In this paper, we answer the question under which conditions the porousmedium equation with convection and with periodic boundary conditions possesses gradient-type Lyapunov functionals (first-order entropies). It is shown that the weighted sum of first-order and zeroth-order entropies are Lyapunov functionals if the weight for the zeroth-order entropy is sufficiently large, depending on the st...

Mixed convection in an obstructed cavity with heated horizontal walls is investigated in this work. Brinkman-Forchheimer-extended Darcy model is utilized to describe the flow characteristics within a porous medium for different angles of attack with respect to the forced convection. Numerical results are obtained for a wide range of Grashof numbers (10–10), Reynolds numbers (10–10), Darcy numbe...

Mixed convection heat transfer in open-ended enclosures has been studied numerically for three different flow angles of attack. Discretization of the governing equations is achieved using a finite element scheme based on the Galerkin method of weighted residuals. Comparisons with previously published work on special cases of the problem are performed and the results show excellent agreement. A ...

In this study, an analysis has been performed for free convection with radiation effect over a thermal forming nonlinearly stretching sheet. Parameters n, k0, Pr, G represent the dominance of the nonlinearly effect, radiation effect, heat transfer and free convection effects which have been presented in governing equations, respectively. The similarity transformation and the finite-difference m...

Vibrational mixed convection inside an open-ended cavity filled with a porous medium is investigated in this work. Vertical vibration on the left wall and buoyancy induced flow are considered. The effect of variations in governing parameters, such as vibrational Reynolds number, modified Rayleigh number, and the Darcy number on streamlines, isotherms, and the average Nusselt number is discussed...

The unsteady two-dimensional laminar g-Jitter mixed convective boundary layer flow of Cu-water and Al2O3-water nanofluids past a permeable stretching sheet in a Darcian porous is studied by using an implicit finite difference numerical method with quasi-linearization technique. It is assumed that the plate is subjected to velocity and thermal slip boundary conditions. We have considered tempera...

Presented in this paper is an analytic approximation to the thermal-fluid problem involving mixed convective heat transfer from a rotating isothermal cylinder placed in a non-uniform stream shear flow. The approximation is obtained using a series expansion of the scaled boundary layer equations in terms of an appropriate boundary layer variable. The resulting approximation is valid both for sma...

Laminar mixed convection of Aluminium oxide (Al2O3)–water nanofluid flow in an inclined annulus using a single-phase approach was numerically studied. Constant heat flux boundary conditions were applied on the inner and outer walls. All the thermophysical properties of nanofluid, such as, viscosity, heat capacity, thermal conductivity, and thermal expansion coefficient...

We study the Rayleigh-Bénard convection in a 2-D rectangular domain with no-slip boundary conditions for the velocity. The main mathematical challenge is due to the no-slip boundary conditions, since the separation of variables for the linear eigenvalue problem which works in the free-slip case is no longer possible. It is well known that as the Rayleigh number crosses a critical threshold Rc, ...

Mixed convection fluid flow and heat transfer of water-Al2O3 nanofluid inside a lid-driven square cavity has been examined numerically in order to find the optimal distribution of discrete heat sources on the wall of a cavity. The effects of different heat source length, Richardson number and Grashof number on optimal heat source location has been investigated. Moreover, the average Nusselt num...