# DRBEM Solution for Unsteady Natural Convection Flow in Primitive Variables with Fractional Step Time Advancement

2012-07-14
Sariaydin, A.
Tezer, Münevver
In this study, two-dimensional, transient flow of an incompressible, laminar, viscous fluid in a cavity is considered with the occurance of heat flux (temperature is not constant). The governing equations which are continuity, momentum and energy equations, define natural convection in differentially heated cavities in terms of primitive variables (velocities, temperature, and pressure). The no-slip condition for the velocity is imposed on the cavity walls. Left and right walls are heated and cooled, respectively, and top and bottom walls are adiabatic. The dual reciprocity boundary element method (DRBEM) is employed for solving natural convection flow equations utilizing fractional step for the time derivatives. This uncouples velocities from the pressure. Then, the predicted velocity and the pseudo-pressure equations together with the energy equation are all solved by using DRBEM with constant elements. DRBEM transforms directly the differential equations to the boundary integral equations, and thus, only the boundary of the problem has to be discretized. This saves considerable computational work. Velocities and the pressure are obtained iteratively in the time direction with a predictor-corrector scheme. Temperature is also obtained in the iteration procedure by using relaxation parameter between consecutive time levels. In the iterative procedure the nonlinear convective terms are approximated explicitly from the two previous steps. The present numerical procedure gives quite accurate results for Rayleigh number values up to 10(4). It has the advantage of treating directly the primitive unknowns and obtaining the pressure field also. Since the time derivatives are discretized at the beginning of the procedure, the solution is obtained iteratively at all transient levels, and also at steady-state with considerably large time increment compared to other explicit time integration procedures. The proposed numerical scheme is also computationally cheap since DRBEM discretizes only the boundary of the region, resulting with small sized systems, compared to other domain-type numerical methods.

# Suggestions

 DRBEM simulation on mixed convection with hydromagnetic effect Bozkaya, Canan (2014-09-25) The steady and laminar mixed convection flow of a viscous, incompressible, and electrically conducting fluid under the effect of an inclined magnetic field is numerically investigated. Specifically, the two-dimensional flow in a lid-driven cavity with a linearly heated wall is considered. The dual reciprocity boundary element method is used for solving the coupled nonlinear differential equations in terms of stream function, vorticity, and temperature. The study focuses on the effects of the physical parame...
 DRBEM solution of biomagnetic fluid flow and heat transfer in cavities-CMMSE2016 Senel, P.; Tezer, Münevver (2017-08-01) In this paper, we investigate the fully developed, laminar, forced convection flow of an electrically non-conducting, viscous, biomagnetic fluid in the 2D cross-section (cavity) of a long impermeable pipe. The fluid is under the influence of a point magnetic source placed below the cavity. The dual reciprocity boundary element method (DRBEM) with constant and linear elements is used for solving the governing equations resulting from the Navier-Stokes and energy equations together with magnetization and buoy...
 DRBEM solution of natural convective heat transfer with a non-Darcy model in a porous medium Pekmen, B.; Tezer, Münevver (2015-03-01) This study presents the dual reciprocity boundary element (DRBEM) solution of Brinkman-Forchheimer-extended Darcy model in a porous medium containing an incompressible, viscous fluid. The governing dimensionless equations are solved in terms of stream function, vorticity and temperature. The problem geometry is a unit square cavity with either partially heated top and bottom walls or hot steps at the middle of these walls. DRBEM provides one to obtain the expected behavior of the flow in considerably small ...
 DRBEM solution to ferrofluid flow and heat transfer in semi annulus enclosure in the presence of magnetic field Oğlakkaya, Fatma Sidre; Bozkaya, Canan (null; 2016-07-11) In this work, ferrofluid flow and heat transfer in a semicircular annulus enclosure filled with Fe3O4- water nanaofluid is studied in the presence of an externally applied magnetic field. The inner and outer circular walls are maintained at constant temperature and two straight boundaries at the bottom are considered adiabatic. The governing equations which are consistent with the principles of ferrohydrodynamics (FHD) and magnetohydrodynamics (MHD) are discretized by using the dual reciprocity boundary ele...
 DRBEM SOLUTION OF THE NATURAL CONVECTIVE FLOW OF MICROPOLAR FLUIDS Gumgum, S.; Tezer, Münevver (Informa UK Limited, 2010-01-01) The main purpose of this article is to present the use of the dual reciprocity boundary element method (DRBEM) in the analysis of the unsteady natural convective flow of micropolar fluids in a differentially heated rectangular cavity. The finite-difference method (FDM) is used for time discretization. All the convective terms and vorticity boundary condition are evaluated in terms of DRBEM coordinate matrix. Solutions are obtained for several values of microstructure parameter (k), Rayleigh number (Ra), and...
Citation Formats
A. Sariaydin and M. Tezer, “DRBEM Solution for Unsteady Natural Convection Flow in Primitive Variables with Fractional Step Time Advancement,” 2012, vol. 1493, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39389.