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Nowadays, the heat thrust liquid electric heater is generally used in profitable applications since it protects upto 2–3 times the energy of ordinary liquid electric heater. The heat pump makes use of a refrigerant for its process. The small-temperature refrigerant engrosses permitted heat from full of atmosphere midair in the evaporator which is crushed by an extremely well-organized electrical compressor to an extraordinary-temperature and high-pressure vapor refrigerant. For entire heat transfer connoisseurs, heat transfer performance in cooling and heating applications has become a top priority. Hence, research towards new heat transfer fluids is extremely intense and challenging. This investigation examines flow and heat transfer analysis in axisymmetric magnetohydrodynamic flow polyethylene glycol (PEG)-based nanofluid, hybrid nanofluid and ternary hybrid nanofluid flow induced by a swirling cylinder. Flow and heat transfer are analyzed and compared for three cases PEG-based copper oxide, magnesium oxide and zirconium oxide ternary nanofluid (PEG$+$ZrO₂$+$CuO$+$MgO), PEG-based copper oxide (PEG$+$CuO) nanoparticles and PEG-based zirconium and magnesium oxide hybrid nanofluid (PEG$+$ZrO₂$+$MgO). Shooting technique (R–K fourth-order) is employed to work out the flow equations numerically. Simulated results are displayed through graphs. The computational results are validated with the published research work and a modest concurrence is found. The main outcome of this study is found to be as follows: It is interesting to note that $C_{fx}\mathrm{\text{Re}}(\frac{x}{R})$ is lesser in nanofluid case compared with ternary and hybrid nanofluid cases. It is found that $C_{f\varphi }\mathrm{\text{Re}}(\frac{G}{HR})$ is more in ternary hybrid nanofluid compared with hybrid and nanofluid cases. Overall, it is observed that heat transfer rate is higher in nanofluid compared with ternary and hybrid nanofluid cases whereas lesser rate of heat transfers in ternary nanofluid case.

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.