This chapter focuses on the momentum and heat transfer characteristics of an isolated rigid and fluid sphere in power-law, and Bingham and Herschel Bulkley fluid models with and without wall Effects. It deals with the momentum and heat transfer characteristics of a single rigid particle and a fluid sphere in different types of concerned and unconfined non-Newtonian fluids. All modern technologies, including modern transportation, entertainment industry, medicine, environment, energy generation and conservation all exploit non-Newtonian characteristics in one form or the other at some stage during the course of their manufacture or application. Most low-molecular-weight substances like gases, organic liquids, inorganic salts and their solutions, molten metals, and electrolytes exhibit Newtonian fluid behavior and are accordingly known as Newtonian fluids. Viscoelastic fluids deviate from Newtonian fluids and time-independent fluids even more dramatically when subject to small amplitude oscillatory shear and extensional deformation.