Thermal Planar and Radial Free Jets for An Ostwald‐de Waele Fluid With Shear‐Rate Dependent Thermal Diffusivity

ABSTRACT The planar and radial thermal free jets for forced convection of a non‐Newtonian power‐law fluid are investigated. The thermal diffusivity is dependent on the shear‐rate and is not a constant. The flow in planar and radial thermal free jets is governed by the momentum, continuity and energy balance equations. In the stream‐function formulation, the governing equations reduce to a system of two coupled partial differential equations for the stream function and temperature. Conservation laws for this system are obtained using the multiplier method. Group invariant solutions for the planar and radial thermal free jets are derived by a Lie point symmetry associated with the conserved vectors. Analytical solutions for the velocity components and temperature function are found in parametric form. It is shown that solutions are only admissible in the representative range . For dilitant fluids, , the jets are characterised by a boundary curve but not for pseudoplastic fluids, , and Newtonian fluids, . It is shown that the jet flow characteristics depend on the flow index, , the effective Prandtl number and the jet strength and convective heat flux across the jet.