Dynamics of Non-Newtonian Tangent Hyperbolic Liquids Conveying Tiny Particles on Objects with Variable Thickness when Lorentz Force and Thermal Radiation are Significant

The flow via needle has prominent applications in the modern world such as nano-wires, microstructure electric gadgets, microsensors, surgical instruments and biological treatments. The present investigation focuses on boundary layer heat, flow, and mass transfer of MHD tangent hyperbolic fluid (conveying tiny particles) via a thin needle under the impacts of activation energy, non-constant thermal conductivity, heat source, and nonlinear thermal radiation. In the description of the Buongiorno model, the significant features of Brownian motion and thermophoresis have been included. Adopting appropriate transformations to the given problem specified by the set of partial differential equations yields the dimensionless form of ordinary differential equations After that, these obtained ODEs are solved numerically via MATLAB bvp4c. A comparative result with previous findings is conducted. Physical parameters’ impact on flow rate, heat, and concentration is exhibited and explained in depth. The main findings of this study are that flow patterns reduce as the magnetic parameter and the Weissenberg number grow. Higher values of Brownian motion, heat source/sink, nonlinear radiation, and thermophoretic parameter improve the thermal profile. Moreover, the rate of heat transfer for the variable property case is significantly improved. Concentration profiles reduce as the thermophoresis parameter and chemical reaction parameter grow but improve as the activation energy and Brownian motion parameter rise. The percentage increase in Sherwood number is 35.07 and 5.44 when the thermophoresis takes input in the range 0 ≤ Nt ≤ 0.2 and activation energy parameters 0 ≤ E ≤ 0.2. The Weissenberg number and power-law index parameters are all designed to boost the Sherwood number.