RBF solution of MHD stokes flow and MHD flow in a constricted enclosure

This paper presents the radial basis function (RBF) approximation for the numerical solution of Stokes and Navier-Stokes equations in a constricted enclosure under the effect of magnetic field with different orientations. RBFs are used for the approximation of the particular solution which becomes also the approximate solution of the problem satisfying the boundary conditions. Numerical results are obtained for several values of Hartmann number and constriction ratio. As the strength of the horizontally applied magnetic field increases, Stokes flow extends covering the whole pipe. Applied magnetic field in the pipe-axis direction generates the electric potential exhibiting behavior similar to streamlines. When the constriction ratio increases, flow squeezes through the left wall regardless of the direction of the magnetic field.Publisher's Versio

The Effect of Lactic Acid Based Propolis Addition on The Shelf Life of Fresh Strawberry Juice

Anthocyanins, carotenoids, vitamins, flavonoids, aroma volatiles, and phenolics are among the natural antioxidants and other bioactive phytochemicals found in strawberries. Strawberry and strawberry juice is a perishable fruit, and as a result of the loss of antioxidants during storage, its health advantages to humans are diminished. It is now frequently used as strawberry fruit juice. The technique employed in juice processing, as well as the chemicals utilized, may have a negative impact on the nutritional content of the product. In this study, propolis extraction, lactic acid-based propolis extract was added to strawberry juice at varied rates (%0, %0,4, %0,7 ve %1), which has a high solvent effect and is not detrimental to health. The preservation effect of propolis emulsion on strawberry juice was tested in this study for up to 14 days. Strawberry juice was added with lactic acid-based propolis extract, which is non-toxic to humans, at various rates (%0, %0.4, %0.7 and %1). In the samples obtained, pH, total viable, mold-yeast, color, total phenolic substance and sensory analyzes performed. At the end of storage, the lowest pH value was measured as 2.20 in the sample with 1% propolis extract. The mold and yeast levels ranged from 4.867.36 log cfu/mL in the samples. As the concentration of propolis added to the strawberry juice increased, it was determined that the number of mold yeasts in the samples decreased. The sample with 0.7% propolis extract had the lowest total number of organisms on the 14th day of storage, with 2.90 log cfu/mL. It was determined that as the ratio of propolis extract added to strawberry juices increased, there was a decrease in the total number of viable samples. The phenolic content of strawberry juices was determined between 512.85 GAE mg kg(-1) and 2896.19 GAE mg kg-1, and it was determined that the total phenolic content increased as the ratio of propolis extract added to the strawberry juices increased (p<0.05). Strawberry juice with 0,7% propolis solution is prefered as optimum. Propolis can be utilized as a natural preservative in strawberry juice or other fruit juices instead of chemical preservatives, according to the findings

Akışkanlar mekaniği problemlerinin radyal baz fonksiyonu ve karşılıklı sınır elemanları yöntemi ile çözümleri.

In this thesis, the two-dimensional, laminar steady or unsteady flow of a viscous, incompressible, electrically conducting fluid is considered in channels of several geometries under the impact of a uniform magnetic field with different orientations. Magnetohydrodynamic (MHD) flow governed by the hydrodynamic and electromagnetic equations is solved numerically with or without Stokes approximation and with or without magnetic induction due to the large or small values of Reynolds and magnetic Reynolds numbers, respectively. The numerical results of these MHD flow problems are obtained by using the radial basis function (RBF) approximation, the dual reciprocity boundary element method (DRBEM) and the direct interpolation boundary element method (DIBEM). The computational efficiency and easy implementation of RBF approximation is made use of to obtain the solutions of the considered MHD flow problems in terms of all the primitive variables. The MHD Stokes and the MHD incompressible flows subjected to the magnetic field in the pipe-axis direction are also studied including electric potential. The RBF approximation is also imposed to solve the MHD and the MHD Stokes convection flows in cavities. The MHD convection flow affected by both the Lorentz force and the buoyancy force is modeled by the MHD flow equations coupled with the temperature equation including the viscous dissipation term. The numerical results for all MHD flow problems are simulated in terms of streamlines, equivorticity lines, isotherms, pressure and electric potential contours in different geometries for several values of physical parameters. The use of radial basis function approximation is also extended to transient Navier-Stokes, MHD convection flow and full MHD flow equations. Since the explicit Euler method is used for the time discretization, the numerical stability analysis is performed computationally through the spectral radius of the coefficient matrices in the RBF discretized systems for the optimal values of the time increment, relaxation parameters and the non-dimensional physical parameters.  Ph.D. - Doctoral Progra

Radyal Baz Fonksiyonları Yaklaşımı ile Manyetik Akış ve Elektrik Potansiyel Denklemlerinin Çözümü

Bu projede radyal baz fonksiyonları kullanılarak magnetohidrodinamik-Stokes ve elektrik potansiyel denklemlerine nümerik çözüm elde edilecektir. Çözüm, sıvının hızı,vortisitesi, elektrik potansiyeli cinsinden elde edilecek ve simülasyonu yapılacaktır. Değişik radyal baz fonksiyonlarının çözüm hassasiyeti üzerindeki etkileri araştırılacaktır. Stokes akış denklemlerine dış bir manyetik alan tesiri eklendiğinde denklemler modifiye Helmholtz denklemine indirgenecek, sağ taraf fonksiyonunu radyal baz fonksiyonuları ile yaklaştırarak özel çözümler üretilecektir

RBF Solution of Incompressible MHD Convection Flow in a Pipe

The steady convection flow of a viscous, incompressible and electrically conducting fluid is considered in a lid-driven cavity under the effect of a uniform horizontally applied magnetic field. The governing equations are the Navier-Stokes equations of fluid dynamics including buoyancy and Lorentz forces and the energy equation including Joule heating and viscous dissipation. These coupled equations are solved iteratively in terms of velocity components, stream function, vorticity, pressure and temperature by using radial basis function (RBF) approximation. Particular solution which is approximated by RBF to satisfy both differential equation and boundary conditions becomes the solution of the differential equation. The results are given for several values of Hartmann (M), Grashof (Gr) and the Reynolds (Re) numbers to visualize the effects on the solution. An increase in Gr moves the central vortex of the flow trough the center of the cavity emphasizing the movement of the top lid. Re increases the circulation of the fluid throughout the cavity. Heat is also circulated between the adiabatic walls when Gr or Re increases. The effect of increasing M is the boundary layer formation close to the moving lid for the flow and isotherms. The solution is obtained in a considerably low computational cost through the use of RBF approximation