Effects of Magnetic Field and Thermal Radiation on Stagnation Flow and Heat Transfer of a Power-Law Fluid over a Shrinking Sheet

An analysis is made on the steady two-dimensional boundary layer magnetohydrodynamic (MHD) stagnation-point flow and radiative heat transfer of an electrically conducting power-law fluid over a shrinking sheet which is shrunk in its own plane with a velocity proportional to the distance from a fixed point. The similarity transformations are used to transform the boundary layer equations into a system of nonlinear ordinary differential equations which are then solved numerically using shooting technique. It is found that multiple solutions exist for a certain range of the ratio of the shrinking velocity to the free stream velocity (i.e., α) which again depends on the magnetic parameter (M) and the power-law index parameter (n). The results pertaining to the present study indicate that as the strength of the magnetic parameter increases, the range of α where similarity solutions exist gradually increases. It is also observed that the temperature at a point decreases with increase in M for the first solution branch, whereas it increases with increase in M for the second solution branch. The reported results are in good agreement with the available published work in the literature. 1. Introduction From a technological point of view, non-linear fluid rheology is of special interest and has practical applications. Hence the study of non-Newtonian fluid is very much important. A large number of industrial fluids such as molten plastics, artificial fibres, food stuff, polymers, and slurries are non-Newtonian in their flow characteristics. Many of the inelastic non-Newtonian fluids encountered in chemical engineering processes and biochemical industries are known to follow the empirical Ostwald-de Waele model (see Metzner [1]) or so-called power-law model. This model is described by a simple nonlinear equation of state for inelastic fluids which includes linear Newtonian fluids as a special case. Also, the study of magnetohydrodynamic (MHD) flow of an electrically conducting fluid is of considerable interest in modern metallurgical and metal-working processes. This type of flow has attracted the interest of many researchers due to its application in many engineering problems such as MHD generators, plasma studies, nuclear reactors, and geothermal energy extractions. Also by the application of magnetic field, hydromagnetic techniques are used for the purification of molten metals from nonmetallic inclusions. Therefore the type of problem that we are dealing with is very useful to polymer technology and metallurgy. Stagnation-point flow is a topic of significance