A Mathematical Study on Non-linear Boundary Value problem for Magnetohydrodynamic Fluid Flow

The influence of MHD upon the Marangoni boundary layer of hybrid nanofluid flow along an extended surface is mathematically analysed and presented in this work. Similarity transformations reduce the controlling equations to dimensionless form. The reduced simultaneous equations can be analytically resolved. The semi-analytical expressions for the dimensionless velocity as well as temperature are attained by utilizing Ananthaswamy Sivasankari technique (ASM) and Modified q-Homotopy analysis approach (Mq-HAM) respectively. The results of the dimensionless quantities for the amounts of physical components including dimensionless skin friction coefficient and non-dimensional Nusselt number are depicted in tabular and graphical forms to interpret significant consequences. The physical parameters involved in the model such as the Marangoni parameter, Magnetic field factor, Prandtl number, volume fraction of nanoparticles and constant mass flux velocity are depicted graphically to show their effects on the velocity and temperature respectively. The applied magnetic field parameter's direction and strength have a significant impact on the fluid flow. The skin friction factor and local Nusselt number are important parameters in MHD Marangoni boundary layers. Our results on these parameters are used in fields where precise control of heat transfer and fluid flow is essential, such as crystal growth, microfluidics, welding processes, and the manufacturing of electronic components. The proposed technique shall be extended to address non-linear challenges in physical science especially MHD flow issues.