No abstract

Purpose -To study the steady mixed convection boundary-layer flow of a micropolar fluid near the region of the stagnation point on a double-infinite vertical flat plate is studied. The results of this paper are important for the researchers in the area of micropolar fluids. Design/methodology/approach -For the case considered the problem reduces to a system of ordinary differential equations, which is solved numerically using the Keller-box method. This method is very efficient for solving boundary-layer problems and it can easily be applied to other general situations than that presented in this paper. Any PhD student can learn and apply it very easily. Findings -Representative results for the velocity, microrotation and temperature profiles, as well as for the reduced skin friction coefficient and the local Nusselt number have been obtained for the case of strong concentration, Prandtl number of 0.7, some values of the material parameter K and the mixed convection parameter lð$ 0Þ: Both assisting and opposing flow cases are considered. Results for the reduced skin friction coefficient and reduced local Nusselt number as well as for the reduced velocity, temperature and microrotation profiles are given in tables and figures. The obtained results are compared with ones from the open literature and it is found that they are in excellent agreement. The important conclusion is, we have been able to show that for opposing flow solutions are possible are possible only for a limited range of values of the mixed convection parameter l.Research limitations/implications -The results of this paper are valid only in the small region around the stagnation point on a vertical surface and they are not applicable outside this region. Practical implications -The theory of micropolar fluids and also the results of the present paper can be used to explain the characteristics in certain fluids such as exotic lubricants, colloidal suspensions or polymeric fluids, liquid crystals, and animal blood. Originality/value -The paper is very well prepared, presented and readable. We believe that the results are original and important from both theoretical and application point of views.

Purpose -The purpose of this paper is to theoretically investigate the steady two-dimensional magnetohydrodynamic (MHD) boundary layer flow over a shrinking sheet. The effects of stretching and shrinking parameter as well as magnetic field parameter near the stagnation point are studied. Design/methodology/approach -A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using Keller-box method. Findings -The solution is unique for stretching case; however, multiple (dual) solutions exist for small values of magnetic field parameter for shrinking case. The streamlines are non-aligned and a reverse flow is formed near the surface due to shrinking effect. Practical implications -The flow due to a stretching or shrinking sheet is relevant to several practical applications in the field of metallurgy, chemical engineering, etc. For example, in manufacturing industry, polymer sheets and filaments are manufactured by continuous extrusion of the polymer from a die to a windup roller, which is located at a finite distance away. In these cases, the properties of the final product depend to a great extent on the rate of cooling which is governed by the structure of the boundary layer near the stretching surface. Originality/value -The present results are original and new for the MHD flow near the stagnation-point on a shrinking sheet. For shrinking case, the velocity on the boundary is towards a fixed point which would cause a velocity away from the sheet. Therefore, this paper is important for scientists and engineers in order to become familiar with the flow behaviour and properties of such MHD flow and the way to predict the properties of this flow for the process equipments.

No abstract

No abstract

No abstract

No abstract

No abstract