A great many industrial processes, such as pneumatic handling of granular materials, drying of particles, gasification of solid fuels, combustion, flow of granular particles through chutes etc., involve interaction between solids and fluids. In most of these cases, a theoretical modeling of the process requires a complete and thorough understanding of the phenomena involved and constitutive modeling of the constituents along with the usual balance laws. There are many types of fluid models available which can accurately describe the characteristics of the fluid. However, theoretical modeling of granular materials require an understanding of the material parameters which can describe the common phenomena exhibited by these granular materials, such as "normal-stress effects" (Dilatancy). Experiments are required to measure the material properties of these materials. However, this branch of rheology has been neglected for a long time due to the complications involved. Here, we have taken up the challenge to devise an instrument, an "Orthogonal Rheometer" which can measure the properties of granular materials. Experimental investigations verify the commonly exhibited phenomena by these materials and estimate the various forces which are generated due to the shearing of these materials.; In the second part of this thesis, I discuss the flow of non-Newtonian fluids. There are many theoretical models available which describe the behavior of polymeric and biological fluids which usually can not be represented by the classical linearly viscous fluid. Our interest here is to study the flow of these viscoelastic fluids which usually exhibit phenomena like "relaxation" and "creep". The Oldroyd-B model is one of the simplest rate type model which does not involve too many material parameter evaluations and at the same time takes some of the memory of the fluid into account, thus capturing many of the characteristics of the fluid. We have studied the non-radial flow of an Oldroyd-B fluid between intersecting planes, the flow of an Oldroyd-B fluid due to a stretching sheet when the fluid far off from the sheet is quiescent and when the fluid is moving with uniform velocity, and the fully developed flow of a generalized fluid of second grade between the heated parallel plates, due to a pressure gradient along the plates. In all these studies, the problem is formulated and the resulting equations are solved numerically. Our results agree qualitatively with previous work whenever such comparisons are possible.
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