Weakly nonlinear analyses on double-diffusive convection of Casson fluid in a porous medium with an internal heat and gravity modulation

The influence of internal heat and gravity modulation on the onset of double-diffusive convection of Casson fluid using weakly nonlinear analysis is examined. Porous material generates its self heat under different types of situations. Casson fluids have found widespread use in food industries. Chocolate production, for instance, relies on controlling rheological behavior, influenced by ingredients and processing techniques. Casson fluid model is also applied in medical research to mimic human blood rheology. Non-newtonian fluid and their viscosity changes with applied stresses. These fluids demonstrate complex flow behavior in food processing. But so far, the influence of internal heat and gravity modulation on casson fluid is not discussed. Power series expansion method is used where disturbances are expressed as power series. Ginzburg–Landau amplitude equation was derived to quantify heat transfer and mass transport using Nusselt and Sherwood number, respectively. Our investigation revealed that increasing values of Darcy number, Casson parameter, and solutal Rayleigh number enhances the Nusselt number and Sherwood number, indicating improved heat and mass transfer. Furthermore, decreasing Nusselt number and Sherwood number by increasing the modulation frequency produces less heat and mass transport. Conversely, increasing the modulation amplitude increases the Nusselt number and Sherwood number. Graphical abstract