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Convective heat transfer in a porous cavity conjugated with an active rotating cylinder is investigated in this paper. Copper–water nanofluid fills the porous cavity. The rotating active cylinder is positioned in such a way conveying heat from the cavity and discharges it outside. The vertical walls of the cavity are thermally insulated while the bottom wall is moving to the right and kept at a constant high temperature. The governing equations are facilitated with the ability to study the tilt of the cylinder-cavity assembly. The effects of Richardson number, Darcy number, inclination angle, conductivity ratio, rotational speed, and nanofluid volume fraction are studied at a constant Rayleigh number of 105. Galerkin finite element method of weak formulation is used to solve the dimensionless governing equation with appropriate boundary conditions. Darcy–Brinkman–Forchheimer model is adopted to govern the flow inside porous medium. Results show that the rotation of the cylinder can enlarge the average Nusselt number more than 223%, while ten times increase of thermal conductivity ratio amplifies Nusselt number by 136%. It is also found that the Richardson number plays an adverse role on the average Nusselt number. Physical explanations and thorough validations are given in the paper.

In this study, the heat transfer, fluid flow and heat capacity ratio are analyzed in an annulus enclosure filled with porous and saturated by a suspension of nanoencapsulated phase change materials (NEPCMs). It consists of phase change material core and a polymer or non-polymer shell. The presence of nanoparticles in the base fluid and the phase change capability of the nanoparticle’s core improve the thermal properties of the base fluid and thermal control process. The inner cylinder wall is reserved at hot temperatures where the encapsulated particles absorb the heat, while the outer cylinder wall is reserved at cold temperatures where the encapsulated particles release the heat. A local thermal non-equilibrium model is adopted for the porous medium. The parameters studied are Rayleigh number (104 ≤ Ra ≤ 106), Stefan number (0.2 ≤ Ste ≤ ∞), melting point temperature of the core (0.05 ≤ θf ≤ 1), the concentration of the NEPCM particles (0% ≤ ϕ ≤ 5%), radius ratio (1.67 ≤ Rr ≤ 2.5), eccentricity (− 0.67 ≤ Ec ≤ 0.67), Darcy number (10−4 ≤ Da ≤ 10−1), porosity (0.3 ≤ e ≤ 0.9) and interface heat transfer coefficient (1 ≤ H ≤ 1000). The results show that the dimensionless temperature of fusion (θf) plays the main role in the improvement in NEPCM on the heat transfer process.

The laminar two-dimensional mixed convection in a trapezoidal enclosure with a rotating inner circular cylinder and a sinusoidal bottom wall is studied numerically. The fluid inside the enclosure is a CuO–water nanofluid layer in the top space of it, while the bottom space includes a CuO–water nanofluid saturated with a porous medium. Both the right and left sidewalls are assumed adiabatic, while the bottom and the top walls of the enclosure are maintained, respectively, at the hot and cold temperatures. The dimensionless governing equations are expressed for velocity and temperature formulation and modeled by using COMSOL code based on the Galerkin finite element method. Parametric studies on the effects of various significant parameters such as Rayleigh number, Darcy number, the inner cylinder radius, the porous layer thickness, the angular rotational velocity, the solid volume fraction and the number of undulations on the flow and thermal fields together with the heat transfer rate have been performed. The highest value of the stream function for (Ra = 103 and Ra = 105) is seen at (R = 0.2 and S = 0.2). The same thing is observed, when the bottom wall is considered wavy. For (Ra = 103 and N = 0) and (0.5 ≤ S ≤ 0.8), it can be seen that as the inner cylinder radius increases from (R = 0.1) to (R = 0.3), the stream function values increase continuously. It is found that the average Nusselt number increases as the Rayleigh and Darcy numbers, the solid volume fraction, inner cylinder radius and the angular rotational velocity of the cylinder increase, while it decreases as the porous layer thickness and the number of undulations increase. Comparisons with previously published numerical works are performed, and good agreements between the results are observed.

This study investigates the effect of Prandtl number on the natural heat convection inside a square cavity filled with two layers of Ag/water nanofluid-saturated porous medium and non-Newtonian fluid separated by a sinusoidal vertical interface. The left wall, which is adjacent to the nanofluid porous layer, has a relatively hot temperature, while the right wall is cold. Other walls of the cavity are thermally insulated. All cavity walls are impermeable except for the sinusoidal vertical interface located between the two layers. Galerkin finite element method was used to numerically solve the governing differential equations. The study examined the effects of power-law index (0.6

Taking a more complex engineering geometry into account, magnetohydrodynamic natural convection of nanofluid (Cu-water) in a wavy walled enclosure having a circular hot cylinder inside is investigated by employing Galerkin-weighted residual formulation. In order to investigate the flow and heat transfer characteristics from several perspectives and increase the ability of adaptation to various engineering applications, the influences of the Hartmann number, Ha, Rayleigh number, Ra, and nanoparticle concentration are examined in detail. In addition to that, heat generation and heat absorption situations are also considered within the present work, which are simulated by a heat coefficient in a range of −10 ≤ q ≤ +10. The results revealed that increasing Ha has an insignificant effect on Nusselt number, Nu, at low Ra, however, it significantly pulls Nu down up to 33% for higher Ra, because of restricting convection. It is found that the heat coefficient, q, has a remarkable impact on Nu at low Ra, while its significance is diminished when Ra is increased. For q 0) conversely reduces Nu up to 48%. Besides, variation in heat coefficient does not considerably affect the improvement impact of nanoparticles.

Heatlines visualization of natural convection heat transfer in trapezoidal-shape cavity filled with nanofluid (TiO2-water) and divided by horizontal porous media partition has been studied numerically using finite element method. Non-uniform temperature is applied at the bottom wall and cold temperature applied to the top wall while two inclined vertical walls were insulated. In this work the influence of many parameters such as, Rayleigh number (103≤Ra≤105), partition porous thickness (0.05≤TH≤0.6), partition porous position (0.15≤HD≤0.75), Darcy number (10−5≤Da≤10−1) and volume of fraction (0≤φ≤0.1). Results are exhibited by means heatlines, isotherms, streamlines rather than local and average Nusselt number. The results show that at a constant Rayleigh number equal to (105) and thickness of porous partition (0.1), the percentage enhancement of heat transfer along the bottom wall with the addition of nanoparticles (ϕ=0.1) is greater than enhancement with the base fluid. While, the maximum value of the percentage enhancement of heat transfer is (4.22%) occurred at porous position equal to 0.5. Also, for a constant position of porous partition (HD=0.5) the percentage enhancement of heat transfer with volume fraction of nanoparticles (0.1) along the bottom wall decreases as the thickness of porous partition and Rayleigh number increased. It can be noticed that there is a good agreement between the current study and those of Chamka and Ismeal, with an approximated absolute error 1.829%.

The natural convection of heat transfer is presented numerically using a temperature gradient from the hot inner corrugated cylinder. Different inner corrugated numbers located inside a cooled wavy-walled enclosure filled with two layers were simulated. The right layer is filled with Ag nanofluid and the left with a fully saturated porous media with similar nanofluid. The porous media with the nanofluid was modeled using the Darcy–Brinkman model. The main dimensionless equations are solved numerically using the method of Galerkin. This study considered the following dimensionless parameters: the Rayleigh number (106 ≥ Ra ≥ 103), the Darcy number (0.1 ≥ Da ≥ 0.00001), the vertical location (0.2 ≥ H ≥ −0.2), the number of sinusoidal inner cylinders (6 ≥ N ≥ 3), fraction volume of the nanoparticle (0.1 ≥ ⱷ ≥ 0), and porous layer thickness (0.8 ≥ XP ≥ 0.2). Results suggest that to increase the fluid flow strength, the internal sinusoidal cylinder must move upward to increase the fluid flow strength. Increasing the thickness of the porous layer reduces the average heat transfer. Results indicate further that highest fluid flow strength occurs at N = 4 when the inner sinusoidal cylinder moves downward vertically.