Entropy generation in Casson methanol-based ZIF-8/GO hybrid nanofluid for solar thermal collector applications

In this work, the flow and thermal characteristics of Casson methanol based ZIF-8/GO hybrid nanofluid over an impermeable stretching absorber sheet in Darcy porous medium are investigated. The influences of magnetic field are incorporated and the convective heat transfer and entropy generation are investigated. The proposed configuration is considered in the context of solar thermal collector applications, where the combined influence of nanoparticle transport, porous-medium resistance, and non-Newtonian rheology can affect the thermal performance and associated irreversibilities. The mathematical formulation incorporates the simultaneous effects of hydrodynamic velocity slip, thermal slip, Rosseland thermal radiation, viscous dissipation, and Joule heating. Suitable similarity transformations reduce the governing partial differential equations to a coupled system of nonlinear ordinary differential equations, which are numerically resolved using the fourth-order finite-difference collocation algorithm ( bvp4c ) in MATLAB with a truncated domain of 𝜂 ∞ = 6 . 0 and an error tolerance of 1 ⁢ 0 − 7 . Grid-independence tests verify numerical stability with variations below 0.001%, and benchmark comparisons confirm excellent agreement with published literature. The second-law thermodynamic performance is comprehensively analyzed through dimensionless entropy generation ( 𝑁 𝑠 ) and the Bejan number ( 𝐵 ⁢ 𝑒 ). The results demonstrate that increasing the magnetic parameter ( 𝑀 ) and porous permeability ( 𝐾 𝑝 ) decelerates the fluid motion due to Lorentz drag and porous structure resistance, but elevates the fluid temperature via Joule heating. Dual interfacial slip effects ( 𝜆 , 𝛿 ) significantly suppress wall shear stress and reduce the local Nusselt number by up to 12%. Dispersing hybrid nanoparticles at 𝜙 = 3 % yields a 33% enhancement in the convective Nusselt number compared to the base fluid; however, this enhancement is accompanied by a 44% increase in total entropy generation. Near the absorber sheet ( 𝜂 < 1 . 0 ), viscous friction and Joule dissipation dominate the exergy destruction ( 𝐵 ⁢ 𝑒 < 0 . 5 ), whereas thermal irreversibility governs the outer flow domain ( 𝐵 ⁢ 𝑒 → 1 . 0 ). Translating these results into solar collector metrics reveal that a dilute loading of 𝜙 ≈ 1 % – 2 % establishes an optimal thermodynamic balance between first-law thermal gains ( 1 2 % – 2 0 % ) and exergy destruction, providing rigorous design guidelines for next-generation solar thermal collectors.