# Numerical simulations of thermal convection under the influence of an inclined magnetic field by using solenoidal bases

2014-11-01
Yarimpabuc, D.
Tarman, Işık Hakan
Yildirim, C.
The effect of an inclined homogeneous magnetic field on thermal convection between rigid plates heated from below under the influence of gravity is numerically simulated in a computational domain with periodic horizontal extent. The numerical technique is based on solenoidal (divergence-free) basis functions satisfying the boundary conditions for both the velocity and the induced magnetic field. Thus, the divergence-free conditions for both velocity and magnetic field are satisfied exactly. The expansion bases for the thermal field are also constructed to satisfy the boundary conditions. The governing partial differential equations are reduced to a system of ordinary differential equations under Galerkin projection and subsequently integrated in time numerically. The projection is performed by using a dual solenoidal bases set such that the pressure term is eliminated in the process. The quasi-steady relationship between the velocity and the induced magnetic field corresponding to the liquid metals or melts is used to generate the solenoidal bases for the magnetic field from those for the velocity field. The technique is validated in the linear case for both oblique and vertical case by reproducing the marginal stability curves for varying Chandrasekhar number. Some numerical simulations are performed for either case in the nonlinear regime for Prandtl numbers Pr=0.05 and Pr=0.1. Copyright (c) 2014 John Wiley & Sons, Ltd.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES

# Suggestions

 Numerical simulation of thermal convection under the influence of a magnetic field by using solenoidal bases Yarımpabuç, Durmuş; Tarman, Işık Hakan; Department of Engineering Sciences (2011) The effect of an imposed magnetic field on the thermal convection between rigid plates heated from below under the influence of gravity is numerically simulated in a computational domain with periodic horizontal extent. The numerical technique is based on solenoidal basis functions satisfying the boundary conditions for both velocity and induced magnetic field. The expansion bases for the thermal field are also constructed to satisfy the boundary conditions. The governing partial differential equations are ...
 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...
 Thermal convection in the presence of a vertical magnetic field Guray, E.; Tarman, H. I. (Springer Science and Business Media LLC, 2007-11-01) The interaction between thermal convection and an external uniform magnetic field in the vertical is numerically simulated within a computational domain of a horizontally periodic convective box between upper and lower rigid plates. The numerical technique is based on a spectral element method developed earlier to simulate natural thermal convection. In this work, it is extended to a magnetoconvection problem. Its main features are the use of rescaled Legendre-Lagrangian polynomial interpolants in expanding...
 Numerical and experimental analysis for comparison of square, cylindrical and plate fin arrays in external flow İnci, Aykut Barış; Bayer, Özgür; Department of Mechanical Engineering (2018) Geometrical optimization of square, cylindrical and plate fins for heat transfer augmentation is numerically performed in the external flow. Heat transfer performance of fins with different profiles are compared with same Reynolds number. The relation between the thermal characteristic of fins and boundary conditions like free-stream velocity and heat input are investigated. Experimental studies are performed using manufacturable fins to validate numerical model. Heat transfer correlations are derived in or...
 Numerical solutions of boundary value problems; applications in ferrohydrodynamics and magnetohydrodynamics Şenel, Pelin; Tezer, Münevver; Department of Mathematics (2017) In this thesis, steady, laminar, fully developed flows in pipes subjected to a point magnetic source or uniform magnetic field are simulated by the dual reciprocity boundary element method (DRBEM). The Navier-Stokes and energy equations are solved in terms of the velocity, pressure and the temperature of the fluid which are all of the original variables of the problem. The missing pressure equation is derived and pressure boundary conditions are generated by a finite difference approximation and the DRBEM c...
Citation Formats
D. Yarimpabuc, I. H. Tarman, and C. Yildirim, “Numerical simulations of thermal convection under the influence of an inclined magnetic field by using solenoidal bases,” MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol. 37, no. 18, pp. 2962–2971, 2014, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/92574.