The propagation of elastic waves in a circular cylinder and cylindrical annulus for two types of power-law constitutive equations is investigated. These power-law constitutive equations can describe elastic responses where the linearised strain and stress are nonlinearly related. These constitutive equations are a subclass of the more general class of implicit constitutive equations and are characterised by expressing the strain as a non-invertible function of the stress. Pseudo-solitary stress wave solutions for both types of constitutive equations in the circular cylinder and cylindrical annulus are derived. We find that for the power-law constitutive equation of Type I, a shock front will develop at the back of the wave while for the power-law constitutive equation of Type II, a shock front will develop at the front of the wave. Estimates of the times at which the shock front will develop are given. Standing wave solutions for both types of constitutive equations in the circular cylinder and cylindrical annulus are also obtained and the periods of oscillation are compared.

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.

This study presents a clinically-derived, real-world paediatric pulmonology dataset across underrepresented areas in South Africa and benchmarks machine le

The two-dimensional thermal liquid jet of a non-Newtonian power-law fluid is investigated under shear-rate-dependent thermal diffusivity, resulting in a one-way coupled nonlinear system governing momentum and thermal transport. Two physically distinct free-surface thermal boundary conditions are examined: adiabatic insulation and convective heat loss. Conservation laws and conserved quantities for the governing system are derived systematically using the multiplier method. By coupling an appropriate conserved vector with an admitted Lie point symmetry, the governing partial differential equations are reduced to a coupled system of ordinary differential equations. Closed-form parametric families of solutions are then obtained for the thermal field. The analysis reveals fundamentally different thermal transport mechanisms across rheological regimes: shear-thinning fluids enhance thermal redistribution and become increasingly sensitive to convective cooling as the Biot number increases, whereas shear-thickening fluids suppress internal thermal transport, promoting greater thermal retention within the jet core and reducing the influence of free-surface cooling. These findings clarify the interplay between rheology, nonlinear thermal diffusion and free-surface cooling and provide new analytical insight into downstream thermal transport in non-Newtonian liquid jets.