The impact of internal heat and gravity modulation on convection of Jeffrey fluid in a porous media: A weakly non-linear analysis

Abstract

Internal heat, primarily generated by nuclear fusion and radioactive decay, serves as a key energy source for celestial bodies. In porous media, small-scale exothermic reactions can contribute to local heat generation, enabling convective flow under various practical conditions. The Jeffrey fluid model, widely used for biological fluids such as blood, synovial fluid, chyme, gastric fluid, and saliva, is considered in this study. This paper examines the influence of internal heat generation and gravity modulation on the convection of Jeffrey fluids using a weak nonlinear analysis and a power series expansion method. Heat transfer is evaluated through the Nusselt number and the mean Nusselt number ($\overline{Nu}$), which is determined as the area under the curve. For an internal Rayleigh number $R{a}_i=0.5$, the area under the curve is smaller, whereas for $R{a}_i=1.5$, it is larger, indicating enhanced heat transport. Similarly, for the Vadasz number, $Va=0.5$ results in a smaller area under the mean Nusselt number curve, while $Va=1.5$ leads to a larger area, suggesting increased heat transport and greater system instability.