Significance of Exponential Thermal Density and Slips Impact on Heat‐Mass Transmission in Magneto‐Hydrodynamic Second‐Grade Nanofluid Over Stretched Porous Media: High Prandtl Number

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This research primarily focuses on significance of heat–mass characteristics of a second‐grade nanofluid that are affected by variable density, (magneto‐hydrodynamic) MHD, and thermal‐concentration slip over‐stretching surface with high Prandtl number, porosity medium, thermophoresis and Brownian movement to minimize excessive heating in high temperature systems. For smoothing the processing and integration, partial differential equations (PDEs) of the present model are transformed into ordinary differential equations (ODEs) by using a similarity variables function. The ODEs are further solved by using central difference and Newton–Raphson methodology. The MATLAB software, along with the Keller Box approach are used to calculate the numerical and graphical results. The temperature ( θ ), mass concentration ( ϕ ), and velocity profiles (), have been displayed together with their slopes for various physical parameters such as Prandtl number (Pr), magnetic number (M) Brownian number (Nb), thermophoresis number (Nt), porosity number (𝛺), second‐grade number (λ), Lewis number (Le), thermal‐concentration slips (Bt, Bc) and power‐law index number ( n ). For numerical asymptotic results, the range of parameters like 0.1 ≤ n ≤ 1.2, 0.1 ≤ Nt ≤ 1.6, 0.2 ≤ Nb ≤ 2.4, 0.01 ≤ M ≤ 5.0, 0.1 ≤ λ ≤ 10.1, 0.1 ≤ Ω ≤ 3.0, 0.1 ≤ Pr ≤ 9.0, 0.1 ≤ Bc ≤ 2.0, 0.1 ≤ Bt ≤ 2.5, 0.1 ≤ Le ≤ 3.5 are used. It is found that (𝛺) has improved the effects of heat transmission due to large surface contact area. The velocity rate has increased with increasing (𝛺) and gained maximum rate at 𝛺 = 0.5 The heat and mass transmission rates are decreased with increasing (λ), and (M). These findings with greater Nusselt and Sherwood values can be utilized in boosting heat transfer efficiency.