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

Natural convection for hot materials confined within two entrapped porous trapezoidal cavities

Bitişik iki trapez ortamda akış ve ısı transfernin analizi sayısal olarak yapılmıştır. Geometrik oran, iletim oranı ve farklı Rayleigh sayılarında enerji analizi yapılmıştır.This paper analyzes the detailed heat transfer and fluid flow within two porous trapezoidal cavities involving cold inclined walls and hot horizontal walls. Flow patterns and temperature distribution were obtained by solving numerically the governing equations, using Darcy's law. Results are presented for different values of the governing parameters, such as Darcy-modified Rayleigh number, aspect ratio of two entrapped trapezoidal cavities and thermal conductivity ratio between the middle horizontal wall and fluid medium. Heat transfer rates are estimated in terms of local and mean Nusselt numbers. Local Nusselt numbers with spatial distribution exhibit monotonic trend irrespective of all Rayleigh numbers for the upper trapezoidal whereas wavy distribution of local Nusselt number occur for the lower trapezoidal

Natural convection in divided trapezoidal cavities filled with fluid saturated porous media

Bölünmüş trapez kapalı ortamda akış ve ısı transferinin analizi yapılmıştır. Uniform olmayan sınır şartlarında sabit akım ve eş sıcaklık eğrileri elde edilmiştir. Gözenekli ortam şartlarında farklı Rayleigh sayılarında Nusselt sayıları hesaplanmıştır.A numerical work was performed to determine the heat transfer and fluid flow due to forces in divided trapezoidal enclosures filled with fluid saturated porous media. In the present investigation, bottom wall was non-uniformly heated while two vertical walls were insulated and the top wall was maintained at constant cold temperature. The divider had constant thermal conductivity. Flow patterns and temperature distribution were obtained by solving numerically the governing equations, using Darcy's law. Results are presented for different values of the governing parameters, such as Rayleigh number for a porous medium, location of the partition, thickness of the partition and thermal conductivity ratio between solid and fluid media. It was observed that the conduction mode of heat transfer became dominant inside the cavity for higher thickness of the partition, low Rayleigh numbers, and low thermal conductivity ratio

Numerical simulation and energy flux vector visualization of radiative-convection heat transfer in a porous triangular enclosure

A detailed theoretical examination laminar natural convection heat flow in a triangular porous cavity with significant radiative heat transfer and porosity variation is presented. Twodimensional laminar incompressible flow is considered with the left slant and right walls are low and high temperature respectively, and the remaining (top) wall prescribed as adiabatic. The Darcy-Brinkman isotropic model is utilized, and the coupled governing equations are solved by a numerical method utilizing finite differences. Visualization of isotherms and streamlines is achieved with the method of Energy Flux Vectors (EFVs). The impacts of the different model parameters (Rayleigh number Ra, Darcy number-Da, porosity-E and radiation parameter-Rd) on the thermo fluid characteristics are studied in detail. The computations show that convective heat transfer is enhanced with greater Darcy parameter (permeability) which also leads to intensification in the density of energy flux vector patterns. The flow is accelerated with increasing buoyancy effect (Rayleigh number) and temperatures are also increased with greater radiative flux. Average Nusselt number is decreased with higher porosity. The simulations are relevant to hybrid porous media solar collectors

Numerical simulation and energy flux vector visualization of radiative-convection heat transfer in a porous triangular enclosure

A detailed theoretical examination laminar natural convection heat flow in a triangular porous cavity with significant radiative heat transfer and porosity variation is presented. Twodimensional laminar incompressible flow is considered with the left slant and right walls are low and high temperature respectively, and the remaining (top) wall prescribed as adiabatic. The Darcy-Brinkman isotropic model is utilized, and the coupled governing equations are solved by a numerical method utilizing finite differences. Visualization of isotherms and streamlines is achieved with the method of Energy Flux Vectors (EFVs). The impacts of the different model parameters (Rayleigh number Ra, Darcy number-Da, porosity-E and radiation parameter-Rd) on the thermo fluid characteristics are studied in detail. The computations show that convective heat transfer is enhanced with greater Darcy parameter (permeability) which also leads to intensification in the density of energy flux vector patterns. The flow is accelerated with increasing buoyancy effect (Rayleigh number) and temperatures are also increased with greater radiative flux. Average Nusselt number is decreased with higher porosity. The simulations are relevant to hybrid porous media solar collectors

Numerical investigation of steady state laminar natural convection of power-law fluids in side-cooled trapezoidal enclosures heated from the bottom

Laminar, steady-state, natural convection of power-law fluids in 2-D trapezoidal enclosures with a heated bottom wall, adiabatic top wall and cooled inclined sidewalls has been analyzed for the first time based on numerical simulations for a range of different values of nominal Rayleigh number (i.e. (Formula presented.)), power-law index (i.e. (Formula presented.)), nominal Prandtl number (i.e. (Formula presented.)) and sidewall inclination angle (i.e. (Formula presented.)). It has been found that the mean Nusselt number (Formula presented.) increases with increasing nominal Rayleigh number (Formula presented.) (up to a 187% increase for (Formula presented.) and up to 2.3% increase for (Formula presented.) between (Formula presented.) and (Formula presented.)) and decreasing power-law index (Formula presented.) (up to a 4.1% increase for (Formula presented.) and up to 193% increase for (Formula presented.) between (Formula presented.) and 1.8) due to the strengthening of advective transport. Moreover, an increase in the sidewall inclination angle (Formula presented.) leads to a decrease in (Formula presented.) (approximately 44% decrease for (Formula presented.) across values of (Formula presented.) and up to 33% decrease for (Formula presented.) across values of (Formula presented.)) due to an increase in the area for heat loss from the cavity. It has been found that (Formula presented.) does not vary significantly with the values of (Formula presented.) considered in the current study. Furthermore, a new correlation for the mean Nusselt number (Formula presented.) in this configuration has been identified which provides adequate approximation of the corresponding values obtained from the simulations

RPIM Meshless method for Numerical Solution of Natural Convection in Porous Square Cavity

This paper proposed meshless Radial Point Interpolation Meshless Methods (RPIM) method for numerical solution of natural convection in Darcy porous square cavity. It is assumed that Boussinesq approximation is valid to characteristic the buoyancy effect as the driving force of the fluid flow. The Galerkin global weak form is used to discretize the system equations. The multiquadratic radial basis function (RBF) is chosen as the shape and test function. Comparing the numerical results obtained using the proposed method with those obtained using the conventional methods shows very good agreement