Impact of hydrospheric density variation and atmospheric thermal jumps on heat transfer between two concentric spheres with temperature-dependent fluid properties

Abstract Heat transfer between the Earth’s hydrosphere and atmosphere is influenced by density variations within water masses and thermal-jump effects in rarefied atmospheric layers. Traditional continuum-based models often neglect these coupled mechanisms, leading to inaccurate predictions of temperature transport across spherical earth regions. To address this limitation, this study investigates the combined effects of hydrospheric density variation and atmospheric thermal-jump conditions on heat transfer between two concentric spherical layers. A two-region mathematical model with temperature-dependent fluid properties is formulated in spherical coordinates, and the governing nonlinear momentum and energy equations are solved using the finite element method. The findings show that increasing hydrospheric density variation enhances thermal retention, producing up to a 14–18% reduction in temperature attenuation near the inner sphere. A reduction in the Grashof number weakens convective circulation, resulting in a 22% decrease in peak momentum intensity and a smoother thermal field. Furthermore, imposing thermal-jump conditions at the interface significantly alters heat exchange between the layers, causing a 10–15% variation in the interfacial heat flux, demonstrating the sensitivity of atmospheric–hydrospheric coupling to jump phenomena.