Laminar Natural Convection Flow Research Articles

Statistical and numerical analysis of magnetic field effects on laminar natural convection heat transfer of nanofluid in a hexagonal cavity

This paper presents a statistical and numerical investigation that examines the optimization and sensitivity analysis of the unsteady laminar natural convective heat transfer flow of Fe3O4-water nanofluid in a hexagonal cavity considering the impacts of a sloping magnetic field in one-component nanofluid model. The inclined walls of the cavity are maintained at a constantly low temperature, while the bottom wall is uniformly heated. The upper wall, however, is regarded as adiabatic. The nanofluid thermal conductivity model incorporates the impact of Brownian motion. The Galerkin weighted residual finite element method has been employed to solve the governing dimensionless equations. The results are provided regarding the average Nu, streamlines, and isotherms. The study uses response surface methodology to analyze the sensitivity of parameters such as the Ha, Ra, and nanoparticle volume percentage. Using a response surface policy allows for optimizing the process and identifying the most favorable circumstances to achieve the maximum thermal transfer rate. The flow pattern of the nanofluid is significantly affected by the magnetic field and its alignment. The numerical results indicate a significant rise in the average Nu as the nanoparticle volume percentage, magnetic field inclination angle, nanoparticle type factor, and Ra increase. Conversely, the Hartmann number and the nanoparticle's diameter have contrasting effects. When considering Brownian motion, the average Nu grows by 225.89 % for Ra = 106 with ϕ = 0.03 and 25.28 % for the other case. The optimal condition for heat transfer occurs when Ra = 106, Ha = 4, and ϕ =0.03 while keeping the other parameters constant.

Similar Solutions for Changing Characteristics of Natural Convection Laminar Flow around a Vertical Rectangular Inclined Plane Surface

The study investigates laminar natural convection flow around a vertical rectangular inclined plane surface, specifically focusing on the effects of viscous and pressure stress work. Previous research primarily addressed these effects in two-dimensional natural convection flow scenarios, while this study extends the analysis to encompass three exterior situations, accounting for variations in fluid properties outside compressible boundary layers. Employing numerical methods, the study aims to predict essential flow parameters including Prandtl’s number (Pr), controlling parameter (C), and additional parameters (A, B, D, E, ∅). The investigation yields velocity profiles (F'(0), S'(0)), temperature profiles , skin frictions (F''(0), S''(0)), and heat transfer coefficients θ'(0). Numerical results are presented to illustrate the impact of different parameters on these flow characteristics. Additionally, tabulated data in Tables-2 and Tables-3 offer further insights into the predicted flow parameters and their variations under varying conditions.

Comparative analysis of entropy generation and heat transfer in a tilted partially heated square enclosure using the finite difference method

PurposeIn recent times, there has been a growing interest in buoyancy-induced heat transfer within confined enclosures due to its frequent occurrence in heat transfer processes across diverse engineering disciplines, including electronic cooling, solar technologies, nuclear reactor systems, heat exchangers and energy storage systems. Moreover, the reduction of entropy generation holds significant importance in engineering applications, as it contributes to enhancing thermal system performance. This study, a numerical investigation, aims to analyze entropy generation and natural convection flow in an inclined square enclosure filled with Ag–MgO/water and Ag–TiO2/water hybrid nanofluids under the influence of a magnetic field. The enclosure features heated slits along its bottom and left walls. Following the Boussinesq approximation, the convective flow arises from a horizontal temperature difference between the partially heated walls and the cold right wall.Design/methodology/approachThe governing equations for laminar unsteady natural convection flow in a Newtonian, incompressible mixture is solved using a Marker-and-Cell-based finite difference method within a customized MATLAB code. The hybrid nanofluid’s effective thermal conductivity and viscosity are determined using spherical nanoparticle correlations.FindingsThe numerical investigations cover various parameters, including nanoparticle volume concentration, Hartmann number, Rayleigh number, heat source/sink effects and inclination angle. As the Hartmann and Rayleigh numbers increase, there is a significant enhancement in entropy generation. The average Nusselt number experiences a substantial increase at extremely high values of the Rayleigh number and inclination.Practical implicationsThis numerical investigation explores advanced applications involving various combinations of influential parameters, different nanoparticles, enclosure inclinations and improved designs. The goal is to control fluid flow and enhance heat transfer rates to meet the demands of the Fourth Industrial Revolution.Originality/valueIn a 90° tilted enclosure, the addition of 5% hybrid nanoparticles to the base fluid resulted in a 17.139% increase in the heat transfer rate for Ag–MgO nanoparticles and a 16.4185% increase for Ag–TiO2 nanoparticles compared to the base fluid. It is observed that a 5% nanoparticle volume fraction results in an increased heat transfer rate, influenced by variations in both the Darcy and Rayleigh numbers. The study demonstrates that the Ag–MgO hybrid nanofluid exhibits superior heat transfer and fluid transport performance compared to the Ag–TiO2 hybrid nanofluid. The simulations pertain to the use of hybrid magnetic nanofluids in fuel cells, solar cavity receivers and the processing of electromagnetic nanomaterials in enclosed environments.

Natural convection laminar flow between two vertical walls with a nonlinear variation of density and viscosity with temperature

AbstractUnder the combined influence of buoyancy force and constant pressure gradient, the free convection flow and heat transmission inside a channel placed vertically and consisting of two parallel walls are examined. Through the application of the Runge–Kutta fourth‐order approach and the shooting procedure, the modeled equations of the problem including nonlinear density–temperature and quadratic viscosity–temperature change at constant but different wall temperatures are numerically solved. For distinct values of the embedded parameters, the fluctuations in fluid's velocity and temperature are examined. For various situations of linear, quadratic, and nonlinear dependence of density on temperature, numerical values for heat transmission rate, volume flow rate and skin friction are determined and tabulated. The fluctuations of the Nusselt number with the Grashof number corresponding to thermal expansion coefficients are depicted through graphical interpretations. It was found that the combined effect of thermal expansion coefficients raises the values of the physical entities, Nusselt number, volume flow rate, and heat transmission rate. For the lower Reynolds number values, the Nusselt number value stays around one, indicating the same impact of conduction and convection on heat transmission.

The effects of thermal radiation, internal heat generation (absorption) on unsteady MHD free convection flow about a truncated cone in presence of pressure work

The aim of present paper is to analyse the effect of radiation, internal heat generation (absorption) on unsteady laminar natural convective boundary layer flow over a truncated cone considering pressure work and magnetic field due to the variation in fluid flow behavior in various physical conditions. Suitable transformation is used to form system of coupled non linear partial differential equations is to governing the flow and heat transfer. These equations have been solved numerically by using an implicit finite difference scheme along with quasilinearization technique. According to numerical findings, the pressure work, internal heat generation (absorption), radiation, and magnetic field have a significant impact on both skin friction and heat transfer. Further, skin friction is found to decrease 12.13%, 30.3% and 41.67% for various values (from 0.0 to 0.5) of pressure work, magnetic field and heat generation (absorption) alongside the cone surface whereas heat transfer rate rises 17.19%, 17.65% and 73.51% respectively due to unsteadiness in the flow. It is observed that the thickness of boundary layer enhances for various values (from 0.0 to 0.5) of heat generation and radiation parameter but diminishes for pressure work and Prandtl number.

BOUNDARY CONDITION ON THE CONVECTION PROCESS INVOLVING NANOFLUIDS

The present numerical investigation deals with the laminar natural convection flow of a nanofluid along an isothermal vertical plate. As indicated by the Boungiorno model [V], nanofluid is considered a two-part combination (base liquid in addition to nanoparticles) where the impacts of Brownian movement and thermophoresis are significant. The boundary condition on the fluid flow is new: the nanoparticle volume fraction at the plate is passively controlled by assuming that its flux there is zero. The outcome of the present study with this new boundary condition is in better agreement with the practical applications of nanofluids.

Analysis of the effects of local thermal non-equilibrium (LTNE) on thermo-natural convection in an elliptical annular space separated by a nanofluid-saturated porous sleeve

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

Numerical modeling of laminar and chaotic natural convection flows using a non-residual dynamic VMS formulation

In this article, the performance of a stabilized VMS-type finite element formulation of a non-residual structure is numerically verified for highly convective natural flows. The novelty of the method is the time-dependent nature of the sub-scales and the introduction of two components for the sub-scale velocities, which allows the resolution of chaotic and highly convective problems without the need to include an additional turbulence model and its using equal order interpolation between velocity and pressure. The natural heat convection problems of the square and cubic cavities are solved up to a Rayleigh number of 1010 and 3.3×107, respectively. Additionally, the stability of the problem is investigated by conducting an analysis of its Hopf bifurcation. As a distinctive feature, the work includes the assessment of the influence of incorporating dynamic sub-scales, with an emphasis on the accuracy of the numerical solutions obtained, that includes a comparison with the results predicted by the quasi-static formulation of the same method. The comparisons between both formulations were made using direct and iterative solvers. The results reported in this article allow verifying the performance, precision, and robustness of the dynamic formulation used to solve highly nonlinear problems with strong thermal coupling.

Finite element analysis on the hydrothermal pattern of radiative natural convective nanofluid flow inside a square enclosure having nonuniform heated walls

AbstractThe present article enlightens us on the hydrothermal pattern of a steady incompressible laminar natural convective nanofluid flow inside a heated square chamber. The square enclosure is filled with water‐based spherical‐shaped ferrous (Fe3O4) nanoparticles. Magnetic effect and thermal radiation are presumed within the flow. The left‐sided vertical wall and one bottom wall of the chamber are nonuniformly and uniformly heated, while the remaining right‐sided vertical wall is isothermally cooled at a constant temperature and the upper wall is insulated. A detailed analysis is conducted to exhibit that how nonuniform and uniform heated walls influence flow within the square chamber. The leading dimensional equations are made into a dimensionless form using apposite similarity variables and the Galerkin finite element technique is executed to solve those equations. The grid independence test and a parallel comparison with existing literature are presented to verify the validity of the outcomes. The streamlines, isotherms, temperature, velocities, and average Nusselt number are depicted through several graphs for several parametric values of Rayleigh number, Hartmann number, thermal radiation, and nanoparticle volume fraction. The outcomes showed that increasing nanoparticle concentration and Rayleigh number lead to improve the Nusselt number, while heat transport is reduced for Hartmann number and radiation parameter. The uniformly heated walls convey better heat transport as compared to nonuniformly heated walls.

Sensitivity Analysis of Schlieren-Particle Image Velocimetry System for Simultaneous Measurement of Flow and Temperature Field of a Free Convective Flow Inside a Cubic Cavity

Abstract Fluid flows characterized by density variations have been studied using the schlieren-particle image velocimetry (PIV) system. The knife-edge location plays a crucial role in determining the system’s sensitivity, which significantly affects the accuracy of the measured quantities. Further, the optimum knife-edge position and the correct combination of image recording speed and interrogation window size are desirable for achieving the most accurate and reliable results. The present paper discusses the above issues on the measured quantities, such as temperature field, local Nusselt number distribution along the conducting walls, average Nusselt number, and velocity field. The experiment is performed to investigate laminar and steady natural convective flow in a water-enclosed cubic cavity with a left hot wall and a right cold wall. The analysis is undertaken for various knife-edge positions (0–90%), different image time separation varying (20–200 ms,) and interrogation window size using two passes varying from W1 = 32 pixels, W2 = 16 pixels to W1 = 128 pixels, W2 = 64 pixels. The results are presented for two distinct Rayleigh number, 1 × 108 and 3 × 108. Three-dimensional simulations have been carried out to check the fidelity of the experiment for Ra = 1 × 108. A high dynamic range of temperature is obtained for the range of knife-edge position in 50–65% while a high-velocity range is realized for knife-edge cutoff of 65% and combination of image time separation of Δt = 100 ms and interrogation window size with two passes of W1 = 64 pixels followed by W2 = 32 pixels.

Numerical simulation of thermal management during natural convection in a porous triangular cavity containing air and hot obstacles

A numerical study is presented of laminar viscous magnetohydrodynamic natural convection flow in a triangular-shaped porous enclosure filled with electrically conducting air and containing two hot obstacles. The mathematical model is formulated in terms of dimensional partial differential equations. The pressure gradient term is eliminated by using the vorticity–stream (\(\omega - \psi\)) function approach. The emerging dimensionless governing equations are employed by the regular finite difference scheme along with thermofluidic boundary conditions. The efficiency of the obtained computed results for isotherms and streamlines is validated via comparison with previously published work. The impact of physical parameters on streamlines and temperature contours for an extensive range of Rayleigh number (Ra = 103–105), Hartmann magnetohydrodynamic number (Ha = 5–30), Darcy parameter (Da = 0.0001–0.1) for fixed Prandtl number (Pr = 0.71) is considered. Numerical results are also presented for local and average Nusselt numbers along the hot base wall. Interesting features of the thermofluid behaviour are revealed. At lower Rayleigh number, the isotherms are generally parallel to the inclined wall and only distorted substantially near the obstacles at the left vertical adiabatic wall; however, with increasing Rayleigh number, this distortion is magnified in the core zone and simultaneously warmer zones expand towards the inclined cold wall. The simulations are relevant to magnetic materials processing and hybrid magnetic fuel cells.

Thermal ignition by vertical cylinders

In this work, thermal ignition of laminar external natural convection flows by vertical cylinders is investigated. Effects of cylinder size are studied, with cylinder height ranging from 12.7 to 25.4 cm, and cylinder surface areas varying from 25 to 200 cm2. The minimum ignition threshold for a stoichiometric hexane-air mixture is 1019 K for a cylinder 25.4 cm long and 200 cm2 in surface area. The ignition threshold is found to have a weak dependence on surface area, in contrast to historical data. The ignition results are consistent with ignition temperature decreasing inversely with the logarithm of surface height. Experiments are performed with multi-component, heavy-hydrocarbon fuels including POSF-4658 Jet A and two surrogate fuels, Aachen and JI, as well as hexane. The setup is heated for multi-component fuel testing. POSF-4658 Jet A has an ignition temperature of 971 K at an ambient temperature of 333 K. All fuels investigated were found to have ignition thresholds within 38 K of the POSF-4658 Jet A ignition threshold. JI is found to be the most appropriate surrogate for POSF-4658 Jet A.

Impact of uniform and non-uniform heated rods on free convective flow inside a porous enclosure: finite element analysis

A numerical study of laminar natural convective flow in a porous rectangular cavity having two heated rods is performed in this article. Both heated rods are placed in the middle of the cavity. Further, it is assumed that the flow and isothermal contours are influenced by permeable medium. Physical laws transform this physical setup into the mathematical form, which is expressed as partial differential equation. Finite element method is adopted to get the solution of these partial differential equations, the results against various flow controlling variables are presented in contour plots and line graphs. Results illustrate that in the case of non-uniform heating, the heat transfer rate is suppressed with the enhancement Rayleigh parameter as compared to uniform heating. In addition, with the increase in heated length of rods, flow field gets stronger due to stronger buoyancy effects. Moreover, the velocity distribution and Nusselt number are enhanced with the rise of permeability of porous medium.

Heat transfer and entropy generation analysis of three-dimensional nanofluids flow in a cylindrical annulus filled with porous media

Laminar natural-convection flow and entropy production within a vertical porous annulus filled with nanofluids are examined. The vertical walls of the external and internal cylinders are maintained at different temperatures TH and TC (TH > TC), respectively. In contrast, the bottom and top of the annulus are adiabatic. Equations of continuity, momentum, energy, and entropy are resolved using the finite volume approach. Our FORTRAN-language programming code is well-validated with other works. The effects of porosity 0.2 ≤ ε ≤ 0.99, nanoparticles 0 ≤ ϕ ≤ 0.08, nanofluid types, Rayleigh 103 ≤ Ra ≤ 105 and Darcy 10−4 ≤ Da ≤ 10−1 numbers on the flow, heat transfer, and entropy production are examined. We find that nanoparticles' inclusion improves heat transfer and increases total entropy production St. Da and ε affect flow structure, thermal field, and entropy generation. Besides, increasing Da and ε, St, the average Nusselt Nu¯in,out, and Bejan Be numbers increase. However, in the opposite case, St and Be decrease. For Ra = 105, the best Nusssetl number is maximum for the Ag-water nanofluid, which increases up to 9.50%. Adding TiO2 nanoparticles, on the other hand, results in a lower Nu¯in,out value. The increase of the inner cylinder size reduces Nu¯in,out and St.

Natural convection of nanoliquid from elliptic cylinder in wavy enclosure under the effect of uniform magnetic field: numerical investigation

In the current article, a three-dimensional numerical simulation is conducted to scrutinize the steady laminar natural convective flow and transfer of heat between a cold wavy porous enclosure and a hot elliptic cylinder. Alumina nanoparticles are dispersed in the water to enhance the heat exchange process. The nanofluid flow is taken as laminar and incompressible, while the advection inertia effect in the porous layer is taken into account by adopting the Darcy–Forchheimer model. The problem is explained in the dimensionless form of the governing equations and solved by the finite element method. The influences of different governing parameters such as nanoparticles volume fraction (ϕ), angle of rotation (α), Darcy number (Da), Hartmann number (Ha), and Rayleigh number (Ra) on the fluid flow, temperature (T) filed and average Nusselt number are presented. The results exhibit that the heat transfer is enhanced when either of Ra, Da and ϕ is raised. The permeability increment achieved a 12.73% enhancement in the heat transfer rate. Also, when $$\mathrm{Ha}$$ is altered from 0 to 100, a reduction in values of the Nusselt number is given up to 22.22%. Furthermore, the optimal inclination angle for the convective process is α = 45°.

Network Simulation Model for Free Convective Flow from a Vertical Cone

An axisymmetric, mathematical models is obtainable for the laminar natural convective laminar flow with effects of heat as well as mass transmission on an incompressible viscid liquid past a cone by uniform wall concentration, variable surface temperature including with effect of chemical reaction. The solutions of non-dimensional leading boundary layer equation of flow which are coupled, unsteady and nonlinear PDE’s were obtained using NSM, a robust statistical method which demonstrate elevated effectiveness and accurateness and the computer code Pspice. The different profiles of temperature, velocity and concentration were analyzed for different parameter, namely λ (chemical reaction), Sc (Schmidt number), Pr, N (buoyancy ratio constraint) and power law exponential of wall temperature n are discussed graphically. The current experiment result is compare with the existing outcome in the open literature and is found to be in outstanding conformity.

Laminar MHD natural convection flow due to non-Newtonian nanofluid with dust nanoparticles around an isothermal sphere: Non-similar solution

The focus of this paper is to examine non-similar solutions of dusty non-Newtonian Casson nanofluid flow around the surface of an isothermal sphere in the presence of magnetic field impact. It is presupposed that the impacts of thermophoresis and Brownian motion are considered into regard in the nanofluid model. In addition to the thermophoresis impact, the normal flux of nanoparticles is equal to zero at the boundary. With respect to the fluid temperature, the surface of the isothermal sphere is preserved at a constant temperature. The dust particles preassumed to having the same size and conform in the spherical shape to the nanoparticles. Suitable non-similarity transformations are utilized to mutate the governing partial differential equations for fluid and dust phases into a system of non-linear, coupled, and non-similar partial differential equations. The generated non-similar equations are solved using numerical technique renown MATLAB function bvp4c and the results are represented in terms of velocity and temperature of fluid and dust phases, and concentration distribution as well as the skin-friction coefficient and heat transfer rate. Obtained results indicate that increasing the mass concentration of the dust particles in the nanofluid leads to depression the motion and an enhancement in the rate of heat transfer. For the nanofluid phase and dust particle phase, the temperature magnitude improves with increasing of the stream wise coordinate additionally the distribution of velocity accelerates away from the sphere surface i.e. with high values of the radial coordinate η.

Parametric Study of Natural Convection inside a Partitioned Cavity in the Presence of a Magnetic Field

Steady laminar natural convection flow is studied numerically. The flow domain is a differentially heated square cavity with two partitions that is exposed to a constant horizontal magnetic field. A finite volume-based code is developed by the SIMPLER algorithm. A parametric study is carried out, using different values of the Rayleigh numbers, partition positions, partition heights, and the Hartmann numbers (from zero to 200). It is found that the Nusselt number is an increasing function of the Rayleigh number, but a decreasing function of the partition height and Hartmann number. The position of the partitions affects the streamlines and isotherms, but has a minimal effect on the mean Nusselt number. In addition, the results show that for low partition heights convective heat transfer in a cavity is significant, the braking effect of the Lorentz force is more pronounced, and the mean Nusselt number decreases considerably with increasing magnetic field strength.

Influence of cross diffusions on natural convection flow through annulus region with Navier slip and convective boundaries

Abstract In this manuscript we present the influence of cross diffusions on incompressible natural convection laminar flow between concentric cylinders with slip and convective boundaries. In addition, the first order chemical reaction is also considered. The governing equations with boundary conditions are transformed to a non - dimensional form with suitable transformations. Homotopy Analysis Method (HAM) is used to solve the system of equations. The influence of the various parameters like Slip, Dufour, Soret, chemical reaction parameters and the Biot number on velocity, temperature and concentration are investigated and presented through plots. It is found from this study that the influence of slip parameter and Biot number, the velocity and temperature profiles increase, while there is a reverse tendency under the effect of chemical reaction parameter.

Microstructure and inertial effects on natural convection micropolar nanofluid flow about a solid sphere

The addition of nanoparticles is one of the modern scientific techniques to improve the heat transfer enhancement. However, micropolar fluid model is not examined under nanoparticle effects. The addition of nanoparticles in a micropolar fluid makes the mixture more complex as compared to the addition of conventional nanofluids. The innovative micropolar nanofluid model is introduced to explore nanofluid characteristics under microstructure and inertial effects. In this study, steady laminar 2D natural convection flow of copper (Cu) and alumina (Al2O3)-suspended micropolar nanofluid over a solid sphere with a constant surface heat flux is investigated. The governing partial differential equations are transformed into a dimensionless form and then solved numerically using an implicit finite difference scheme known as the Keller-box method. The behaviours of different parameters on temperature, velocity and angular velocity have been examined graphically for both Cu/Al2O3–water and Cu/Al2O3–kerosene oil. From the graphical results, it is found that the temperature and velocity fields of Al2O3–water have higher values as compared to those of Al2O3–kerosene oil.