Nonhomogeneous Dynamic Model Research Articles

Shape optimization study for heat and mass transport of magnetic fluid in a closed domain using a nonhomogeneous dynamic model

The current study deeply investigates nanofluid's heat and mass transport in a staggered-shaped enclosure with wavy walls. A nonhomogeneous mathematical model with thermophoresis and Brownian diffusion is considered in our study. The finite element method is implemented to solve the set of governing equations. Impacts of magnetic field (B0) and its orientation (γ), undulation number (N), amplitude (A) and nanoparticle types are examined for heat and mass flow. Investigations show that the most demoting trend is obtained when the inclination of B0 is either vertical or horizontal. It is concluded that mean Nusselt (Nuavg) and Sherwood number (Shavg) are increasing functions of Ra. When Ra is changed from 103 to 107, the Shavg value is increased up to six times. The impacts of wall shape show that as we increase A, the Nuavg decreases while the maximum can be obtained for the flat boundary. For small N, Shavg is an increasing function. Shape optimization revealed that there exists a critical point between Shavg and N after which it declines. Investigations further show that this point can be changed. Some critical points have been calculated that can be counted as novel results.

An Inhomogeneous Model for Laser Welding of Industrial Interest

An innovative non-homogeneous dynamic model is presented for the recovery of temperature during the industrial laser welding process of Al-Si 5% alloy plates. It considers that, metallurgically, during welding, the alloy melts with the presence of solid/liquid phases until total melt is achieved, and afterwards it resolidifies with the reverse process. Further, a polynomial substitute thermal capacity of the alloy is chosen based on experimental evidence so that the volumetric solid-state fraction is identifiable. Moreover, to the usual radiative/convective boundary conditions, the contribution due to the positioning of the plates on the workbench is considered (endowing the model with Cauchy–Stefan–Boltzmann boundary conditions). Having verified the well-posedness of the problem, a Galerkin-FEM approach is implemented to recover the temperature maps, obtained by modeling the laser heat sources with formulations depending on the laser sliding speed. The results achieved show good adherence to the experimental evidence, opening up interesting future scenarios for technology transfer.

Numerical Study of MHD Natural Convection inside a Cubical Cavity Loaded with Copper-Water Nanofluid by Using a Non-Homogeneous Dynamic Mathematical Model

Free convective flow in a cubical cavity loaded with copper-water nanofluid was examined numerically by employing a non-homogeneous dynamic model, which is physically more realistic in representing nanofluids than homogenous ones. The cavity was introduced to a horizontal magnetic field from the left sidewall. Both the cavity’s vertical left and right sidewalls are preserved at an isothermal cold temperature (Tc). The cavity includes inside it four isothermal heating blocks in the middle of the top and bottom walls. The other cavity walls are assumed adiabatic. Simulations were performed for solid volume fraction ranging from (0 ≤ ϕ ≤ 0.06), Rayleigh number varied as (103 ≤ Ra ≤ 105), the Hartmann number varied as (0 ≤ Ha ≤ 60), and the diameter of nanoparticle varied as (10 nm ≤ dp ≤ 130 nm). It was found that at (dp = 10 nm), the average Nusselt number declines when Ha increases, whereas it increases as (Ra) and (ϕ) increase. Furthermore, the increasing impact of the magnetic field on the average Nusselt number is absent for (Ra = 103), and this can be seen for all values of (ϕ). However, when (dp) is considered variable, the average Nusselt number was directly proportional to (Ra) and (ϕ) and inversely proportional to (dp).

Thermal Instability Analysis for Natural Convective Heat Transport within a Horizontal Layer Filled with Nanoparticles Using Non-Homogeneous Dynamic Model

Thermal Instability Analysis for Natural Convective Heat Transport within a Horizontal Layer Filled with Nanoparticles Using Non-Homogeneous Dynamic Model

Natural convective heat transfer in a nanofluid-filled square vessel having a wavy upper surface in the presence of a magnetic field

Copper oxide makes an excellent nanomaterial for various efficient heat transfer devices because of its high specific surface area,lightweight, high specific heat capacity, and high thermal conductivity. Heat transfer intensification using nanofluids has strong potential to improve innovative cost-efficient chilling technologies. The present study aims to analyze the heat transfer intensifications for various parameter settings in a practical application. In recognition of possible applications, the problem of natural convective heat transfer in a copper oxide nanofluid-filled square vessel having the wavy upper wall in the presence of a uniform magnetic field using a nonhomogeneous dynamic model is analyzed. The temperature of both the bottom and the near walls of the vessel are hot, while the upper wavy surface is cold. The remaining vertical wall is considered adiabatic. A Galerkin finite element method is applied to the governing equations, along with suitable boundary conditions. The effects of a wide range of control parameters, such as the Hartmann number, magnetic field inclination angle, gravity inclination angle, solid-volume fraction, nanoparticle diameter, and dimensionless time, on the flow and thermal fields, are studied. The results show that early steady-state heat transfer occurs and that the flow, thermal, and concentration fields become suitable for enhanced heat transfer with increases in the Rayleigh number, wall wavenumber, nanosolid volumetric ratio, and geometry inclination angle, and with decreases in the Hartmann number and the nanoparticle diameter. A 20% improvement in heat transfer can be achieved by increasing the number of waves on the upper surface of heat transfer devices.

Numerical simulation of convective heat transport within the nanofluid filled vertical tube of plain and uneven side walls

Two-dimensional transient natural convective flow in a vertical tube of plain and uneven side-walls containing cobalt-kerosene nanofluids is analyzed using a nonhomogeneous dynamic model. The vertical right wall of the enclosure is maintained at a constant low temperature and the left wall is heated by a uniform thermal condition whereas the horizontal side-walls are insulated. The Brownian motion and thermophoretic phenomena of the nanoparticles are considered in the model. The governing nonlinear momentum, energy, and concentration equations are solved numerically using a Galerkin weighted residual finite element method. The thermal, flow and concentration fields are obtained to understand the flow dynamics of cobalt-kerosene nanofluid in two types of enclosures. The local and average Nusselt numbers are analyzed for plain and uneven side walls of the tube for different parameters of the problem. The simulated results are compared with the experimental as well as with the numerical data available in the literature for some special cases. The outcomes show that the tube of having uneven vertical side-walls give higher heat transfer for lower values of the thermal Rayleigh number; whereas for the higher values of the thermal Rayleigh number, the tube of plain vertical side-walls exhibit significantly higher heat transfer rate.

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.

Convective Heat Transfer Utilizing Magnetic Nanoparticles in the Presence of a Sloping Magnetic Field Inside a Square Enclosure

Unsteady natural convection flow and heat transfer utilizing magnetic nanoparticles in the presence of a sloping magnetic field inside a square enclosure are simulated numerically following nonhomogeneous dynamic model. Four different thermal boundary conditions: constant, parabolic in space, sinusoidally in space, and time for the bottom hot wall are considered. The top wall of the enclosure is cold while the vertical walls are thermally insulated. Galerkin weighted residual finite element method is used to solve the governing nondimensional partial differential equations. For simulations, 12 types of nanofluids consisting magnetite (Fe3O4), cobalt ferrite (CoFe2O4), Mn–Zn ferrite (Mn–ZnFe2O4), and silicon dioxide (SiO2) nanoparticles along with water, engine oil, and kerosene as base fluids are used. The effects of the important model parameters such as Hartmann number, magnetic field sloping angle, and thermal Rayleigh number on the flow fields are investigated. The results show that the average Nusselt number, shear rate, as well as the nanofluid velocity decreases as the Hartmann number intensifies. Moreover, the rate of heat transfer in nanofluid exaggerates with the increase of the thermal Rayleigh number and the magnetic field sloping angle. Sinusoidally varied in space thermal boundary condition at the bottom wall provides the highest average Nusselt number and the shear rate compared to the other types of thermal boundary conditions studied here. For this case, the highest average Nusselt number is obtained for the Mn–ZnFe2O4–Ke nanofluid. On the other hand, Fe3O4–H2O nanofluid delivers the highest shear rate compared to the other premeditated nanofluids.

Finite element computational procedure for convective flow of nanofluids in an annulus

In the present study, the detailed procedures of Galerkin weighted residual technique of finite element method (FEM) for solving two-dimensional incompressible natural convective flow of nanofluids using nonhomogeneous dynamic model are discussed for the first time. The physical domain is discretized by using unstructured triangular elements. The governing partial differential equations of nanofluids are made dimensionless using the suitable transformation of variables for weak formulations. The method of weighted residuals is used for obtaining the approximate solutions. This approach typically leads to a sparse and indefinite matrix that is difficult to solve efficiently. The formation of an indefinite matrix is avoided in the present work by introducing an artificial compressibility term in the continuity equation. Unequal order interpolation functions are used for pressure, velocity, temperature and concentration variables. The coefficient matrices are calculated using interpolation functions. Assembling of triangular elements in the discretized domain is discussed elaborately. The process of calculating boundary integrals is also discussed. The Newton-Raphson iteration technique along with Euler-backward scheme is used to solve the global matrix. The sample results are obtained for the convective flow of nanofluids in a concentric annulus. It shows that the annulus of having higher thickness is the best performer enhancing convective heat transfer rates.

Numerical computation of natural convective heat transport within nanofluids filled semi-circular shaped enclosure using nonhomogeneous dynamic model

In this paper, the problem of unsteady natural convective flow of nanofluids inside a semicircular shaped enclosure using the newly developed nonhomogeneous dynamic model has been investigated numerically. The Galerkin weighted residual finite element technique has been employed to solve the governing nonlinear and coupled dimensionless partial differential equations. The streamlines, the isotherms, and the isoconcentrations are displayed graphically to show the flow and thermal fields as well as concentration levels of nanofluid. The average Nusselt numbers at the heated wall of the enclosure for 16 types of nanofluids are calculated for different flow parameters. Comparisons are made with the numerical as well as the experimental data available in the literature. The results show that nanoparticles uniformly suspend in a base fluid when the particle diameter ranges from 1 to 10nm. The average Nusselt number increases significantly with the increase of the nanoparticle volume fraction as well as with different shapes of nanoparticles, whereas it decreases remarkably with the increase of nanoparticles diameter. It is noted that Cu-water and CuO-water nanofluids are the best performer to enhance heat transfer rates compared to the other nanofluids considered in the analysis.

Analysis of natural convective heat transport in homocentric annuli containing nanofluids with an oriented magnetic field using nonhomogeneous dynamic model

In this paper, the time-dependent natural convective heat transport in homocentric annuli containing nanofluids accompanying an oriented magnetic field using a nonhomogeneous dynamic mathematical model is numerically investigated. The analysis is carried out for four different shapes of inner walls such as triangular, square, elliptical and cylindrical. The outermost cylindrical boundary of the annulus is regarded at an unvarying low temperature and undifferentiated thermal condition on the inner surface of the annulus is considered. A finite element method is implemented for finding the solutions to the nanofluid equations of the problem. The magnetite iron oxide–kerosene nanofluid has been taken to gain insight into the thermal fields and concentration levels in terms of isotherms and isoconcentrations, respectively. The local Nusselt number distributions along the interior and exterior boundaries have been displayed for various flow parameters of the problem. To find the best performer, the average Nusselt number enhancements are demonstrated varying four different shapes of inner wall for ten sorts of nanofluids compared to that of base fluids. Results show that the dispersion of local Nusselt number decreases with the increase in the nanoparticle diameter and Hartmann number, whereas it enhances with the increase in the measure of nanoparticle by volume, magnetic field inclination angle and Rayleigh number. It is also found that the inner shape of the annulus significantly affects the thermal flow as well as the Nusselt number.

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.

Investigations of Natural Convection Heat Transfer in Nanofluids Filled Horizontal Semicircular-Annulus using Nonhomogeneous Dynamic Model

In this paper, the problem of unsteady convective flow of nanofluid in a horizontal semicircular‐annulus using nonhomogeneous dynamic mathematical model has been investigated. The outer wall of the annulus is considered a colder wall and the inner is maintained at three different temperatures (constant, quadratic and sinusoidal) while two other walls are thermally insulated. The Galerkin weighted residual finite element method has been employed to solve the governing partial differential equations after converting them into non‐ dimensional form using suitable transformation of variables. In the numerical simulations, the cobalt‐ kerosene nanofluid has been taken to gain insight into the flow, thermal fields as well as concentration levels of nanofluids. Local Nusselt number and temperature gradient magnitude on the hotter and colder wall are displayed as line graphs. The average Nusselt number for cobalt‐ kerosene nanofluid is displayed as line graphs for different flow parameters including amount, shape and size of nanoparticles. Also, the average Nusselt number is presented as a bar diagram for 12 types of nanofluids. The result shows that 1‐20 nm size nanoparticles are uniform and stable in the solution. The average Nusselt number increases significantly, as nanoparticle volume fraction, Rayleigh number increases and nanoparticle diameter decreases. Sinusoidal heating inner wall of annulus exhibits higher heat transfer rate. Average Nusselt number of cobalt‐ kerosene nanofluid is much higher than that of other 11 types of nanofluids which are studied in the present analysis.