The present analysis is concerning the criteria for the onset of flow reversal of the fully developed flow mixed convection of nanofluids in a vertical channel filled with porous medium. The governing equations and the critical values of the buoyancy force are solved and calculated numerically via dsolve package in MAPLE. It was found that the critical values of mixed convection parameter for the occurrence of reversed flow decreases with increasing temperature difference ratio and increases with increasing nanoparticles mass flux.

An anisotropic porous layer saturated with a viscoelastic double diffusive binary fluid is examined numerically for the onset of Darcy-Rayleigh convection. From below, the system is heated, while from above, it is cooled. The temperature-dependent viscosity was added to the double diffusive binary fluid, and the Galerkin expansion method was used to determine the critical Darcy-Rayleigh number. When their values are raised, the impacts of strain retardation, thermal anisotropy parameter and Dufour number slow the production of heat transfer and stabilise the system. When the values are increased, the stress relaxation, Darcy-Prandtl, mechanical anisotropy parameters, temperature dependent viscosity and Soret number accelerate the heat transfer process in convection, which destabilises the system

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The heat transfer process of combined convection and its flow pattern in a vertical channel is important, especially in environmental, industrial and engineering applications. There has been some concern regarding the heat transfer process in which it is difficult, expensive and time consuming. There are three main objectives to satisfy the purpose of this study which are to determine the impact on flow and heat transfer of the Robin temperature boundary condition, to verify whether the viscous dissipation plays a classical role in fluid flow and heat transfer and lastly to compare the degree of heat transfer facilitated by the boundary conditions of Dirichlet, Neumann and Robin. In this study, the effects of different dimensional parameters were tested and the flow reversal phenomenon was discussed. The Boundary Value Problem (BVP) was solved numerically using Maple using a built-in routine, dsolve. Validation study to the previously published problem was carried out to verify the accuracy of the present computation. The transformation of partial differential equation to ordinary differential equation involved similarity technique. The numerical results of the flow and temperature variables were presented graphically. The flow reversal occurred when the value of internal heat generation (G) and combined convection parameter (λ) were large. There was no occurrence of flow reversal when the values of local heating exponent (p) and the Biot Numbers (Bi) increase. However, the value of mass transfer coefficient (N) was different, gave no significant impact.