Mixed Convection in a Square Cavity Filled with Porous Medium with Bottom Wall Periodic Boundary Condition

Transient mixed convection heat transfer in a confined porous medium heated at periodic sinusoidal heat flux is investigated numerically in the present paper. The Poisson-type pressure equation, resulted from the substituting of the momentum Darcy equation in the continuity equation, was discretized by using finite volume technique. The energy equation was solved by a fully implicit control volume-based finite difference formulation for the diffusion terms with the use of the quadratic upstream interpolation for convective kinetics scheme to discretize the convective terms and the temperature values at the control volume faces. The numerical study covers a range of the hydrostatic  pressure sinusoidal  amplitude  range and  time  period  values  of . Numerical results show that the pressure contours lines are influenced by hydrostatic head variation and not affected with the sinusoidal amplitude and time period variation. It is found that the average Nusselt number decreases with time and pressure head increasing and decreases periodically with time and amplitude increasing. The time averaged Nusselt number decreases with imposed sinusoidal amplitude and cycle time period increasing

Double diffusion in a rectangular duct using metals or oxides suspended in a viscous fluid

In this study, double diffusive free convection of nanofluid within a confined rectangular duct is investigated numerically. The momentum and energy equations are placed in the form of difference equations and solved numerically. The left wall conditions for the concentration and temperature are lesser than those of the right wall and the upper and lower walls are insulated. Different nanofluids are considered such as mixtures with copper, diamond, silicon oxide and titanium oxide, suspended in water. Brinkman and Maxwell models are used to characterize the nanofluid. Tiwari and Das model is opted to define the nanofluid behavior. The simulations are conducted using different nanoparticles, thermal Grashof number 1 ≤ GrT ≤ 20, solute Grashof number 1 ≤ GrC ≤ 15, solid volume fraction 0 ≤ Φ ≤ 0.05, Dufour number 0 ≤ Df ≤ 1, Brinkman number 0 ≤ Br ≤ 2, and Soret number 0 ≤ Sr ≤ 5. Additionally, behavior of volumetric flow strength, skin friction, heat transport intensity and Sherwood number is also examined. The thermal Grashof number, Brinkman number, Dufour, Soret and Schmidt parameters accelerate the velocity and temperature and dwindle the concentration whereas the reversal effect was obtained for the solid volume fraction. The concentration Grashof number diminishes the velocity and temperature and intensifies the concentration. The silver nanoparticles produce the highest velocity whereas diamond nanoparticles cause the lowest velocity and temperature. The maximum temperature is attained with silicon oxide

MHD natural convection in an inclined cavity filled with a fluid saturated porous medium with heat source in the solid phase

A numerical investigation of unsteady magnetohydrodynamic free convection in an inclined square cavity filled with a fluid-saturated porous medium and with internal heat generation has been performed. A uniform magnetic field inclined with the same angle of the inclination of the cavity is applied. The governing equations are formulated and solved by a direct explicit finite-difference method subject to appropriate initial and boundary conditions. Two cases were considered, the first case when all the cavity walls are cooled and the second case when the cavity vertical walls are kept adiabatic. A parametric study illustrating the influence of the Hartmann number, Rayliegh number, the inclination angle of the cavity and the dimensionless time parameter on the flow and heat transfer characteristics such as the streamlines, isotherms and the average Nusselt number is performed. The velocity components at mid section of the cavity as well as the temperature profiles are reported graphically. The values of average Nusselt number for various parametric conditions are presented in tabular form

Conjugate Effect of Joule Heating and Unsteady MHD Natural Convection in a Differentially Heated Skewed Porous Cavity Saturated by Cu-water Nanofluid

Conjugate effect of Joule heating and Lorentz force in a differentially skewed porous lid-driven cavity saturated by Cu-water nanofluid have been examined numerically. A coordinate transformation is utilized to transform the physical domain to the computational domain in an orthogonal coordinate. The Darcy-Brinkman-Forchheimer model with Boussinesq approximation is adopted and the developed mathematical model is solved by finite volume method based on SIMPLE algorithm. The influence of porous medium permeability (Darcy number), Joule heating (Eckert number), nanoparticle volume fraction, as well as inclination angle of skewed cavity on fluid flow and heat transfer characteristics are studied. The entropy generation and Bejan number also evaluated to examine thermodynamic optimization of the MHD mixed convection in porous media. The results have been presented in terms of streamlines, average Nusselt number, entropy generation, and Bejan number for a wide range of key parameters

Simulation of natural convection heat transfer in a 2-D trapezoidal enclosure

Natural convection within trapezoidal enclosures finds significant practical applications. The natural convection flows play a prominent role in the transport of energy in energy-related applications, in case of proper design enclosures to achieve higher heat transfer rates. In the present study, a two-dimensional cavity with adiabatic right side wall is studied. The left side vertical wall is maintained at the constant hot temperature and the top slat wall is maintained at cold temperature. The dimensionless governing partial differential equations for vorticity-stream function are solved using the finite difference method with incremental time steps. The parametric study involves a wide range of Rayleigh number, Ra, 10(3)<ra<10(5) and Prandtl number (Pr=0.025, 0.71 and 10). The fluid flow within the enclosure is formed with different shapes for different Pr values. The flow rate is increased by enhancing the Rayleigh number (Ra=10(4)). The numerical results are validated with previous results. The governing parameters in the present article, namely Rayleigh number and Prandtl number on flow patterns, isotherms as well as local Nusselt number are reported

Free convection in a triangular cavity filled with a porous medium saturated by a nanofluid: Buongiornos mathematical model

Purpos

Simulation of steady mixed convection in a lid-driven cavity filled with newtonian fluid by finite volume method

The steady mixed convection flow in a lid-driven cavity was simulated. The cavity was filled with a Newtonian fluid, both vertical walls are adiabatic, while the horizontal walls were either fixed cold and uniformly/oscillatory heated. Firstly, the effect of internal heat generation or absorption on the fluid flow and heat transfer behaviours was studied. The moving upper wall was uniformly heated while the bottom wall was kept cold. The effect of magnetic field on fluid flow and heat transfer was analysed in the second problem. An inclined magnetic field was considered in the third problem. In the fourth problem, the flow inside an inclined cavity was simulated, where the top wall was subjected to an heated oscillating temperature. Finally, the mixed convection within an inclined cavity with the presence of an inclined magnetic field was studied. The dimensionless governing equations were formulated by using appropriate reference variables. These equations were solved using the finite volume method. The convection-diffusion terms were discretized using the power law scheme while the pressure and velocity components were coupled using the SIMPLE algorithms. The resultant matrices were then solved iteratively using the Tri- Diagonal Matrix Algorithm coded in FORTRAN90. The present solutions obtained were then compared with those of previous studies and a good agreement was found. The numerical results were presented in the forms of isotherm and streamline. It was found that the heat transfer rate in an inclined cavity increased mildly for both forced convection dominated and mixed convection dominated regimes. However, for natural convection dominated regime, the heat transfer rate decreased when the inclination angle was 30◦ and increased when the inclination angles reached 60◦. The presence of external forces would affect the local heat transfer and fluid flow behaviours significantly

Heat transfer in cavities: configurative systematic review

No abstract available