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This article investigates the nonlinear convection transport of heat transfer in a nanoparticle laden two-layer flow in a vertical channel under the additional effects of magneto hydrodynamic (MHD) and radiation. Water and compressed air are chosen as the fluids in two-layer flow. This type of flow is commonly seen in the transportation of oil and gas in pipelines, therefore, correct understanding of flow dynamics including convective transport phenomenon, layers interaction, and graphical interpretation of flow variables is important for better designing of equipments. Titanium dioxide (Ti O 2 ) nanoparticles are added into the air to magnify the transport mechanism. The mathematical model incorporating buoyancy, nonlinear convection, MHD, viscous dissipation, and radiation effects is presented in the form of nonlinear Ordinary Differential Equation (ODE's). Then utilizing homotopy analysis method, these interconnected differential equations are resolved. A visual illustration shows how different physical factors affect fluid rate and temperature. Tabulated values of Nusselt number at both walls are presented to discuss the numerical data of convection and found that it decreases toward the left boundary but rises toward the right wall by increasing Eckert number and Prandtl number. The results of this two-layer flow will help in understanding this complex flow which has practical applications in various engineering processes and further enhance the scientific knowledge related to multilayer problems. [ABSTRACT FROM AUTHOR]

The motivation for this comparative examination is to verify and account for the appropriate source of heat energy needed in production industries, and to expunge the contradictions between Fourier's law and the theory of relativity. In heat management such as in engineering systems, the required heat for effective melting, production rate, etc. dictates the appropriate heat generation/injection module to be deployed. However, the material medium of heat transmission can be a hindering factor for a successful convection process, to this, an investigation of the instantaneous heat propagation paradox is required. An assumption of induced flow due to stretching characteristics is made, and an appropriate similarity transformation is deployed for the governing systems. By means of the Galerkin-weighted residual method, numerical solutions to the system of equations are approximated and validated. In a limited case, the solution compares favourably with existing literature, while the novel comparative investigation predicts the dominance of the Temperature-Dependent Heat Source (TDHS) capable of weakening the fluid cohesive force and upsurging the energy rate in short time in contrast to the Space-Dependent Heat Source (SDHS) module. The material relaxation phenomenon indicated that more time will be needed for prosperous/equal heat energy transfer. Further heat transfer enhancement is called for higher discharge of radiation and boosting of thermal conductivity, while TDHS module is strongly recommended in highly required heat systems. [ABSTRACT FROM AUTHOR]

AbstractDue to practical applications, we are motivated in the present study to analyze the effects of nonlinear natural convection in a nanofluid flow past a vertical plate in the presence of a first-order chemical reaction and thermophoresis (the normal flux of the nanoparticles is zero at the boundary). The two-phase model for the nanofluid is also considered. The governing partial differential equations (PDEs) are transformed to ordinary differential equations (ODEs) using similarity transformations. Numerical solutions for the transformed equations are attained by using a Runge-Kutta method with a shooting technique. The effects of the relevant physical parameters on the velocity, the temperature, and the nanoparticle volume fraction are analyzed. Also, the consequences of the parameters on the flow, heat, and mass transport phenomena are observed and analyzed explicitly. The results of this study are interesting and motivating for further investigations on the problem for different situations and with different geometries. [ABSTRACT FROM AUTHOR]