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Time-periodic thermal boundary effects on porous media saturated with nanofluids : CGLE model for oscillatory mode

Kiran Palle, Manjula Sivaraj H.

Advances in Materials Science

2022

Vol. 22, nr 4(74)

98--116

The stability of nonlinear nanofluid convection is examined using the complex matrix differential operator theory. With the help of finite amplitude analysis, nonlinear convection in a porous medium is investigated that has been saturated with nanofluid and subjected to thermal modulation. The complex Ginzburg-Landau equation (CGLE) is used to determine the finite amplitude convection in order to evaluate heat and mass transfer. The small amplitude of convection is considered to determine heat and mass transfer through the porous medium. Thermal modulation of the system is predicted to change sinusoidally over time, as shown at the boundary. Three distinct modulations IPM, OPM, and LBMOhave been investigated and found that OPM and LBMO cases are used to regulate heat and mass transfer. Further, it is found that modulation frequency (ωf varying from 2 to 70) reduces heat and mass transfer while modulation amplitude (δ1varying from 0.1 to 0.5 ) enhances both.

Local Heaviside weighted MLPG meshless method approach to extended Flamant problem using radial basis functions

Ossowski R.

Studia Geotechnica et Mechanica

2008

Vol. 30, nr 1-2

173-180

The meshless local Petrov-Galerkin (MLPG) method with Heaviside step function as the weighting function is applied to solve the extended Flamant problem. There are two different classes of trial functions considered in the paper: classical radial basis functions (RBF) as extended multiquadrics and compactly supported radial basis functions (CSRBF) as Wu and Wendland functions. The method presented is a truly meshless method based on a set of nodes only. This approach allows direct imposing of essential boundary conditions; moreover, no domain integration is needed and no stiffness matrix assembly is required. The solution of the extended Flamant problem is presented. The performance of RBFs and CSRBFs proposed is compared and the effect of the sizes of local subdomain and interpolation domain is studied. The results obtained show the accuracy and numerical performance of the method.