A spectral Petrov-Galerkin method for thermal convection between rigid plates

2009-09-18
Yıldırım, Cihan
Tarman, Işık Hakan
A numerical approach to the transition in the problem of thermal convection between rigid plates under the influence of gravity is presented. The approach uses solenoidal basis functions that satisfy the continuity equation and the boundary conditions under a Petrov-Galerkin procedure. A numerical experiment on the linear stability of thermal convection is performed to test the formulation and the implementation.
6th International Symposium on Turbulence, Heat and Mass Transfer

Suggestions

A Spectral Solenoidal-Galerkin Method for Rotating Thermal Convection between Rigid Plates
Yıldırım, Cihan; Yarımpabuç, Durmuş; Tarman, Hakan I. (Hindawi Limited, 2013)
The problem of thermal convection between rotating rigid plates under the influence of gravity is treated numerically. The approach uses solenoidal basis functions and their duals which are divergence free. The representation in terms of the solenoidal bases provides ease in the implementation by a reduction in the number of dependent variables and equations. A Galerkin procedure onto the dual solenoidal bases is utilized in order to reduce the governing system of partial differential equations to a system ...
Numerical study of Rayleigh Bènard thermal convection via solenoidal bases
Yıldırım, Cihan; Tarman, Işık Hakan; Department of Engineering Sciences (2011)
Numerical study of transition in the Rayleigh-B\'enard problem of thermal convection between rigid plates heated from below under the influence of gravity with and without rotation is presented. The first numerical approach uses spectral element method with Fourier expansion for horizontal extent and Legendre polynomal for vertical extent for the purpose of generating a database for the subsequent analysis by using Karhunen-Lo\'eve (KL) decomposition. KL decompositions is a statistical tool to decompose the...
A pseudospectral analysis of laminar natural convection and heat transfer between two inclined parallel plates
Kasapoğlu, Serkan; Tarı, İlker; Department of Mechanical Engineering (2005)
Three dimensional laminar natural convection flow of and heat transfer in incompressible air between two inclined parallel plates are analyzed with the Boussinesq approximation by using spectral methods. The plates are assumed to be infinitely long in streamwise and spanwise directions. For these directions, periodic boundary conditions are used and for the normal direction constant wall temperature and no slip boundary conditions are used. Unsteady Navier-Stokes and energy equations are solved using a pseu...
A numerical study on magneto-hydrodynamic mixed convection flow
Bozkaya, Canan (2014-01-01)
This paper, describes a study conducted to numerically investigate the two-dimensional, steady, laminar, magneto-hydrodynamic mixed convection flow and heat transfer characteristics in a lid-driven enclosure beneath an externally applied magnetic field. A solid square block is placed inside the cavity. The governing equations in the form of a stream function-vorticity-temperature formulation are solved numerically using the dual reciprocity boundary element method with constant elements. Treatment of nonlin...
A Numerical approach for the solutions of fluid dynamics problems in the presence of magnetic field
Oğlakkaya, Fatma Sidre; Bozkaya, Canan; Department of Mathematics (2018)
This thesis is conducted to investigate numerically the two-dimensional steady or unsteady, laminar flow of viscous, incompressible and electrically conducting fluids in complex geometries subject to either uniform inclined magnetic field or nodal magnetic sources. Specifically, the hydromagnetic natural/mixed convection of either conventional fluid or water-based nanofluid flow and the heat transfer are considered in irregular enclosures with wavy walls. The equations governing the steady magnetohydrodynam...
Citation Formats
C. Yıldırım and I. H. Tarman, “A spectral Petrov-Galerkin method for thermal convection between rigid plates,” presented at the 6th International Symposium on Turbulence, Heat and Mass Transfer, Rome, ITALY, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/55371.