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The document discusses the dimensional and dimensionless momentum equations presented in a paper by Nawaz et al. The equations describe fluid flows in boundary layers. The document highlights the differences between the dimensional equation and the dimensionless equations, particularly in terms of the time derivative. It points out that the fractional parameter is absent in the dimensional equation, suggesting that the two terms are not compatible. The given text discusses the compatibility between the dimensional and dimensionless equations for fluid flow. It also identifies errors in equations presented in a study by Nawaz et al., including terms with different units and incorrect values of alpha. The authors of the study declare no conflicts of interest. [Extracted from the article]

The flow induced by a sphere rotating inside an incompressible, non-Newtonian, Carreau fluid has been investigated numerically. The rotating sphere is enclosed in a concentric cubic box with solid boundaries. The fluid power-law index varied between 0.2 and 2 thereby covering both shear-thinning and shear-thickening fluids, the Reynolds number varied between 0.01 and 1000 and the Carreau number varied between 1 and 1000. The torque applied on the sphere has been calculated and is presented in tables and figures. It was found that at low Reynolds numbers the torque is independent of the Reynolds number and increases with increasing the power-law index. As the Carreau number increases the torque decreases in shear-thinning fluids and increases in shear-thickening fluids. In all cases, four vortices appear at the vertical plane passing through the sphere centre. [ABSTRACT FROM AUTHOR]

Some errors exist in the above paper. [ABSTRACT FROM AUTHOR]

Some errors exist in the above paper. [ABSTRACT FROM AUTHOR]

The above corrigendum is not correct. [ABSTRACT FROM AUTHOR]

The flow of a non-Newtonian, power-law fluid directed either tangentially or normally to a flat plate of finite length and infinite width (two-dimensional flow) is considered. The problem is investigated numerically using the code ANSYS FLUENT. This problem has been investigated in the past but only for shear-thinning fluids ( n < 1). We extend the investigation for the case of shear-thinning, Newtonian and shear-thickening fluids, covering a wide range of Reynolds numbers (from very low to very high). For low Reynolds numbers and low power-law index ( n < 0.6) the drag coefficient obeys the relationship c = A/Re, both for tangential and normal flow. Equations for the quantity A have been derived as functions of the power-law index. For normal flow, the drag coefficient tends to become independent of the power-law index, both for shear-thinning and shear-thickening fluids at high Reynolds numbers. [ABSTRACT FROM AUTHOR]

In a previous paper (Pantokratoras and Magyari, 2009), the Electro-Magnetohydro dynamic (EMHD) free convection flow of a weakly conducting fluid from an electromagnetic actuator was considered. In the present note, we study the cases where the Riga-plate either moves with constant velocity (Sakiadis flow) or the Riga-plate is situated in a constant free stream (Blasius flow). The results are obtained with the numerical simulation of the governing equations. Velocity profiles are presented, as well as values of the skin friction. Results are presented for both impermeable and permeable Riga-plate with uniform suction or uniform injection. [ABSTRACT FROM AUTHOR]

We investigate the fully developed flow in a fluid-saturated porous medium channel with an electrically conducting fluid under the action of a parallel Lorentz force. The Lorentz force varies exponentially in the vertical direction due to low fluid electrical conductivity and the special arrangement of the magnetic and electric fields at the lower plate. Exact analytical solutions are derived for fluid velocity and the results are presented in figures. All these flows are new and are presented for the first time in the literature. [ABSTRACT FROM AUTHOR]

The work of Mahmood and Merkin (ZAMP 39:186–203, 1988) concerns the mixed convection flow along a stationary cylinder in a constant free stream. In the present note, we extend the above work to general situations involving a moving cylinder. [ABSTRACT FROM AUTHOR]

The present comment concerns some errors found in the above paper. [ABSTRACT FROM AUTHOR]

The present comment concerns a wrong comparison made in the above paper. [ABSTRACT FROM AUTHOR]

In the above paper, some basic equations are wrong. [ABSTRACT FROM AUTHOR]

The present comment concerns some doubtful results in the above paper. [ABSTRACT FROM AUTHOR]