A mathematical analysis of a model for nutritional exchange in a capillary-tissue exchange system is presented in this paper. This model consists of a single file flow of red blood cell in capillary when diameter of red blood cell is greater than tube diameter. In this case, the cell must be deformed. Due to concentration gradients, the dissolved nutrient in substrate diffuses into surrounding tissue. Introducing approximations of the lubrication theory, squeezing flow of plasma in between the gap between cell and capillary wall have been solved with the help of approximate mathematical techniques. The computational results for concentration of dissolved nutrients, diffusive flux and normal component of velocity have been presented and discussed through graphs. We have also shown the effect of deformation parameter and permeability on these results.

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The flow of rheologically complex fluids in industrial equipment poses a number of challenges, not least from a modeling point of view. Research is needed to further understand and be able to predict the flow behavior of such materials and to investigate ways of improving their processing. The Non-Newtonian Solid-Liquid fluid flow behavior in horizontal and vertical pipes can be predicted by various methods which are mention in the paper. In the literature, it is also shows that Computational Fluid dyanamices (CFD) has sufficient capability to deal with such type of flow and was capable of giving predictions of pressure drop which were probably better and more reliable than the correlations available in the literature.

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