This paper presents a numerical investigation on heat transfer and flow behavior for non-Newtonian nanofluids with different nanoparticles (Al2O3 and CuO) and carboxymethyl cellulose (CMC) with water as a base fluid. The analysis has been carried out in an elliptical tube. Power-law model is adopted to depict the non-Newtonian nature of nanofluid. The present study has been done with a range of nanosized particles 0–4% by volume, and the variation of Reynolds number is kept under the laminar condition. The physical model covers two concentric tubes used to create an annular space. The effects of volume fraction, particle type, and base fluid have been investigated at different Reynolds numbers numerically. Also, the effect of pressure and heat transfer coefficient on the flow behavior of non-Newtonian nanofluids is analyzed. The results concluded that Al2O3 particles showed 219% and CuO particles give 195% higher heat transfer coefficient as compared with pure water.