Boundary layer stagnation point flow towards an exponentially stretching/shrinking sheet - Sayed Qasim, Alavi (2015)
The problem of boundary layer flow has many applications in industries and engineering field. Some of these applications are drawing of plastic films, glass fiber production, hot rolling and many others in industrial manufacturing processes. The final product characteristics requested depends on the cooling liquid used and the rate of stretching. Four common boundary conditions are used in modelling of convective boundary layer flow problems, which are constant or prescribed wall temperature, constant or prescribed surface heat flux, Newtonian heating and convective boundary conditions. In this thesis, the mathematical modelling for the effects of radiation and MHD on stagnation point flow and heat transfer over an exponentially stretching/shrinking sheet is investigated. In this study, the governing boundary layer equations are first transformed using an appropriate similarity transformation, which are then solved numerically by using Keller-box method. MATLAB software is used as a tool in order to obtain the numerical solution. Five parameters are investigated in this problem, which are Prandtl number Pr, velocity ratio parameter E, conjugate parameter Y, magnetic parameter M and thermal radiation parameter R N . In conclusion, there are dual solution when velocity ratio parameter E satisfies -1.487068<E<-0.9734, unique solution for E>-0.9734 and no solution exist for E < -1.487068 . To get a physically acceptable value in second solution, the value of Prandtl number Pr must be smaller than a critical value Prc . It depends on conjugate parameter Y . While, the values of conjugate parameter Y must be greater than some critical values Yc which also depends on the Prandtl number Pr. Furthermore, increasing values of Prandtl number Pr and velocity ratio parameter E has led to decrease in temperature profile while the increasing in radiation parameter R N and magnetic parameter M has enhanced the temperature profiles.