Numerical simulation of natural convection in a horizontal enclosure with a heat-generating conducting body

The physical model considered here is a horizontal layer of fluid heated below and cold above with heat-generating conducting body placed at the center of the layer. The dimensionless thermal conductivities of body considered in the present study are 0.1, 1 and 50. The dimensionless temperature difference ratios considered are 0.0, 0.25, 2.5 and 25. Two-dimensional solution for unsteady natural convection is obtained using an accurate and efficient Chebyshev spectral methodology for variety of Rayleigh number from 10³ to 10⁶. Multi-domain technique is used to handle square-shaped heat-generating conducting body. The fluid flow, heat transfer and time- and surface-averaged Nusselt number are investigated for various ranges of Rayleigh number, thermal conductivity ratio and dimensionless temperature difference ratio. The results for the case of conducting body with heat generation are also compared to those without heat generation to see the effects of heat generation from the conducting body on the fluid flow and heat transfer in the enclosure.     

Natural convection in cavities with a thin fin on the hot wall

A numerical study has been carried out in differentially heated square cavities, which are formed by horizontal adiabatic walls and vertical isothermal walls. A thin fin is attached on the active wall. Heat transfer by natural convection is studied by numerically solving equations of mass, momentum and energy. Streamlines and isotherms are produced, heat and mass transfer is calculated. A parametric study is carried out using following parameters: Rayleigh number from 10⁴ to 10⁹, dimensionless thin fin length from 0.10 to 0.90, dimensionless thin fin position from 0 to 0.90, dimensionless conductivity ratio of thin fin from 0 (perfectly insulating) to 60. It is found that Nusselt number is an increasing function of Rayleigh number, and a decreasing function of fin length and relative conductivity ratio. There is always an optimum fin position, which is often at the center or near center of the cavity, which makes heat transfer by natural convection minimized. The heat transfer may be suppressed up to 38% by choosing appropriate thermal and geometrical fin parameters.     

TWO-DIMENSIONAL AND UNSTEADY NATURAL CONVECTION IN A HORIZONTAL ENCLOSURE WITH A SQUARE BODY

A two-dimensional solution for unsteady natural convection in an enclosure with a square body is obtained using an accurate and efficient Chevyshev spectral collocation method. A spectral multidomain methodology is used to handle a square body located at the center of the computational domain. The physical model considered here is that a square body is located at the center between the bottom hot and top cold walls. To see the effects of the presence of a body on natural convection between the hot and cold walls, we considered the cases that the body maintains the adiabatic and isothermal thermal boundary conditions for different Rayleigh numbers varying in the range of 103 to 106. When the Rayleigh number is small, the flow and temperature distribution between the hot and cold walls shows a symmetrical and steady pattern. At the intermediate Rayleigh number, the fluid flow and temperature fields maintain the steady state but change their shape to the nonsymmetrical pattern. When the Rayleigh number is high, the flow and temperature fields become time dependent, and their time-averaged shapes approach the symmetric pattern again. The Rayleigh number for the fluid flow and temperature fields to become nonsymmetrical and time dependent depends on the thermal boundary conditions of a body. The variation of time- and surface-averaged Nusselt numbers on the hot and cold walls and at the body surfaces for different Rayleigh numbers and thermal boundary conditions are also presented to show the overall heat transfer characteristics in the system.     

Effect of Heat-Generating Solid Body on Mixed Convection Flow in a Ventilated Cavity

The mixed convection flow and heat transfer characteristics inside a square ventilated cavity with a heat-generating solid circular body located at the center have been investigated numerically. The inlet opening is at the bottom of the left wall, while the outlet one is at the top of the right wall, and all the walls of the cavity are considered to be adiabatic. A Galerkin weighted residual finite element method is used to solve the governing equations of mass, momentum, and energy. The behavior of the fluid in the ranges of dimensionless cylinder diameter from 0.1 to 0.6 of the heat generating body, thermal conductivity ratio range from 0.2 to 50 between solid and fluid, and heat generating parameter range from 1 to 5 is described in detail. The medium considered is air with a Prandtl number of 0.71. It is found that the flow and temperature field is strongly dependent on the already-mentioned parameters for the ranges considered. The variation of the mean Nusselt number, the dimensionless average drag force, and the average temperature of the fluid versus Richardson number are presented for these parameters.     

Uniform lateral mass flux effect on natural convection of non-Newtonian fluids over a cone in porous media

In this paper, we have investigated a boundary layer analysis for uniform lateral mass flux effect on natural convection of non-Newtonian power-law fluids along an isothermal or isoflux vertical cone embedded in a porous medium. Numerical results for the dimensionless temperature profiles as well as the local Nusselt number are presented for the mass flux parameter, viscosity index n and geometry shape parameter λ. The local surface heat transfer increases for the case withdrawal of fluid, the increase of the value of λ. The local Nusselt number is found to be significantly affected by the surface mass flux than the viscosity index.     

A numerical investigation of transient natural convection heat transfer of aqueous nanofluids in a differentially heated square cavity

Transient natural convection heat transfer of aqueous nanofluids in a differentially heated square cavity is investigated numerically. The effective thermal conductivity and dynamic viscosity of nanofluids are predicted by using the proposed models that take the contribution of Brownian motion of nanoparticles into account. Three different Rayleigh numbers and five different volume fractions of nanoparticles are considered. The development of natural convection is presented through the evolutions of the average Nusselt number along the cold side wall. The predicted flow development times and time-averaged Nusselt numbers are scaled with Rayleigh number. In addition, the time-averaged Nusselt numbers are presented in terms of volume fraction of nanoparticles. It is shown that at constant Rayleigh numbers, the time-averaged Nusselt number is lowered with increasing volume fraction of nanoparticles.     

Natural convection in porous triangular enclosure with a centered conducting body

A numerical work was performed to examine the heat transfer and fluid flow due to natural convection in a porous triangular enclosure with a centered conducting body. The center of the body was located onto the gravity center of the right-angle triangular cavity. The Darcy law model was used to write the governing equations and they were solved using a finite difference method. Results are presented by streamlines, isotherms, mean and local Nusselt numbers for the different parameters such as the Rayleigh number, thermal conductivity ratio, and height and width of the body. It was observed that both height and width of the body and thermal conductivity ratio play an important role on heat and fluid flow inside the cavity.     

Conduction-combined forced and natural convection in lid-driven enclosures divided by a vertical solid partition

Numerical simulations of the conduction-combined forced and natural convection (mixed convection) heat transfer and fluid flow have been performed for 2-D lid-driven square enclosure divided by a partition with a finite thickness and finite conductivity. Left vertical wall of enclosure has two different orientations in positive or negative vertical coordinate. Buoyancy forces are taken into account in the system. Horizontal walls are adiabatic while two vertical walls are maintained isothermal temperature but the temperature of the left moving wall is higher than that of the right stationary wall. Thus, heat transfer regime between moving lid and partition is mixed convection. Conduction occurs along the partition. And, pure natural convection is formed between the partition and the right vertical wall. This investigation covers a wide range of Richardson number which is changed from 0.1 to 10, thermal conductivity ratio varies from 0.001 to 10. It is observed that higher heat transfer was formed for higher Richardson number for upward moving wall for all values of thermal conductivity ratio. When forced convection becomes effective, the orientation of moving lid becomes insignificant. Heat transfer is a decreasing function of increasing thermal conductivity ratio for all cases and Richardson numbers.     

Natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium

This work studies the natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium with uniform wall temperature. The two-velocity two-temperature formulation is used to derive the governing equations of this system. The Prandtl coordinate transformation is used to transform the wavy surface into a regular plane, and the obtained equations are then simplified further by the order-of-magnitude analysis to give the boundary layer equations. The cubic spline collocation method is used to solve the boundary layer governing equations. The effects of dimensionless amplitude, angle of inclination, inter-phase heat transfer parameter, modified thermal conductivity ratio, and permeability ratio on the heat transfer and flow characteristics are studied. Increasing the modified thermal conductivity ratio and the permeability ratio can effectively enhance the natural convection heat transfer of the inclined plate in bidisperse porous media. Moreover, the thermal non-equilibrium effects are significant for low values of the inter-phase heat transfer parameter. As the dimensionless amplitude increases, both the fluctuations of the local Nusselt number for the f-phase and the p-phase with the streamwise coordinate are enhanced.     

Numerical Investigation of Unsteady Natural Convection in an Inclined Square Enclosure With Heat-Generating Porous Medium

The unsteady laminar natural convection in an inclined square enclosure with heat-generating porous medium whose heat varies by a cosine function is investigated by a thermal equilibrium model and the Brinkman–Darcy–Forchheimer model numerically, with the four cooled walls of closure as isothermal. The numerical code based on the finite-volume method has been validated by reference data before it was adopted. Influence of dimensionless frequency and inclination angle on heat transfer characteristics in a square enclosure, such as flow distribution, isotherm, averaged Nusselt number on each wall, and time-averaged Nusselt number, are discussed, with specified value for Rayleigh number = 10⁸, Darcy number = 10^?4, Prandtl number = 7, porosity = 0.4, and specific heat ratio = 1. It is found that when the internal heat source varies by cosine, the Nusselt numbers of the four walls oscillate with the same frequency as the internal heat source; however, phase difference occurs. Moreover, frequency has little impact on time-averaged Nusselt number of the four walls, which is different from the phenomenon discovered in natural convection with suitable periodic varying wall temperature boundary condition. Moreover, inclination angle plays an important role in the heat transfer characteristics of the walls studied.     

Effects of variable thermophysical properties on mixed convection slip flow over a wedge

This paper reveals the characteristics of mixed convection slip flow of an electrically conducting fluid over a wedge subject to temperature dependent viscosity and thermal conductivity variations. The system of dimensionless nonsimilar governing equations has been solved by an implicit finite difference method. We also use stream‐function formulation to reduce the governing equations into a convenient form, which are valid for small and large time regimes. These are solved employing the perturbation method for small time and the asymptotic method for large time. Numerical solutions yield a good agreement with the series solutions. Because of the increase in the mixed convection parameter, the peak of the velocity profile increases whereas the maximum temperature decreases. In contrast, the local skin‐friction coefficient and local Nusselt number are found to increase with the mixed convection parameter. For higher values of the velocity slip and temperature jump conditions, the local skin‐friction coefficient and the local Nusselt number are found to increase. The viscosity parameter enhances the local skin friction and the local Nusselt number. But the converse characteristic is observed for the thermal conductivity parameter. The results could be used in microelectromechanical systems, fabrication, melting of polymers, polishing of artificial heart valves, etc.     

Transient natural convection with temperature-dependent viscosity in a square partially porous cavity having a heat-generating source

A numerical study is performed on the transient natural convection with a temperature-dependent viscosity inside a square partially porous cavity with a local heat-generating and heat-conducting source. The vertical walls of the cavity are kept at constant cooling temperature while the horizontal walls are adiabatic. The discrete heat-conducting and heat-generating source is located on the bottom wall. A porous layer is located under the clear fluid layer. Governing equations formulated in dimensionless stream function, vorticity and temperature variables with corresponding initial and boundary conditions are solved using implicit finite difference schemes of the second order. The control parameters are the Darcy number, Ostrogradsky number, viscosity variation parameter, height of the porous layer, and dimensionless time. The effects of these parameters on the average Nusselt number along the heat source surface, average temperature of the heater, fluid flow rate inside the cavity, as well as on the streamlines and isotherms are analyzed. The results show that porous layer thickness and viscosity of the working fluid are very good control parameters for optimization of the passive cooling system.     

Unsteady conjugate natural convection in a porous cavity boarded by two vertical finite thickness walls

The objective of this study is to investigate unsteady conjugate natural convection in a porous cavity sandwiched by finite conductive walls considering time-periodic boundary conditions and local thermal non-equilibrium. The top and bottom boundaries are assumed to be isolated and the continuity of temperature and heat transfer are considered in interface boundaries. The effect of varying a plethora of parameters such as Rayleigh number, Thermal conductivity ratio, wall thickness, and non-dimensional frequency on the streamlines, isotherms, and Nusselt number has been studied. It is shown that, apart from non-dimensional frequency and wall thickness, the amplitude of periodic fluid Nusselt number is an increasing function of all aforementioned parameters. Furthermore, aside from Rayleigh number and heat transfer coefficient, the behavior of the solid Nusselt number is the same as fluid Nusselt number. Eventually, the time-averaged Nusselt number and heat transfer through the vertical walls for different values of non-dimensional frequencies are calculated.     

HEAT TRANSFERPREDICTIONS AROUND THREE HEATED CYLINDERS BETWEEN TWO PARALLEL PLATES

The objective of this article is to investigate the heat transfer of convective flow across three heated cylinders arranged in an isosceles right-angled triangle between two parallel plates. The variations in drag coefficient and time-averaged Nusselt number around the surface of the three cylinders as well as the surface-averaged values of the time-averaged Nusselt number for each cylinder are investigated. This investigation is considered under the conditions where the gap-to-diameter ratio is changed (0.5 to 1.25) with forced convection (Re = 100 to 300) and mixed convection (Gr = 80,000 and 200,000). The maximum value of surface- and time-averaged Nusselt number for both forced convection and mixed convection is obtained at a gap-to-diameter ratio equal to 0.75 among the gap-to-diameter ratios considered in this article.     

Unsteady natural convection boundary-layer flow along a vertical isothermal plate in a linearly stratified fluid with Pr>1

In this study, the unsteady natural convection boundary-layer flow along an impulsively heated vertical isothermal plate immersed in a stably stratified semi-infinite ambient fluid is explored using scaling analysis and direct numerical simulation. Scaling relations are obtained for the thermal and velocity boundary layer thicknesses, the boundary layer velocity, the development time and the Nusselt number, in terms of the Rayleigh and Prandtl numbers and the stratification parameter. The scaling results are validated using the numerical simulations.     

Heat transfer in micropolar fluid along an inclined permeable plate with variable fluid properties

This paper studies the heat transfer process in a two-dimensional steady hydromagnetic natural convective flow of a micropolar fluid over an inclined permeable plate subjected to a constant heat flux condition. The analysis accounts for both temperature dependent viscosity and temperature dependent thermal conductivity. The local similarity equations are derived and solved numerically using the Nachtsheim–Swigert iteration procedure. Results for the dimensionless velocity and temperature profiles and the local rate of heat transfer are displayed graphically delineating the effect of various parameters characterizing the flow. The results show that in modeling the thermal boundary layer flow when both the viscosity and thermal conductivity are temperature dependent, the Prandtl number must be treated as a variable to obtain realistic results. As the thermal conductivity parameter increases, it promotes higher velocities and higher temperatures in the respective boundary layers. The wall shear stress increases with the increase of thermal conductivity parameter. This is true of electrically conducting as well as electrically non-conducting fluids. The presence of heat generation invigorates the flow and produces larger values of the local Nusselt number compared with the case of zero heat generation.     

Entropy generation for natural convection by heated partitions in a cavity

Entropy generation for natural convection in a partitioned cavity, with adiabatic horizontal and isothermally cooled vertical walls, is studied numerically by both a FORTRAN code and the commercially available CFD-ACE software. Effects of the Rayleigh number, the position of the heated partition, and the dimensionless temperature difference on the local and average entropy generation rate are investigated. Proper scale analysis of the problem showed that, while fluid friction term has nearly no contribution to entropy production, the heat transfer irreversibility increases monotonically with the Nusselt number and the dimensionless temperature difference.     

Study of conjugate natural convection between vertical coaxial rectangular cylinders

Laminar natural convection between two coaxial vertical rectangular cylinders is numerically studied in this work. The outer cylinder is connected with vertical rectangular inlet and outlet pipes. The inner cylinder dissipates volumetric heat. The fluid flow and heat transfer characteristics between the cylinders are analyzed in detail for various Grashof numbers. The heat transfer rates on the individual faces of the inner cylinder are reported. The bottom face of the inner cylinder is found to associate with much higher heat rates than those of the other faces. The average Nusselt number on bottom face is more than 2.5 times of the Nusselt number averaged on all the faces. At a given elevation, local Nusselt number on the inner cylinder faces increases towards cylinder edges. The effect of thermal condition of the walls of outer cylinder, inlet and outlet on the natural convection is analyzed. The thermal condition shows strong qualitative and quantitative impact on the fluid flow and heat transfer. The variation of induced flow rate, dimensionless maximum temperature and average Nusselt numbers with Grashof number is studied. Correlations for dimensionless buoyancy-induced mass flow rate and temperature maximum are presented.     

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.     

Unsteady Conjugate Natural Convection in a Vertical Cylinder Partially Filled with a Porous Medium

Transient natural convection in a vertical cylinder containing both a fluid layer overlying a horizontal porous layer saturated with the same fluid and heat-conducting solid shell of finite thickness in conditions of convective heat exchange with an environment has been studied numerically. The Beavers-Joseph empirical boundary condition is considered at the fluid-porous interface with the Darcy model for the porous layer and the Boussinesq approximation for the pure fluid. The governing equations formulated in dimensionless variables, such as the stream function, the vorticity, and the temperature have been solved by a finite difference method. Particular efforts have been focused on the effects of five types of influential factors, such as the Darcy number 10^?5 ≤ Da ≤ 10^?3, the porous layer height ratio 0 ≤ d/L ≤ 1, the solid shell thickness ratio 0.1 ≤ l/L ≤ 0.3, the thermal conductivity ratio 1 ≤ k_1,3 ≤ 20, and the dimensionless time 0 ≤ τ ≤ 1000 on the fluid flow and heat transfer. Comprehensive analysis of an effect of these key parameters on the Nusselt number at the bottom wall, on the average temperature in the cavity, and on the maximum absolute value of the stream function has been conducted.