MAGNETOHİDRODİNAMİK KANAL AKIŞLARININ KARŞILIKLI SINIR ELEMANLARI METODU İLE ÇÖZÜMÜ

In the thesis, four different MHD duct flow problems are solved by using the Dual Reciprocity Boundary Element Method (DRBEM) with the suitable boundary conditions according to the physics of the problem. The two-dimensional, steady or unsteady, fully-developed MHD flow of a viscous, incompressible and electrically conducting fluid is considered in a long pipe of rectangular cross-section (duct) under the effect of an externally applied magnetic field which is either uniform or time-dependent or axially changing. The inductionless MHD flow with temperature dependent viscosity and heat transfer is the first considered problem. In this problem, the induced magnetic field is neglected due to the small magnetic Reynolds number assumption. Secondly, the MHD duct flow under a time-varied external magnetic field is studied. Then, we turn our concern to MHD flow problems under an axial-dependent magnetic field varying in the streamwise direction (pipe-axis direction) in the third and the fourth problems. Specifically, the inductionless MHD flow with electric potential is considered under the effect of the axially-changing magnetic field as the third problem. Adding the induced magnetic field to the velocity and electric potential equations as a triple is the last MHD flow problem considered in the thesis. The parametrix BEM implementation is also presented for the solution of the variable coefficient convection-diffusion type equations. The influence of the magnetic fields on the MHD flows is investigated and simulated in terms of the velocity, temperature, induced magnetic field and electric potential contours for several values of physical parameters.Bu tezde, dört farklı Magnetohidrodinamik (MHD) kanal akış problemi, problemin fiziğine göre uygun sınır koşulları ile birlikte karşılıklı sınır elemanları metodu (DRBEM) kullanılarak çözülmüştür. Viskoz, sıkıştırılamaz ve elektrik ileten sıvının dikdörtgen kesitli bir kanal içerisindeki iki boyutlu, zamana bağlı veya zamandan bağımsız tam gelişmiş akışı dışarıdan uygulanan bir manyetik alan etkisinde incelenmiştir. Akışı etkileyen manyetik alan ya tek düzedir ya zamana bağlıdır ya da eksenel olarak değişmektedir. Ele alınan ilk problem, sıcaklığa bağlı viskoziteye ve ısı transferine sahip indüksiyonsuz MHD akışıdır. Bu problemde, indüklenen manyetik alan küçük manyetik Reynolds sayısı varsayımından dolayı ihmal edilmiştir. İkinci problem olarak, dışarıdan uygulanan ve zamana bağlı manyetik alan etkisindeki MHD akış çalışılmıştır. Daha sonra ise, üçüncü ve dördüncü problem olarak akım yönündeki eksen boyunca değişen bir manyetik alan etkisindeki MHD akış problemleri çözülmüştür. Üçüncü problemdeki MHD akışı elektrik potansiyeline sahip fakat indüksiyonsuz bir akıştır. Dördüncü problemde ise üçüncü problemdeki MHD akışa indüklenen manyetik alan eklenerek problem denklemleri hız, elektrik potansiyel ve indüklenen manyetik alan olarak üçlü çözülmüştür. Değişken katsayılı konveksiyon-difüzyon tipi denklemlerin çözümü için parametre sınır elemanı metodu (parametrix BEM) da kullanılmıştır. Uygulanan manyetik alanların MHD akışlarına etkisi, çeşitli fiziksel problem parametre değerleri için hız, sıcaklık, indüklenen manyetik alan ve elektrik potansiyeli açısından incelenmiş ve simülasyonları yapılmıştır.Ph.D. - Doctoral Progra

DRBEM Solution of MHD flow in a rectangular duct with time-varied external magnetic field

This paper investigates the flow behavior of a viscous, incompressible and electrically conducting fluid in a long channel subjected to a time-varied oblique magnetic field B-0(t) = B(0)f(t). The time-dependent MHD equations are solved by using the dual reciprocity boundary element method (DRBEM). The transient level velocity and induced magnetic field profiles are presented for moderate Hartmann number values, several direction of applied magnetic field and for several functions f(t) as polynomial, exponential, trigonometric, impulse and step functions. It is observed that, when f(t) is a polynomial or exponential function, the velocity magnitude increases up to a certain time level where the flow shows an elliptical elongation and then starts to decrease for all values of Hartmann numbers. For the trigonometric function f(t), the flow repeats its behavior with a period. An impulse function changes flow behavior with an elongation at the level where the impulse is applied to the magnetic field. Then, it behaves as if a uniform magnetic field is applied. Having a step function f(t), the behavior of the flow shows both impulse and polynomial functions features. This study shows that time-varied magnetic field changes the flow behavior significantly at all the transient levels

The application of BEM to MHD flow and heat transfer in a rectangular duct with temperature dependent viscosity

The steady, laminar, fully developed MHD flow of an incompressible, electrically conducting fluid with temperature dependent viscosity is studied in a rectangular duct together with its heat transfer. Although the induced magnetic field is neglected due to the small Reynolds number, the Hall effect, viscous and Joule dissipations are taken into consideration. The momentum equation for the pipe-axis velocity and the energy equation are solved iteratively. Firstly, the momentum equation is solved by using the boundary element method (BEM) with a parametrix (Levi function) since the diffusion term contains variable viscosity parameter depending on the temperature exponentially. Then, the energy equation is solved by using the dual reciprocity boundary element method (DRBEM). The temperature and the velocity behaviours are examined for several values of Hartmann number 0 ≤ Ha ≤ 10, dimensionless viscosity parameter B = 0,1,2, Brinkmann number Br = 0,1,2 and the Hall parameter m = 0,3,8. As Ha is increasing, the velocity magnitude drops which is a well known property of the MHD duct flow. Increasing B reduces both the flow and the temperature magnitudes whereas the increase in the Hall parameter accelerates the flow and increases the fluid temperature