Conjugate Natural Convection Flow Research Articles

Entropy Generation Due to Magneto-Convection of a Hybrid Nanofluid in the Presence of a Wavy Conducting Wall

The two-dimensional, time-independent conjugate natural convection flow and entropy generation are numerically investigated in three different cases of a wavy conducting solid block attached to the left wall of a square cavity. A hybrid nanofluid with titania (TiO2) and copper (Cu) nanoparticles and base fluid water in the fluid part is considered in the presence of a uniform inclined magnetic field. The leftmost wall of the cavity is the hot one and the rightmost one is the cold one. Radial-basis-function-based finite difference (RBF-FD) is performed on an appropriate designed grid distribution. Numerical results in view of streamlines and isotherms, as well as average Nusselt number in an interface and total entropy generation are presented. The related parameters such as Hartmann number, Rayleigh number, conductivity ratio, amplitude in wavy wall, number of waviness, and inclination angle of magnetic field are observed. Convective heat transfer in the fluid part is an increasing function of kr,Ra,γ, while it deflates with the rise in Ha in each case. Total entropy generation increases with the increase in Ra and kr but it decreases with Ha values. Average Bejan number ascends with the rise in Ha and descends with the rise in Ra.

Conjugate natural convection flow of a nanofluid with oxytactic bacteria under the effect of a periodic magnetic field

Conjugate natural convection flow in a cavity is numerically investigated under the effect of a periodic magnetic field. The cavity has a vertical thermally conducting solid block and a part where the nanofluid flows. The most left wall of the cavity is the hot one and the most right one is the cold one. The problem is considered as two-dimensional and time independent, and a vertical periodic magnetic field is taken into account. Nanoparticle is chosen as SiO2 and the host fluid is water. Inside of the nanofluid, the existence of oxytactic microorganisms is also assumed. Brownian motion and thermophoresis effects are also considered in governing equations. The influence of pertinent parameters biconvection Rayleigh number Rb=1–100, Lewis number Le=1–20, Peclet number Pe=0.1–5, Brownian motion parameter Nb=0.1–1, thermophoresis parameter Nt=0.1–1, Hartmann number Ha=0–100, period of periodic magnetic field λ=0.1–1, amplitude of periodic magnetic field A=0.1–1 and conductivity ratio kr=0.1–10 are examined on fluid flow, heat and mass transfer. Numerical results in view of isolines as well as average Nusselt and Sherwood numbers are presented. Conductivity ratio kr=10 has more impact on convective heat and mass transfer. Convective mass transfer depends on the vertical wall considered as solid–fluid interface or the right cold vertical wall. It is an increasing function of Le, Pe, Ha, Nt and Nb and decreasing function of Rb in interface.

Effect of thermal radiation on conjugate natural convection flow of a micropolar fluid along a vertical surface

This article investigates the behavior of conjugate natural convection over a finite vertical surface immersed in a micropolar fluid in the presence of intense thermal radiation. The governing boundary layer equations are made dimensionless and then transformed into suitable form by introducing the non-similarity transformations. The reduced system of parabolic partial differential equations is integrated numerically along the vertical plate by using an implicit finite difference Keller-box method. The features of fluid flow and heat transfer characteristics for various values of micropolar or material parameter, K, conjugate parameter, B, and thermal radiation parameter, Rd, are analyzed and presented graphically. Results are presented for the local skin friction coefficient, heat transfer rate and couple stress coefficient for high Prandtl number. It is found that skin friction coefficient and couple stress coefficient reduces whereas heat transfer rate enhances when the micro-inertia parameter increases. All the physical quantities get augmented with thermal radiation.

Conjugate natural convection flow of Ag–MgO/water hybrid nanofluid in a square cavity

The conjugate natural convection of a new type of hybrid nanofluid (Ag–MgO/water hybrid nanofluid) inside a square cavity is addressed. A thick layer of conductive solid is considered over the hot wall. The governing partial differential equations (PDEs) representing the physical model of the natural convection of the hybrid nanofluid along with the boundary conditions are reported. The thermophysical properties of the nanofluid are directly calculated using experimental data. The governing PDEs are transformed into a dimensionless form and solved by the finite element method. The effect of the variation of key parameters, such as the volume fraction of nanoparticles, Rayleigh number, and the ratio between the thermal conductivity of the wall and the thermal conductivity of the hybrid nanofluid (Rk), is studied. Furthermore, the effects of the key parameters are investigated on the temperature distribution, local Nusselt number, and average Nusselt number. The results of this study show that the heat transfer rate increases by adding hybrid nanoparticles for a conduction-dominant regime (low Rayleigh number). The heat transfer rate is an increasing function of both the Rayleigh number and the thermal conductivity ratio (Rk). In the case of a convective-dominant flow (high Rayleigh number flow) and an excellent thermally conductive wall, the local Nusselt number at the surface of the conjugate wall decreases substantially by moving from the bottom of the cavity toward the top.

Two phase flow simulation of conjugate natural convection of the nanofluid in a partitioned heat exchanger containing several conducting obstacles

In this paper, numerical results for conjugate natural convection flow and heat transfer in a heat exchanger divided by a partition with finite thickness and thermal conductivity are presented using Buongiorno's two phase model. A series of numerical simulation is carried out using the finite volume method over a wide range of the Rayleigh number (104 ≤ Ra ≤ 107), volume fraction (0 ≤ φ ≤ 0.05), diameter (25 nm ≤ dp ≤ 145 nm) and type of the nanoparticles (Cu, Al2O3 and TiO2). In addition, the effects of three types of influential factors such as: thermal conductivity ratio (0.1 ≤ Kr ≤ 25), orientation of conductive partition and segmentation of the conductive obstacle on fluid flow and heat transfer characteristics are investigated. Results show that at low Ra, by dividing the conductive obstacle into the nine small segments, the heat transfer rate and absolute values of stream function decrease significantly. It is also observed that by increasing the Ra and thermal conductivity ratio (Kr) the heat transfer rate increase. Moreover, it is found that by changing the orientation of the conductive partition from vertical to horizontal mode, the heat transfer rate alters significantly. Finally, the results demonstrate that the effect of the thermophoresis force for solid particles with high thermal conductivity (like Cu) is negligible.

Conjugate natural convection heat transfer in a partitioned differentially-heated square cavity

In this study numerical results for conjugate natural convection flow and heat transfer in a differentially-heated square cavity divided by a partition with finite thickness and thermal conductivity are presented. A series of numerical simulation is carried out using the finite volume method over a wide range of the Rayleigh number (105–109), with three dimensionless partition thicknesses (0.05, 0.1 and 0.2) and three dimensionless partition positions (0.25, 0.5 and 0.75), both are non-dimensionalized by the cavity width. The results show that the average Nusselt number increases with the Rayleigh number but decreases with partition thickness. It is also found that the partition position has a negligible effect on the average Nusselt number for the whole range of Rayleigh number considered.

Conjugate natural convection flow over a vertical surface with radiation

Numerical study of conjugate natural convection flow over a finite vertical surface with radiation is reported in this article. Rosseland diffusion approximation is used to express the radiative heat flux term. The governing boundary-layer equations are made dimensionless by means of a suitable form of non-similarity transformation. These equations are obtained in three regimes: (1) upstream (when \(\xi \rightarrow 0\)), (2) downstream (when \(\xi \rightarrow \infty \)) and (3) entire regime and are solved numerically. The solutions in the upstream and downstream regimes are obtained via shooting method whereas two-point implicit finite difference method is used to get the solutions for the entire regime. It is seen that asymptotic solutions give accurate results when compared with the numerical solution of the entire regime. The results indicate that the flow field and the temperature distributions are greatly influenced by thermal radiation parameter , \(R_d\), surface temperature parameter, \(\theta _w\) and Prandtl number Pr. It is established from the analysis that recirculation occurs in the flow specifically for \(R_d=1.5\).

Conjugate natural convection in a square enclosure under horizontal magnetic field effect

Steady, laminar, conjugate natural convection flow in a square enclosure is considered. Both effects: conduction in a vertical wall and the presence of a magnetic field are taken together. The enclosure is filled with liquid gallium and subjected to horizontal temperature gradient. The main focus of the study is examining the effect of Hartmann number on fluid flow and heat transfer. The effect of Rayleigh number and conduction in the left wall is also considered. The obtained result show in the absence of a magnetic field that natural convection can be strengthed by the increase of both Rayleigh number and conductivity ratio, because of the increase of the effective temperature difference driving the flow. For poor conducting wall, where the solid part is an insulated material and the thermal resistance is more important the average Nusselt number is approximately constant and having low values comparing with equal and high conducting wall, indicating that most of heat transfer is by heat conduction. In the presence of a magnetic field the results show that for a given Rayleigh number, as the value of Hartmann number increases, convection is suppressed progressively and the rate of heat transfer is reduced in the enclosure.

Effect of Magnetic Field and Wall Conductivity on Conjugate Natural Convection in a Square Enclosure

Steady, laminar, conjugate natural convection flow in the presence of a magnetic field in a square enclosure is considered. The left vertical wall of the enclosure is thick with a finite thermal conductivity, while the other three walls are taken to be of zero thickness. The enclosure is filed with liquid gallium and subjected to horizontal temperature gradient: the vertical boundaries are isothermal at different temperatures, whereas the remaining walls are adiabatic. Finite volume method is used to solve the dimensionless governing equations. The physical problem depends on seven parameters: Rayleigh number (500 ≤ Ra ≤ 106), the Prandtl number (Pr = 0.020), the wall to fluid thermal conductivity ratio (0.1 ≤ Kr ≤ 10), wall thickness (D = 0.2), the Hartmann number (50 ≤ Ha ≤ 200), the inclination angle of the magnetic field (ϕ = 0°, 45° or 90°) and the wall to fluid thermal diffusivity ratio (α* = 1). The main focus of the study is on examining the effect of both inclination angle and Hartmann numbers on fluid flow and heat transfer. The effect of Rayleigh number and conduction in the left wall is also considered. The obtained results, in the absence of a magnetic field, show that natural convection can be strengthened by the increase of both Rayleigh number and conductivity ratio, because of the increase of the effective temperature difference driving the flow. For poor conducting wall (Kr = 0.1), where the solid part is an insulated material and the thermal resistance is more important, the average Nusselt number is approximately constant and having low values comparing with equal (Kr = 1) and high (Kr = 10) conducting wall, indicating that most of heat transfer is by heat conduction. The interface temperature is found to be quite non-uniform, especially for high Ra and Kr. This non-uniformity tends to make the flow pattern in the enclosure asymmetric. In the presence of a magnetic field, the results show that for a given Ra, as the value of Hartmann number increases, convection is suppressed progressively and the rate of heat transfer is reduced in the enclosure. Convection mechanism is also affected by the direction of the magnetic field. It is found that the rate of convection heat transfer is more reduced with the x direction of the magnetic field (inclination angle ϕ = 0°). Also the results show that for poor conducting wall (Kr = 0.1), where the convection is dominated by heat conduction, the presence of a magnetic field is not important and its effect in this case can be neglected.

MHD-Conjugate Free Convection from an Isothermal Horizontal Circular Cylinder with Joule Heating and Heat Generation

The present work is devoted to the numerical study of laminar magnetohydrodynamic (MHD) conjugate natural convection flow from a horizontal circular cylinder taking into account Joule heating and internal heat generation. The governing equations and the associated boundary conditions for this analysis are made nondimensional forms using a set of dimensionless variables. Thus, the nondimensional governing equations are solved numerically using finite difference method with Keller box scheme. Numerical outcomes are found for different values of the magnetic parameter, conjugate conduction parameter, Prandtl number, Joule heating parameter, and heat generation parameter for the velocity and the temperature within the boundary layer as well as the skin friction coefficients and the rate of heat transfer along the surface. It is found that the skin friction increases, and heat transfer rate decreases for escalating value of Joule heating parameter and heat generation parameter. Results are presented graphically with detailed discussion.

Characteristics of conjugate free convection in a corium pool formed during a severe reactor accident

Conjugate natural convection flow in a thick walled semi-circular cavity containing molten core material has been analysed numerically. The lower plenum debris bed represents decay heating, heat conduction, and heat convection within the debris. The internal heat generation resulting from the radioactive decay of fission products ensures that most of the pool remains molten and also causes natural convection in the pool. Bottom circular wall of the cavity is taken to be thick with finite conductive properties, while top wall is considered to be isothermal. In carrying out the analysis, various constituents of the core material are assumed to be mixed homogenously. Thus a homogeneous fluid, for which Pr number is 0.45, has been considered while Ra number range from 3.2×10 7 to 3.2×10 12 has been investigated. Present results for non-conjugate semi-circular cavity compare very well with previously published experimental studies.

Conjugate free convection heat transfer analysis of a vertical plate fin embedded in non-Darcian porous media

The influence of non-Darcian flow phenomena on the natural convection heat transfer from a vertical plate fin embedded in a porous medium was studied. With the thin-fin approximation for the plate fin and the non-Darcy flow model for the convective fluid, numerical solutions were generated to demonstrate the importance of non-Darcian effects on conjugate natural convection flow adjacent to the fin. These effects, which are often involved in convective transport of fluid through porous media, include high-flow-rate inertial force, solid-boundary viscous resistance, nonuniform porosity distribution, and thermal dispersion. The present work aims to investigate these effects on the fin heat-transfer characteristics such as fin temperature distributions, the local heat transfer coefficient, the local heat flux, and the overall rate of heat transfer.