Analysis of general unified MHD boundary-layer flow of a viscous fluid - a novel numerical approach through wavelets

Abstract

The common boundary-layer equations are derived in which the boundary-layer forms either due to the flow of a viscous fluid over a moving wedge or due to the stretching of the surface with a non-uniform velocity using the concept of the velocity ratio (free stream velocity to the stretching surface velocity). The extreme values of the velocity ratio parameter then characterize both former and latter boundary-layer flows. The model also considers the effect of uniform magnetic field which is applied normal to the flow. Once the mainstream flow is approximated either in the form of the power of distance along the wedge surface or as zero, the self-similar solutions exist. Using suitable transformations, the boundary-layer equations have been converted into the Falkner–Skan-type equation over the unbounded domain that accounts the velocity ratio parameter. The governing problem over an unbounded domain is solved using a novel numerical scheme which makes use of the power of Haar wavelets coupled with collocation method and quasilinearization technique. The wavelet solutions have been verified to be very accurate when compared with numerous previously observed results. Several interesting physical aspects of the considered problem are focused and justified through both theoretical as well as numerical approach. The results show that there are over- and under-shoots in the solutions. Also, the flow divides into near-field (the solutions are confined to a viscous region) and far-field region (inviscid region). It is noticed that the boundary-layer thickness decreases for increasing pressure gradient and magnetic field parameters. Further, interestingly, our study leads to dual solutions for some range of physical parameters, which is explored for the first time through wavelet method in the literature. The physical hydrodynamics is explored and discussed.