Wyniki wyszukiwania - Biblioteka Nauki

1

Steady and unsteady boundary layers due to a stretching vertical sheet in a porous medium using Darcy-Brinkman equation model

100%

Ishak A. , Nazar R. , Pop I.

International Journal of Applied Mechanics and Engineering

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2006

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tom Vol. 11, no 3

623-637

EN

The present paper deals with the analysis of steady and unsteady boundary layer flow and heat transfer past a vertical stretching sheet in a viscous fluid-saturated porous medium by using the Darcy-Brinkman equation model. It is assumed that unsteadiness is caused by the impulsive stretching of the sheet and by sudden increase in the surface temperature. The problem is reduced to parabolic partial differential equations, which are solved numerically using the Keller-box method. The small time (initial unsteady flow) as well as the large time (final steady-state flow) solutions are also included in the analysis. It is shown that there is a smooth transition from the small time solution to large time solution, respectively.

2

Free convection boundary layer flow on a horizontal circular cylinder with constant heat flux in a micropolar fluid

100%

Nazar R. , Amin N. , Pop I.

International Journal of Applied Mechanics and Engineering

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2002

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tom Vol. 7, no 2

409-431

EN

Numerical solutions for the steady laminar free convection boundary layer flow over a horizontal circular cylinder subjected to a constant surface heat flux in a micropolar fluid are presented in this paper. The governing boundary layer equations are first transformed into a non-dimensional form. These equations are then transformed into a set of nonsimilar boundary layers, which are solved numerically using a very efficient implicit finite-difference method known as the Keller-box scheme. The obtained solution for the material parameter K=0 (Newtonian fluid) and different values of the Prandtl number Pr are used to compare the accuracy of the present method with that known from the open literature. The results are shown to compare very well. The effects of various values of K on the velocity and temperature fields as well as on the wall temperature and local skin friction coefficient are presented through graphs and tables for Pr=0.72 and 1.

3

Post-stagnation-point boundary layer flow and mixed convection heat transfer over a vertical, linearly stretching sheet

100%

Ishak A. , Nazar R. , Pop I.

Archives of Mechanics

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2008

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tom Vol. 60, nr 4

303-322

EN

A theoretical analysis is made for the steady two-dimensional post-stagnationpoint flow of an incompressible viscous fluid over a stretching vertical sheet in its own plane. The stretching velocity, the free stream velocity and the surface temperature are assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a coupled system of ordinary differential equations, which is then solved numerically by a finite-difference method. Results are presented in terms of the skin friction coefficient and local Nusselt number, along with a selection of velocity and temperature profiles. It was shown that for both cases of a fixed surface (? = 0) and a stretching surface (? = 0), dual solutions exist for the assisting flow (positive values of the buoyancy parameter ?), besides that usually reported in the literature for the opposing flow (? < 0). It was also found that for the assisting flow, a solution exists for all values of ? (> 0), while for the opposing flow, a solution exists only if the magnitude of the buoyancy parameter is small.

4

Mixed convection boundary layer flow about a solid sphere with Newtonian heating

100%

Salleh M. Z. , Nazar R. , Pop I.

Archives of Mechanics

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2010

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tom Vol. 62, nr 4

283-303

EN

In this paper, the steady mixed convection boundary layer flow about a solid sphere, generated by Newtonian heating in which the heat transfer from the surface is proportional to the local surface temperature, is considered. The governing boundary layer equations are first transformed into a system of non-dimensional equations via the non-dimensional variables, and then into non-similar equations before they are solved numerically, using an implicit finite-difference scheme known as the Keller-box method. Numerical solutions are obtained for the skin friction coefficient and the wall temperature, as well as the velocity and temperature profiles with several parameters considered, namely the mixed convection parameter lambda, the Prandtl number Pr and the conjugate parameter gamma.

5

Flow of a micropolar fluid on a continuous moving surface

100%

Ishak A. , Nazar R. , Pop I.

Archives of Mechanics

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2006

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tom Vol. 58, nr 6

529-541

EN

The present paper deals with the analysis of steady boundary layer flow and heat transfer of a micropolar fluid on an isothermal continuously moving plane surface. It is assumed that the microinertia density is variable and not constant, as in many other published papers. Also, the viscous dissipation effect is taken into account. The basic partial differential equations are reduced to a system of nonlinear ordinary differential equations, which is solved numerically using the Keller-box method. Numerical results are obtained for the skin friction coefficient, local Nusselt number, as well as velocity, temperature and microrotation profiles. Results are shown in graphical form and the numerical values for the skin friction coefficient and local Nusselt number are given in the form of tables. The effects of material parameter K, Prandtl number Pr and Eckert number Ec on the flow and heat transfer characteristics are discussed.

6

Salicylic acid-mediated changes in photosynthesis, nutrients content and antioxidant metabolism in two mustard (Brassica juncea L.) cultivars differing in salt tolerance

75%

Syeed S. , Anjum N. A. , Nazar R. , Iqbal N. , Masood A. , Khan N. A.

Acta Physiologiae Plantarum

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2011

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tom 33

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nr 3

EN

Mustard (Brassica juncea L.) cultivars Alankar (salt-tolerant) and PBM16 (salt-sensitive) plants were grown with 50 mM NaCl and were sprayed with 0.1, 0.5, and 1.0 mM salicylic acid (SA) to study the physiological processes determining salt tolerance and to observe the influence of SA application on the alleviation of NaClinduced adverse effects. The content of leaf Na⁺, Cl⁻, H₂O₂, TBARS, and electrolyte leakage and the activity of SOD were higher in PBM16 than Alankar. In contrast, nutrients content, activity of APX and GR, glutathione content, photosynthetic and growth characteristics were higher in Alankar. Treatment of 50 mM NaCl resulted in increase of Na⁺ and Cl⁻, oxidative stress, activity of antioxidant enzymes and glutathione content, while nutrients content, photosynthetic, and growth characteristics decreased in both the cultivars. Application of 0.5 mM SA alleviated the negative effects of 50 mM NaCl maximally, but 1.0 mM SA proved inhibitory. The effect of SA was more conspicuous in Alankar than PBM16. It is concluded that the higher tolerance of Alankar was due to its lower leaf Na⁺ and Cl⁻ content, higher nutrients content, and efficient antioxidant metabolism. The application of 0.5 mM SA substantially alleviated salt-induced adverse effects in Alankar.