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The thermal radiation and Fourier flux have drawn the attention of scientists and experts due to their extensive applications in the fields of medicine, manufacturing modern airplanes, water distillation, more efficient electronic devices, more efficient batteries, radiating treatment, and the textile industry. Through careful consideration of this, the mathematical investigation of natural convection and Fourier flux on the flow of energy and diffusion transmission of a body of cone and cylinder revolution, located in a saturated medium, has been described for the dual situations (flow over a cone and a cylinder). After then, the Runge–Kutta technique was used to explain the leading mechanism. Possessions of governing physical measures of local Nusselt and Sherwood numbers as well as velocity, thermal and diffusion figures are provided with support of tables and diagrams. It is motivating to declare that mass transfer rate is advanced in cone kind of revolution matched to cylinder kind of revolution with rising $N_R,N_t,Q_S$. Also, the heat transmission rate is upper in cylinder revolution equated to cone revolution.

Heat and mass transfer acquired the attention of investigators and experts because of massive uses in the field of medicine, manufacturing of modern aircrafts, uses in advanced water filtration plants, distillation process of water, more efficient electronic instruments, more efficient batteries, textile industry, uses as manufacturer in cosmetics industry and modern defense equipment. By viewing this, we considered the numerical study of Fourier flux and buoyancy driven forces on the flow of thermal and diffusion transmission of body revolutions (Paraboloid and cone), situated in a water-logged Darcy medium by allowing the radiation, Brownian motion, time-space dependent heat source or sink, and thermopheretic. Later on, the governing system is solved via Runge–Kutta method. Properties of convoluted governing measures of the organisms on local Nusselt and Sherwood numbers along with velocity, thermal and diffusion shapes are described with the aid of graphically and tabular form. It is stimulating to declare that the non-uniform heat source or sink is highly dominated in cone form of revolution as associated to paraboloid form of flow due to more distribution of mass transfer. From this, one can draw the conclusion that wherever there are higher mass transportation phenomena, cone-shaped body of revolution can be used. It is found that the time- and space-dependent heat source or sink performs as a regulating factor of the transmission of flow phenomena.