Mathematical Analysis of Cross Fluid Flow Over Exponentially Stretching Sheet with Heat and Mass Transfer

Objective: To examine the heat and mass transfer of cross-fluid flow over exponentially stretchable sheet for the flow, temperature, and concentration profile. Method: This work examines the heat and mass transfer rate for the various profiles viz. velocity, temperature, and concentration for different values of the skin friction constraint, Nusselt quantity, and Sherwood quantity. The equations of momentum, flow, thermal, and concentration aspects have been governed as per the physical aspects considered for this research. Suitable similarity variables are applied to simplify the momentum equation and to alter the remaining governing equations to non-linear ordinary differential equations for solution. The R-K Felhberg (Runge -Kutta Fifth order) method evaluates the complex system of equations based on the shooting technique. Findings: The heat transfer rate exhibits a 40% increase with enhancements in the Prandtl number values (1, 5, 10). Additionally, the stretching parameter directly influences velocity, leading to a 56% improvement in the heat transfer rate for the corresponding parameter values (1.0, 1.5, and 2.0). Novelty: This research presents a pioneering approach to fluid mechanics by investigating non-Newtonian fluids on stretching surfaces, offering crucial insights for engineering advancements. Notably, it introduces the Cross-fluid model to analyze heat and mass transfer rates over an exponentially stretching sheet, employing the Runge-Kutta Fehlberg method for precise numerical evaluation. This novel framework enhances existing literature by addressing complex rheological behaviours and improving predictive accuracy in thermal and mass transport applications. Keywords: Exponentially stretching sheet, Skin friction coefficient, Cross fluid, Heat and mass transfer, Shooting technique