Unsteady Radiative MHD Casson Fluid Flow Over an Impulsively Started Porous Plate With Caputo Fractional Derivatives

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Abstract
This study investigates the unsteady natural convection flow of a hydromagnetic Casson fluid past a suddenly accelerated porous plate, incorporating thermal radiation and internal heat generation. The key novelty lies in employing fractional calculus via the Caputo derivative to generalize classical conservation equations, enabling the modeling of memory and hereditary effects crucial for non‐Newtonian fluid dynamics. Unlike prior studies focusing on classical or steady‐state models, this work develops a fractional‐order framework to capture complex unsteady transport phenomena. Exact analytical solutions for momentum, thermal, and concentration equations are derived using Laplace transforms, providing closed‐form expressions in the Laplace domain and explicit time‐dependent solutions. These serve as rare benchmarks for such systems. The study uniquely integrates thermal radiation and heat generation—often examined separately—while considering porous media and sudden plate motion, enhancing relevance to thermal systems, biomedical flows, and filtration processes. Key findings indicate that increasing the fractional order boosts velocity, temperature, and concentration fields, underscoring the significance of memory effects in transport dynamics. The magnetic field suppresses flow due to Lorentz forces, while thermal radiation and heat generation enhance thermal diffusion. Analytical expressions for skin friction, Nusselt number, and Sherwood number are derived, offering validation benchmarks. A comparison with published results shows strong agreement. The study advances analytical modeling of radiative, magnetized non‐Newtonian flows in porous media, with applications in biofluid mechanics, thermal engineering, and industrial processes involving complex fluids. The fractional approach provides a more accurate and generalized framework for such systems.

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