scholarly journals Combined of magnetic field and thermophoresis particle deposition in free convection boundary layer from a vertical flat plate embedded in a porous medium

2007 ◽  
Vol 11 (1) ◽  
pp. 65-74 ◽  
Author(s):  
Yousof Bakier ◽  
Ahmed Mansour
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Porous Medium ◽  
Flat Plate ◽  
Particle Deposition ◽  
Saturated Porous Medium ◽  
Convection Boundary Layer ◽  
Similarity Equation ◽  
Thermophoresis Particle Deposition ◽  
Vertical Flat Plate

Deals with heat and mass transfer by steady laminar boundary layer flow of Newtonian, viscous fluid over a vertical flat plate embedded in a fluid-saturated porous medium in the presence of thermophoretic and magnetic field. The resulting similarity equation are solved by finite difference marching technique. The nature of variation of particle concentration profile and magnetic field with respect to buoyancy force, Fw, and Prandtl number is found to be similar. Comparisons with previous published work are performed and the results are found to be in excellent agreement. .

Mixed convection boundary layer flow past a vertical flat plate embedded in a non-Darcy porous medium saturated by a nanofluid

2014 ◽  
Vol 24 (5) ◽  
pp. 970-987 ◽  
Author(s):  
Natalia C. Roşca ◽  
Alin V. Roşca ◽  
Teodor Groşan ◽  
Ioan Pop
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Differential Equations ◽  
Mixed Convection ◽  
Flat Plate ◽  
Boundary Layer Flow ◽  
Convection Boundary Layer ◽  
Content Type ◽  
Layer Flow ◽  
Vertical Flat Plate

Purpose – The purpose of this paper is to numerically solve the problem of steady mixed convection boundary layer flow past a vertical flat plate embedded in a fluid-saturated porous medium filled by a nanofluid. The non-Darcy equation model along with the mathematical nanofluid model proposed by Tiwari and Das (2007) has been used. Design/methodology/approach – Using appropriate similarity transformations, the basic partial differential equations are transformed into ordinary differential equations. These equations have been solved numerically for different values of the nanoparticle volume fraction, the mixed convection and the non-Darcy parameters using the bvp4c function from Matlab. A stability analysis has been also performed. Findings – Numerical results are obtained for the reduced skin-friction, heat transfer and for the velocity and temperature profiles. The results indicate that dual solutions exist for the opposing flow case (λ<0). The stability analysis indicates that for the opposing flow case, the lower solution branch is unstable, while the upper solution branch is stable. In addition, it is shown that for a regular fluid (φ=0) a very good agreement exists between the present numerical results and those reported in the open literature. Research limitations/implications – The problem is formulated for three types of nanoparticles, namely, copper (Cu), alumina (Al2O3) and titania (TiO2). However, the paper present results here only for the Cu nanoparticles. The analysis reveals that the boundary layer separates from the plate. Beyond the turning point it is not possible to get the solution based on the boundary-layer approximations. To obtain further solutions, the full basic partial differential equations have to be solved. Practical implications – Nanofluids have many practical applications, for example, the production of nanostructured materials, engineering of complex fluids, for cleaning oil from surfaces due to their excellent wetting and spreading behavior, etc. Social implications – Nanofluids could be applied to almost any disease treatment techniques by reengineering the nanoparticle properties. Originality/value – The present results are original and new for the boundary-layer flow and heat transfer past a vertical flat plate embedded in a porous medium saturated by a nanofluid. Therefore, this study would be important for the researchers working in porous media in order to become familiar with the flow behavior and properties of such nanofluids.

Free Convective Heat Transfer Over a Nonisothermal Body of Arbitrary Shape Embedded in a Fluid-Saturated Porous Medium

1987 ◽  
Vol 109 (1) ◽  
pp. 125-130 ◽  
Author(s):  
A. Nakayama ◽  
H. Koyama
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Flat Plate ◽  
Wall Temperature ◽  
Arbitrary Shape ◽  
Saturated Porous Medium ◽  
Axisymmetric Body ◽  
Two Dimensional ◽  
Vertical Flat Plate

The problem of free convective heat transfer from a nonisothermal two-dimensional or axisymmetric body of arbitrary geometric configuration in a fliud-saturated porous medium was analyzed on the basis of boundary layer approximations. Upon introducing a similarity variable (which also accounts for a possible wall temperature effect on the boundary layer length scale), the governing equations for a nonisothermal body of arbitrary shape can be reduced to an ordinary differential equation which has been previously solved by Cheng and Minkowycz for a vertical flat plate with its wall temperature varying in an exponential manner. Thus, it is found that any two-dimensional or axisymmetric body possesses a corresponding class of surface wall temperature distributions which permit similarity solutions. Furthermore, a more straightforward and yet sufficiently accurate approximate method based on the Ka´rma´n-Pohlhausen integral relation is suggested for a general solution procedure for a Darcian fluid flow over a nonisothermal body of arbitrary shape. For illustrative purposes, computations were carried out on a vertical flat plate, horizontal ellipses, and ellipsoids with different minor-to-major axis ratios.

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