... the stability of the flow are derived and solved using two prominent numerical methods: the Galerkin method (GM) and the Chebyshev collocation method (CCM). Basis functions and their derivatives are constructed through symbolic integration to enhance computational accuracy. The resulting eigenvalue problem...

... hitherto used. nanofluid Brownian motion thermophoresis natural convection Galerkin method internal heating Recently, there has been a great interest in nanofluids, which are suspensions of solid particles whose size is of order tens or hundreds nanometres. The interest is because...

...-order statistical moment (variance) ⊗ = tensor product In this paper, the Galerkin method was used to construct numerical solutions to the reaction-diffusion equation with uncertain reaction and diffusion coefficients. A stochastic version of the Lax–Milgram lemma was used to state...

... approach is adopted to comprehensively describe thermal characteristics of that new device. With a view to obtaining more practical expressions than accepted before, the Galerkin method based on the variational principle is used to solve governing partial differential equations. The induced tidal...

... for such systems of nonlinear differential equations. 30 10 2010 10 03 2011 10 03 2011 08 07 2011 08 07 2011 confined flow Couette flow finite element analysis Galerkin method heat transfer nonlinear differential equations non-Newtonian flow non-Newtonian fluids Poiseuille...

... change in heat transfer is observed due to aiding solutal buoyancy force for Ri ≤ 1 irrespective of the Reynolds number. 19 08 2009 03 05 2010 13 08 2010 13 08 2010 confined flow convection finite element analysis Galerkin method laminar flow mass transfer Poisson...

.... , 2009 , “ Modeling Heat Transfer in Bi2Te3–Sb2Te3 Nanostructures ,” Int. J. Heat Mass Transfer 0017-9310 , 52 , pp. 860 – 869 . 10.1016/j.ijheatmasstransfer.2008.09.004 Cockburn , B. , Karniadakis , G. E. , and Shu , C. -W. , 2000 , Discontinuous Galerkin Methods: Theory...

.... Application of proper orthogonal decomposition has been suggested by various authors ( 6 7 8 9 10 11 ) for the purpose of model reduction for complex electronic systems. computational fluid dynamics finite volume methods Galerkin method heat transfer matrix decomposition thermal management...

... by the Galerkin method. Accordingly, W , Θ , and Φ are written as 22 W = ∑ i = 1 n A i W i ( z ) ,     Θ ( z ) = ∑ i = 1 n C i Θ i ( z ) ,     Φ ( z ) = ∑ i = 1 n D i Φ i ( z ) where A i...

... time electron-phonon interactions finite element analysis Galerkin method gold laser beam effects melting metallic thin films Runge-Kutta methods specific heat The physics of short-pulse laser heating of metallic films is very complex and has been the subject of many investigations ( 1...

... as a decrease in Biot number are to destabilize the system. Further, the nonlinearity of fluid magnetization is found to have no effect on the onset of ferroconvection in the absence of the Biot number. convection ferromagnetism flow instability Galerkin method magnetic fluids magnetisation...

...-step hybrid technique, which combines perturbation methods based on the parameter ρ = Δ t ∕ ( Δ x ) 2 with the Galerkin method, provides a systematic way to develop new finite difference methods, referred to as hybrid equations. The main contributions of this paper include the (1) recovery of classical...

... eigenvalues and eigenfunctions Galerkin method heat transfer interpolation splines (mathematics) proper orthogonal decomposition fast and efficient method numerical simulation of fluid flow and heat transfer Many important applications in science and engineering need robust online control...

... . Maji , P. K. , and Biswas , G. , 1999 , “ Analysis of Flow in the Spiral Casing Using a Streamline Upwind Petrov Galerkin Method ,” Int. J. Numer. Methods Eng. 0029-5981 10.1002/(SICI)1097-0207(19990520)45:2<147::AID-NME581>3.0.CO;2-G 45 , pp. 147 – 174 . Prakash , K...

... of the fluid layer consists of a steady part and a time-dependent oscillatory part. Only infinitesimal disturbances are considered. The combined effect of permeability, rotation, vertical magnetic field, and temperature modulation has been investigated using Galerkin’s method and Floquet theory. The value...

..., the interfacial flows are largely driven by the inertia forces of the outer layer fluid. 03 12 2004 30 11 2005 convection drops two-phase flow electrohydrodynamics heat conduction surface tension stratified flow Galerkin method finite element analysis galerkin finite element...

... flaw detection thermal diffusion Galerkin method finite element analysis Thermal imaging has become an important nondestructive evaluation method in the last decade. The development of highly sensitive infrared imaging systems has resulted in widely utilized thermal inspection systems...

... solving Eq. ( 1 ), ( 2 ), and ( 3 ). The implicit dependence of velocity and pressure is decoupled by a fractional-step method, which is second-order accuracy in time. The Galerkin method is used to construct the weighted residual formulation...

... , “ An Efficient Method of Solving the Navier-Stokes Equations for Flow Control ,” Int. J. Numer. Methods Eng. , 41 , pp. 1131 – 1151 . Park , H. M. , Chung , O. Y. , and Lee , J. H. , 1999 , “ On the Solution of Inverse Heat Transfer Problem Using the Karhunen-Loe`ve Galerkin Method ,” Int...

... of magnetization. A first order Galerkin method is performed to reduce the governing linear system to the Mathieu equation with damping term. Therefore, the Floquet theory is used to determine the convective threshold for the free-free and rigid-rigid cases. With an appropriate choice of the ratio of the magnetic...