Natural convective heat transfer in a fluid saturated variable porosity medium

This paper demonstrates the application of the density-based topology optimisation approach for the design of heat sinks and micropumps based on natural convection effects. The problems are modelled under the assumptions of steady-state laminar flow using the incompressible Navier-Stokes equations coupled to the convection-diffusion equation through the Boussinesq approximation. In order to facilitate topology optimisation, the Brinkman approach is taken to penalise velocities inside the solid domain and the effective thermal conductivity is interpolated in order to accommodate differences in thermal conductivity of the solid and fluid phases. The governing equations are discretised using stabilised finite elements and topology optimisation is performed for two different problems using discrete adjoint sensitivity analysis. The study shows that topology optimisation is a viable approach for designing heat sink geometries cooled by natural convection and micropumps powered by natural convection. Copyright c © 2013 John Wiley & Sons, Ltd.

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Topology optimisation for natural convection problems

Thermal instability in Brinkman porous media with Cattaneo–Christov heat flux

Natural convection of nanofluids in a shallow cavity heated from below

A study of natural convection, in a vertical rectangular cavity filled with a non-Newtonian fluid and subjected to uniform heat flux along the vertical side walls, is carried out numerically by solving the full governing equations. In the limit of a tall enclosure, these equations are considerably reduced by using the parallel flow approximation. Solutions for the flow and temperature fields, and the heat transfer rate, are obtained as functions of the governing parameters. Good agreement is found between the results of the two approaches for a wide range of governing parameters.

Natural Convection in a Vertical Rectangular Cavity Filled with a Non-Newtonian Power Law Fluid and Subjected to a Horizontal Temperature Gradient

The Brinkman model is used to study steady-stale natural convection in a shallow porous cavity with uniform heating and cooling through opposite walls. The horizontal boundaries are considered rigid-rigid, rigid-free, or free-free, and heating is through the bottom or the side wall. An approximate solution is obtained by assuming parallel flow in the core region of the cavity and a numerical solution by solving the complete governing equations. The flow and heat transfer variables are obtained in terms of the Darcy-Rayleigh number R and the Darcy number Da. The critical Darcy-Raleigh number for the onset of convection in a bottom-heated cavity is predicted. The results for a viscous fluid (Da → ∞) and the Darcy porous medium (Da → 0) emerge from the present analysis as limiting cases.

The brinkman model for natural convection in a shallow porous cavity with uniform heat flux

Natural Convection in an Inclined Rectangular Porous Slot: the Brinkman-Extended Darcy Model

The stability and natural convection in a system consisting of a horizontal fluid layer over a layer of porous medium saturated with the same fluid, with heating from below, are considered. The upper surface is either rigid or dynamically free with surface-tension effects allowed for. The solution is obtained using a parallel flow assumption for constant-flux thermal boundary conditions for which the onset of cellular convection corresponds to a vanishingly small wavenumber. The critical Rayleigh number and Nusselt number are found to depend on the depth ratio, the Darcy number, the viscosity ratio, the thermal conductivity ratio, and the Marangoni number. Results are given for a range of values of each of the governing parameters. The results are compared with limiting cases of the problem for standard terrestrial conditions or microgravity, and are found to be in agreement.

Thermal instability and natural convection in a fluid layer over a porous substrate

The mechanism of natural and Marangoni convection in a system with two stratified fluid layers without mass transfer at the interface is investigated. The basis of the analytical solution is an assumption of parallel flow over a large portion of the system. The two cases of heat fluxes through horizontal or vertical opposite walls are considered. It is demonstrated that four different patterns of convection can be observed in the present system. The zone of occurrence of these flow patterns are specified in terms of non-dimensional parameters. Velocity and temperature distributions, stream function and Nusselt number are presented over a wide range of the governing parameters. The results obtained are explained in terms of the basic physical mechanisms that govern these flows showing many interesting aspects of the complex interaction between the buoyant and surface tension mechanisms.

C. H. Wang

Papers

The brinkman model for natural convection in a shallow porous cavity with uniform heat flux

Natural Convection in an Inclined Rectangular Porous Slot: the Brinkman-Extended Darcy Model

Thermal instability and natural convection in a fluid layer over a porous substrate

Analytical investigation of Bénard-Marangoni convection heat transfer in a shallow cavity filled with two immiscible fluids