The Cheng-Minkowycz problem for quadratic convective and radiative heat transfer in a nanofluid saturated porous medium: A revised model

The characteristics of heat transport in a porous medium saturated by a nanoliquid subject to non-linear variations of density-temperature relation and a novel quadratic thermal radiation are studied. For the first time, the well-known Cheng-Minkowycz problem was revisited by nonlinear convection and radiation. The governing equations, based on Darcy's law and Buongiorno's model, are simplified using boundary layer theory, which is further solved by the finite element method. The parameterization of the problem is used to describe the characteristics of the Boussinesq quadratic approximation, Brownian diffusion, quadratic radiation, thermophoretic diffusion, and no-mass flux conditions on the rheological and heat transport features. Our results demonstrate that the rate of heat transport (Nusselt number) is reduced due to thermophoretic diffusion, and the rate of reduction increases with increasing Lewis number values. The Nusselt number is improved due to increasing the values of the Brownian motion parameter at the rate of 0.00616835 and 0.00113362 for the cases of linear thermal radiation and quadratic thermal radiation, respectively. The improvement/reduction rate of the Nusselt number is higher for the case of quadratic thermal convection than for linear thermal convection. Furthermore, the heat transfer rate is achieved for the convection parameter, temperature ratio, and radiation parameter.