Thermosolutal Marangoni convective flow of MHD tangent hyperbolic hybrid nanofluids with elastic deformation and heat source

In this work, the Marangoni convective flow of magnetohydrodynamic tangent hyperbolic ( F e 3 O 4 − Cu / {{\rm{F}}{{\rm{e}}}_{3}{\rm{O}}}_{4}-{\rm{Cu}}/ ethylene glycol) hybrid nanofluids over a plate dipped in a permeable material with heat absorption/generation, heat radiation, elastic deformation and viscous dissipation is discussed. The impact of activation energy is also examined. Hybrid nanofluids are regarded as advanced nanofluids due to the thermal characteristics and emerging advantages that support the desire to augment the rate of heat transmission. The generalized Cattaneo–Christov theory, which takes into account the significance of relaxation times, is modified for the phenomena of mass and heat transfer. The fundamental governing partial differential equations are converted to ordinary differential equations (ODEs) by adopting similarity variables. The Runge–Kutta–Fehlberg-45 technique is utilized to solve nonlinear ODEs. Regarding the non-dimensional embedded parameters, a graphic investigation of the thermal field, concentration distribution, and velocity profile is performed. The results show that the increasing Marangoni ratio parameter enhances velocity and concentration distributions while decreases the temperature distribution. The velocity profile is decreased and the efficiency of heat transfer is improved as the porosity parameter is increased. Nusselt number is diminished with the rising values of the porosity variable.