Heat transfer and natural convection of nanofluids in porous media

“…The solution approximation, T h (x), is described following the Moving Least Squares technique [20,22], as the product of a vector of polynomial base, p(x), and a vector of coefficients, a(x).…”

Section: Methodsmentioning

confidence: 99%

“…Thus, when it comes to complex geometries, this method may have advantages over the conventional FDM and FEM ones, or even more sophisticated methods such as the Lattice-Boltzmann method [18]. The results obtained herein are compared with those of ordinary FEM solutions applied to the same physical problem [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Transient thermal conduction with variable conductivity using the Meshless Local Petrov–Galerkin method

Karagiannakis

Bourantas

Kalarakis

et al. 2016

Applied Mathematics and Computation

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a b s t r a c tA numerical solution of the transient heat conduction problem with spatiotemporally variable conductivity in 2D space is obtained using the Meshless Local Petrov-Galerkin (MLPG) method. The approximation of the field variables is performed using Moving Least Squares (MLS) interpolation. The accuracy and the efficiency of the MLPG schemes are investigated through variation of (i) the domain resolution, (ii) the order of the basis functions, (iii) the shape of the integration site around each node, (iv) the conductivity range, and (v) the volumetric heat capacity range. Steady-state boundary conditions of the essential type are assumed. The results are compared with those calculated by a typical Finite Element method. Specific rectangular-type integration sites are introduced during both steady-state and transient MLPG integration, in order to provide complete surface coverage of the domain without overlapping, and the accuracy of the method is demonstrated in all cases studied. Computational efficiency is also investigated with this MLPG method and found to be slower than FE methods during construction stage, but it clearly surpasses that of FEM approaches during the solution stage on a wide parameter range.

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“…In this study the thermal properties of solid matrix and the nanofluid are considered to be identical, resulting in σ = 1 and k e = k nf as this is common practice [6,20].…”

Section: Problem Definition and Governing Equationsmentioning

confidence: 99%

Numerical simulation of convective flow in a non-darcy porous cavity filled with nanofluid

Stajnko¹,

Jecl²,

Ravnik³

2016

Int. J. CMEM

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Suspensions of nanoscale particles and fluids have been recently subject of intense research, since it was proved that they considerably improve heat transfer capabilities of the fluid which can be crucial in several technological processes. Several applications can be found in the field of porous media flow, such as oil recovery systems, thermal and geothermal energy, nuclear reactors cooling. Since nanofluids are a mixture of a solid and fluid phase, in general, the two phase mathematical model would be the most appropriate to use. However, due to very small size of nanoparticles (1-100 nm) can be assumed, that they behave as a water molecule and a single phase model along with empirical correlations for nanofluid properties can be used. In the present study a convective flow through porous cavity fully saturated with nanofluid is analyzed in detail using the single phase mathematical model based on the Navier-Stokes equations taking into account the non-Darcy parameters. The mathematical model is written at a macroscopic level enabling the simulation of the porous media flow. The solutions are obtained with the in house numerical code based on the Boundary Element Method, which was already proved to have some unique advantages when considering fluid flow problems in different configurations. The effects of the presence of different types of nanoparticles as well as the porous matrix were investigated in detail for different values of governing parameters in order to examine the improved heat transfer characteristics of added nanoparticles.

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Heat transfer and natural convection of nanofluids in porous media

Cited by 136 publications

References 22 publications

Effect of the feed and draw solution temperatures on PRO performance: Theoretical and experimental study

Effect of the feed and draw solution temperatures on PRO performance: Theoretical and experimental study

Transient thermal conduction with variable conductivity using the Meshless Local Petrov–Galerkin method

Numerical simulation of convective flow in a non-darcy porous cavity filled with nanofluid

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