volume of nanoparticles (ϕ). It was inferred that the thermal-natural convective flow and overall heat transmission were reinforced by boosting Ra and Da, and lowering Ha. Changing the relative position of the hot cylinder has a remarkable effect on nanoliquid flow patterns, convective heat transfer and entropy generation characteristics.

This paper focuses on a numerical investigation of steady two-dimensional natural convection and volumetric radiation interactions in a concentric annulus between two square isothermal cylinders. T...

This paper deals with a numerical study of free convection in a horizontal cylindrical annulus filled with a fluidsaturated porous medium in the presence of a transverse magnetic field and the heat generation or absorption effect. It is assumed that the inner and outer walls of the cylindrical annulus are maintained at constant temperatures Ti and To , respectively, as Ti > To . In addition to the heat equation, the model consists of the equation of motion under the Darcy law and Boussinesq approximation. The system of equations is solved numerically by the alternatingdirection implicit finite difference method. This investigation concerns the effects of the magnetic field inclination angle, Hartmann number, and the heat generation or absorption coefficient on heat transfer and the flow pattern. The results demonstrate that the heat transfer rate and flow regime depend mainly on the characteristics mentioned. The obtained data are presented graphically in terms of the streamlines and isotherms.

In the present work, the analysis of natural convection and entropy generation in a square porous cavity, having either a flat or a wavy vertical wall, filled with a non-Newtonian nanofluid is repo...

The present study encountered the impact of non-dimensional fusion temperature on the free convection of conducting nanofluid within a porous enclosure filled with nano-encapsulated phase change materials (NEPCMs). The enclosure is equipped with two parallel fins that have ability to move in both directions such as vertically as well as horizontally. In particular the particles are structured as core-shell with phase change materials. The phase change of the materials is obtained from the solid to liquid and absorbs the surrounding temperature in the hot region and releases in the cold region. The governing transformed equations are tackled by using the Finite Element Method (FEM). The numerical simulation of the isotherms, streamlines and heat transfer coefficient ratio along with velocity distribution for various parameters are presented. These are affecting a key role on the average and local Nusselt number as well as on the local Bejan number. However, the measure outcomes are; both the longitudinal and transverse velocity profiles boost up with an augmented Rayleigh number; however, the weaker flow field is generated for the increasing Hartmann number.

Natural convection in a partially porous cavity with a heat generating source in the solid phase is studied numerically under a local thermal nonequilibrium condition. The right and left walls of t...

The present work focuses on the study of mixed convection of a purely viscous shear-thinning fluid in a horizontal annular eccentric duct. The inner and outer cylinders are heated with constant and uniform heat flux densities. The objective of this work is to study the effect of the variation of eccentricity, rheological behavior of the fluid as well as the thermodependency of the rheological parameters on the reorganization of the flow and thermal stratification caused by the buoyancy forces. At the entrance of the heating zone, the dynamic regime is assumed to be established and the temperature profile uniform. The conservation equations are solved numerically using a finite difference method with implicit schemes. A secondary azimuthal flow, induced by natural convection, develops downstream of the inlet section. This flow creates a stratification of the thermal field on a given section of the duct, which intensifies downstream from the entrance. On the other hand, the decrease in consistency with increasing temperature near the heated walls produces a centrifugal radial flow towards the walls. The presence of an eccentricity induces in turn a significant effect on the main dynamic field and the stratification of the thermal field. Two cases of upward and downward eccentricity are treated. These show that an upward shift increases the stratification of the thermal field, while the stratification begins to weaken from a certain amount of eccentricity in the case of downward shift. This represents an important result in terms of possible industrial applications. We may indeed conclude that an appropriate choice of downward eccentricity can reduce the thermal stratification, observed experimentally in the case of a concentric heated annular duct [1], when this stratification is undesirable. The choice of this eccentricity depends on rheological and thermal properties of the fluid.