In this PhD dissertation, studies on heat and mass transfer in boundary layer flow of some non-Newtonian nanofluids are presented. Attempts were made to improve cer tain existing fluid transport models by considering various features of flow realities. Efforts were also made to simplify and make the governing equations convenient for computations. Further, a relatively recent and more efficient mathematical method, namely the optimal homotopy analysis method was employed successfully. The cor responding algorithms of the method were established to each problem and imple mented in Mathematica computational software. To ensure the validity of the results, comparisons of the present study were made with previously published study find ings. Extensive parametric studies were also carried out to examine the influences of pertinent parameters on various flow field profiles and the corresponding physi cal quantities of practical interest. The results of the studies have been presented by using graphs and tables followed by detailed interpretation and discussion. Among the many findings of this study work, it was found that the rates of heat and mass transfer can be facilitated by increasing the non-Newtonian Casson parameter or by decreasing the Williamson parameter. The coefficient of skin friction can be reduced by decreasing values of the Williamson parameter or the non-Newtonian Casson pa rameter. It was also noted that in all the investigations, the new results are in very close agreements with the previous study reports under common assumptions. The findings of this study are believed to contribute in the efforts made by the scientific community to give a more realistic descriptions and more reliable predictions to such fluid transport phenomena. Applied scientists and various practitioners can also be benefited from these findings to make knowledge-based decisions in the design, im plementation and regulation of their real flow systems. Thus, among other things, the results of the present model analyses will contribute in improving quality of industrial products