The fact that most fluids in nature do no obey Navier-Stokes eqs. manifests engineering & industrial importance of non-Newtonian fluids. The 2nd and 3rd grade fluids which form a subclass of differential type fluids can predict shear thinning and thickening properties but lack other feathers such as stress relaxation and retardation. Maxwell and Oldroyd-B fluids models which are viscoelastic rate type fluids can show relaxation and retardation phenomena. Burgers'' fluid which is a viscoelastic fluid model includes an Oldroyd-B, Maxwell and Newtonian fluid models as special cases. Unlike Maxwell & Oldroyd-B models, it involves the stress being differentiated twice w.r.t. upper convected derivative. It turns out that in general we need additional conditions. This issue crops up with regards to several non-Newtonian fluid models. This thesis, hence, provides a new metric of success for non-Newtonian fluids, supplemental to the viscoelastic fluids analysis. The results & analysis should help shed some light on new directions, and should be especially useful to workers who may be considering MHD flows and heat transfer problems.