Natural Convection Heat Transfer 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.

MHD natural convection in a corrugated enclosure with discrete isothermal heating

AbstractIn this study, we numerically examine the unsteady two‐dimensional natural convective heat transfer flow problem in a corrugated enclosure containing an electrically conducting fluid whose top wall is nonuniformly heated. The vertical sidewalls of the corrugated enclosure are kept isothermally cold, while square‐shaped undulations at the bottom wall are discretely heated. Five different cases are considered depending upon the location of the heat sources. A higher‐order compact scheme is used to discretize the governing equations, and an advanced iterative solver, like the hybrid biconjugate gradient stabilized method, is used to solve the system of algebraic equations generated by the numerical discretization. We first validate our results with existing experimental and numerically computed results for the case of a square cavity with and without a heat source. Then, the computed results are analyzed over a range of key parameters, like Rayleigh number (), Hartmann number (), and Prandtl number (), to study the effect of these parameters on the characteristics of heat transfer and the flow field in the corrugated enclosure. Computed results are presented in the form of streamlines, isotherms, local and averaged Nusselt number plots, and so forth. It is found that, with the increase in the heat sources, the convection rate becomes stronger in the core region of the corrugated enclosure at higher Rayleigh numbers. Variations in the Hartmann and Prandtl numbers also have significant effects on the temperature distribution and flow field. Our simulated results show various flow features that have not been studied before.

Natural convective heat transfer in a square enclosure utilizing magnetic nanoparticles

In the present paper, unsteady natural convective heat transfer flow inside a square enclosure filled with nanofluids containing magnetic nanoparticles using nonhomogeneous dynamic model is investigated numerically. The horizontal top wall of the enclosure is considered a colder wall and the bottom wall is maintained at uniform temperature whereas two other vertical walls of the cavity are thermally insulated. The Galerkin weighted residual finite element method has been used to solve the governing non-dimensional partial differential equations. In numerical simulations, four types of nanoparticles such as magnetite (Fe3O4), cobalt ferrite (CoFe2O4), Mn-Zn ferrite (Mn-ZnFe2O4), and silicon dioxide (SiO2), and three types of base fluids such as water (H2O), engine oil (EO) and kerosene (Ke) have been considered. Comparisons with previously published work are performed and excellent agreement is obtained. The effects of various model parameters such as thermal Rayleigh number, nanoparticles volume fraction and nanoparticles shape factor are studied. The results show that the average Nusselt number increases as the thermal Rayleigh number and nanoparticles volume fraction intensify. The results indicate that the average Nusselt numbers are higher for the blade shape of nanoparticles. Kerosene-based nanofluids exhibit higher heat transfer rate. Mn-ZnFe2O4-kerosene nanofluid has a higher average Nusselt number than that of other 11 types of nanofluids which are studied in the present analysis.

Hall Current and Viscous Dissipation Effects on Boundary Layer Flow of Heat Transfer Past a Stretching Sheet

The effect of Hall current and viscous dissipation on MHD natural convective heat transfer flow of a compressible viscous fluid past a stretching surface in the presence of strong magnetic field has been considered in the present work. A magnetic field is applied transversely to the direction of the flow. By means of similarity transformation the governing equations are transformed into nonlinear ordinary flow and heat transfer characteristics which are evaluated by making the use of Nachtsheim–Swigert iteration technique along with the sixth order Runge–Kutta integration scheme. Validation is achieved through the use of Mathematica software as well. The influence of various parameters is then presented graphically in the form of non-dimensional velocity (primary and secondary) and temperature within the boundary layer entering into the problem. Also the effects of the pertinent parameters on the skin-friction coefficients and rate of heat transfer in terms of the Nusselt number, which are of physical interest, are sorted out and presented in the form of table and the conclusion is drawn that the flow field and other quantities of physical interest are significantly influenced by these parameters.

Natural Convective Heat Transfer Flow of Nanofluids Inside a Quarter-Circular Enclosure Using Nonhomogeneous Dynamic Model

In this paper, we have studied the problem of two-dimensional transient convective flow and heat transfer in nanofluids in a quarter-circular-shaped enclosure using newly proposed nonhomogeneous dynamic mathematical model. The round wall of the enclosure is maintained at constant low temperature and the variable thermal condition on the bottom heated wall is considered, whereas the vertical wall is regarded as adiabatic. The enclosure is permeated by an inclined uniform magnetic field. The Galerkin weighted residual finite element method has been employed to solve the governing nondimensional partial differential equations. The result shows that 1- to 10-nm-sized nanoparticles are uniform and stable in the solution. The external magnetic field and its direction control the flow pattern of nanofluid significantly. The average Nusselt number increases significantly, as nanoparticle volume fraction, magnetic field inclination angle and Rayleigh number increase. Average Nusselt number of cobalt–kerosene nanofluid is much higher than other 17 types of nanofluids which are studied in the present analysis. The flow behaviors and the heat transfer rates of 18 types of nanofluids have been presented for the scientific and engineering community to become familiar with such nanofluids and apply them in practical applications.

Hydromagnetic natural convective heat transfer flow in an isosceles triangular cavity filled with nanofluid using two-component nonhomogeneous model

In this paper, a numerical investigation is presented to study Buongiorno's mathematical model for hydromagnetic free convection flow in an isosceles triangular cavity filled with nanofluid. The inclined walls of the cavity are maintained at constant cold temperature whereas various combinations of the thermal boundary conditions at the bottom heated wall are considered. The cavity is permeated by an inclined uniform magnetic field and the effects of Brownian motion and thermophoresis are incorporated into the nanofluid model. The Galerkin weighted residual finite element method has been employed to solve the governing partial differential equations after converting them into a non-dimensional form using a suitable transformation of variables. In the numerical simulations, alumina-water based nanofluid has been taken into account. Comparisons with previously published work are performed and excellent agreement is obtained. The effects of various parameters such as Hartmann number, Rayleigh number and inclined magnetic field angle on streamlines, isotherms and isoconcentrations have been displayed graphically. The heat transfer augmentation for various combination of model parameters as well as various thermal boundary conditions have been done in light of the average Nusselt number from the bottom heated wall. The results show that the heat transfer rate can be decreased with the increasing values of the Hartmann number and inclination angle of the magnetic field but it can be increased by increasing the Rayleigh number and by reducing the diameter of the nanoparticles. The obtained numerical results also indicate that the variable thermal boundary conditions have significant effects on the flow and thermal fields.

Finite Element Analysis of Unsteady Natural Convective Heat Transfer and Fluid Flow of Nanofluids inside a Tilted Square Enclosure in the Presence of Oriented Magnetic Field

In this paper, the problem of unsteady natural convective heat transfer flow of nanofluids having various sizes of nanoparticles inside an inclined square enclosure in the presence of oriented magnetic field is investigated numerically. The Brownian motion of nanoparticles is taken into consideration in the thermal conductivity model construction. Two opposite walls of the enclosure are insulated and the other two walls are kept at different temperatures. Galerkin weighted residual finite element technique has been employed to solve the governing nonlinear dimensionless equations. In order to ensure the accuracy of the present numerical code, comparisons with previously published works are performed and excellent agreement is obtained. The effects of model parameters such as Rayleigh number, Hartmann number, nanoparticles volume fraction, inclination angle of magnetic field, inclination angle of the geometry, diameter and Brownian motion of the nanoparticles on the fluid flow and heat transfer are investigated. The results indicate that an increment in Rayleigh number and nanoparticle volume fraction increases the heat transfer rate in a significant way, whereas, an increment in Hartmann number decreases the overall heat transfer rate. It is also observed that the heat transfer enhancement strongly depends on the diameter of the nanoparticles as well as the types of the nanofluids. It is observed that the time taken to reach the steady state is controlled by the different model parameters and in particular, it is longer for low Rayleigh number and shorter for high Rayleigh number. A comparison between the two studies of with and without Brownian motion shows that when Brownian motion is considered, the solid volume fraction has more significant effects on the heat transfer rate at all Rayleigh numbers considered in the square cavity. Finally, the distribution of average heat transfer rate for different cavity inclination angle along with various model parameters has been found as almost parabolic shape.

Mixed Convective Heat and Mass Transfer Flow of Nanofluids in Concentric Annulus

This paper studies the non-Darcy natural convective heat transfer flow of nanofluid flow through a porous medium in a co-axial cylindrical duct where the boundaries are maintained at constant temperature and concentration. The flow in the porous material is given by a linear Brinkman-Forchheimer-extended Darcy equation. The Boussinesq approximation is invoked so that the effect of density variation is combined to the buoyancy forces. The equations of momentum, energy and diffusion are coupled and linear. Galerkin finite element analysis is employed with quadratic polynomial approximations. At different axial positions, analysis is conducted for the behaviour of velocity, temperature and concentration.

Free Convective Heat Transfer Flow of Temperature Dependent Thermal Conductivity Along a Vertical Flat Plate with Heat Generation

The natural convection heat transfer flow of temperature dependent thermal conductivity on an electrically conducting fluid along a vertical flat plate with heat generation have been investigated in this paper. The governing equations with associated boundary conditions for this phenomenon are converted to dimensionless forms using a suitable transformation. The transformed non-linear equations are then solved using the implicit finite difference method. Numerical results of the velocity and temperature profiles for Prandtl number and heat generation parameter, skin friction and local rate of heat transfer profiles for different values of the thermal conductivity variation parameter, Prandtl number and heat generation parameters are presented graphically. Detailed discussion is given for the effects of the aforementioned parameters. Significant effects are found in velocity and temperature profiles for Prandtl number. Remarkable effects are found in skin friction and heat transfer for heat generation parameter. Also significant effect is found in heat transfer for thermal conductivity variation parameter.

NATURAL CONVECTION HEAT TRANSFER FLOW VISUALIZATION OF PERFORATED FIN ARRAYS BY CFD SIMULATION

The present paper reports, the validation of result s of modeling and simulation in CFD by experiment othe fluid flow and heat transfer characteristics of a fin arrays with later al circular perforation and its external dimensiona lly equivalent solid fin arrays equipped on horizontal flat surface a problem of na tural convection. The simulation is carried out usi ng the fluid flow (CFX) workbench of ANSYS 12.0. In this study, results sho ws that formation of the stagnant layer around the solid fin array which slowdowns the heat dissipation rate. Increase in the fl uid flow movement around the fin results increase i n the heat dissipation rate. It can be achieved by adding perforation to the fins. Natu ral convection is a buoyancy driven phenomenon; the state of the art of CFX was used to carry the study of fluid flow separation an d velocity field over a fin array. New designed per forated fins have an improvement in average Nusselt number, over its external dimens ionally equivalent solid fin arrays.

Conduction-combined forced and natural convection in a lid-driven parallelogram-shaped enclosure divided by a solid partition

Conduction-combined forced and natural convection heat transfer flow of air in a differentially heated lid-driven parallelogram-shaped enclosure divided by a solid partition has been formulated and solved numerically using the finite-volume method with the SIMPLE algorithm. For the two-dimensional problem, numerical solutions are obtained for a wide range of Richardson numbers (0.1 ≤Ri ≤ 10), inclination angles of enclosure from the vertical direction (-60° ≤Φ≤ 60°), and thermal conductivity ratios (0.001 ≤K ≤ 10). The results indicate that all of the studied parameters and direction of moving lid have significant effects on Nusselt number and the average skin friction coefficient.

Influence of presence of inclined centered baffle and corrugation frequency on natural convection heat transfer flow of air inside a square enclosure with corrugated side walls

The main objective of this study is to investigate the effect of presence of insulated inclined centered baffle and corrugation frequency on the steady natural convection in a sinusoidal corrugated enclosure. The present study is based on such a configuration where the two vertical sinusoidal walls are maintained at constant low temperature whereas a constant heat flux source whose length is 80% of the width of the enclosure is discretely embedded in the bottom wall. The remaining parts of the bottom wall and the top wall are adiabatic. The finite volume method has been used to solve the governing Navier–Stokes and the energy conservation equations of the fluid medium in the enclosure in order to investigate the effects of baffle inclination angles, corrugation frequencies and Grashof numbers on the fluid flow and heat transfer in the enclosure. The values of the governing parameters are the Grashof number Gr (10 3–10 6), the corrugation frequencies CF (1, 2 and 3), baffle inclination angles (0° ≤ Φ ≤ 150°) and Prandtl number Pr (0.71). Results are presented in the form of streamline and isotherm plots. The results of this investigation are illustrated that the average Nusselt number increases with increase in both the Grashof number and corrugation frequency for different baffle inclination angles and the presence of inclined baffle and increasing the corrugation frequency have significant effects on the average Nusselt numbers, streamlines and isotherms inside the enclosure. The obtained numerical results have been compared with literature ones, and it gives a reliable agreement.

Solution of N-S equations based on the quadtree cut cell method

With the characteristic of the quadtree data structure, a new mesh generation method, which adopts square meshes to decompose a background domain and a cut cell approach to express arbitrary boundaries, is proposed to keep the grids generated with a good orthogonality easily. The solution of N-S equations via finite volume method for this kind of unstructured meshes is derived. The mesh generator and N-S solver are implemented to study two benchmark cases, i.e. a lid driven flow within an inclined square and a natural convection heat transfer flow in a square duct with an inner hot circular face. The simulation results are in agreement with the benchmark values, verifying that the present methodology is valid and will be a strong tool for two-dimensional flow and heat transfer simulations, especially in the case of complex boundaries.

Effects of discrete isoflux heat source size and angle of inclination on natural convection heat transfer flow inside a sinusoidal corrugated enclosure

The main objective of this article is to study numerically a two-dimensional, steady and laminar viscous incompressible flow in a sinusoidal corrugated inclined enclosure. In this analysis, two vertical sinusoidal corrugated walls are maintained at a constant low temperature whereas a constant heat flux source whose length is varied from 20 to 80% of the total length of the enclosure is discretely embedded at the bottom wall. The Penalty finite element method has been used to solve the governing Navier–Stokes and energy conservation equation of the fluid medium in the enclosure in order to investigate the effects of inclination angles and discrete heat source sizes on heat transfer for different values of Grashof number. Results are presented in the form of streamline and isotherm plots. It is concluded that the average Nusselt number increases as inclination angle increases for different heat source sizes.