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Paper presents the numeral results of transient natural convection in a partially porous enclosure with a heat-conducting and heat-generating element. The horizontal walls of the cavity are adiabatic, while the vertical ones are isothermal and have low temperature. A mathematical model formulated in dimensionless variables such as vorticity, stream function and temperature have been solved by means of the finite difference method. The governing parameters are the porous layer thickness and dimensionless time. The effects of these parameters are shown using streamlines, isotherms and average temperature of the heat-conducting element. The results demonstrate an opportunity to intensify the passive cooling system using the porous layer.

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. [ABSTRACT FROM AUTHOR]

Laminar natural convection in a square cavity having two centered adherent porous blocks filled with an alumina/water nanofluid under the effect of horizontal temperature gradient is studied numerically. Each porous block has the unique values of the porosity and permeability. Water-based nanofluids with alumina nanoparticles are chosen for investigation. The control characteristics of this study are the Darcy number of the first porous block ( $10^{-7}\le Da_{1}\le 10^{-3}$ ), the dimensionless porous blocks size ( $0.1\le\delta\le 0.4$ ) and nanoparticles volume fraction ( $0\le\phi\le 0.04$ ). The developed computational code has been validated comprehensively using the grid independency test and experimental data of other authors. The obtained results revealed the heat transfer enhancement at the hot wall with the Darcy number, while a growth of the porous layers size reduces the heat transfer rate at this hot wall. The behavior of the average Nusselt number at the right cold wall is opposite. [ABSTRACT FROM AUTHOR]

Thermal convection is one of the main mechanisms that are implemented in different cooling systems. Most often this phenomenon occurs in such practical areas as microelectronics, instrumentation and building construction. In this article, the numerical simulation of thermogravitational convection of medium having dependent viscosity inside closed enclosure with isothermal heating/cooling from vertical walls has been conducted. Other borders of the chamber are heat insulated. The control relations have been written employing non-dimensional vector potential functions, vorticity vector and temperature. The finite difference procedures are applied for solving of the considered differential equations. Obtained outcomes have been compared with numerical data for thermal convection within a differentially heated square cabinet. An influence of third coordinate, Rayleigh number and viscosity variation parameter on thermal distribution and flow structures combined with mean Nusselt number has been demonstrated. Obtained outcomes have shown that for the considered 3D problem an evaluation of the mean Nusselt number can be performed by employing 2D data when the aspect ratio is greater than or equal to unity. [ABSTRACT FROM AUTHOR]

Convective heat transfer is a major phenomenon in different technical and natural systems. This process can be found in enclosures under the different temperature distributions at bounded walls. In this research, the thermogravitation energy transport of a non-constant viscosity medium inside a 3D region under the non-uniform or uniform temperature profile at one of the vertical walls is addressed. The opposite border is at a low constant temperature, and the remaining borders are well insulated. The control equations with the border restrictions are reduced into a non-dimensional form and then integrated by the finite difference procedures. The control characteristics are the Rayleigh number and viscosity changeable magnitude. The impacts of these characteristics on the energy transference and flow structures are studied. [ABSTRACT FROM AUTHOR]

Cooling of heat-generating elements is a challenging problem in engineering. In this article, the transient free convection of a temperature-dependent viscosity liquid inside the porous cavity with copper radiator and the heat-generating element is studied using mathematical modeling techniques. The vertical and top walls of the chamber are kept at low constant temperature, while the bottom wall is kept adiabatic. The working fluid is a heat-conducting liquid with temperature-dependent viscosity. A mathematical model is developed based on dimensionless stream function, vorticity, and temperature variables. The governing properties are the variable viscosity, geometric parameters of the radiator, and size of thermally insulated strip on vertical surfaces of the cavity. The effect of these parameters on the energy transport and circulation patterns are analyzed numerically. Based on the numerical results obtained, recommendations are given on the optimal values of the governing parameters for the effective operation of the cooling system. It is shown that the optimal number of radiator fins for the cooling system configuration under consideration is 3. In addition, the thermal insulation of the vertical walls and the increased thickness of the radiator fins have a negative effect on the operation of the cooling system. [ABSTRACT FROM AUTHOR]