In the present work, free convection heat transfer of nanofluid in a closed square cavity with a hot circular barrier has been investigated. The location of the circular obstacle and the walls are fixed. The governing equations are solved by finite volume method and using simple algorithm. The purpose of this work is to study the effect of Rayleigh number and adding nanoparticles, taking into account the change in the dimensions of the circular barrier in the cavity, as well as taking into account different density approximation models for modeling the heat transfer of the nanofluid in the cavity. The most important results showed that heat transfer along the walls increased with the increase in the dimensions of the circular barrier, the Rayleigh number and the volume fraction of nanoparticles. Also, the most important results showed that with the increase of the Rayleigh number, the average Nusselt number along the walls and the temperature values increase, in addition to the effect of considering different models for approximating the density in modeling of nanofluid free convection heat transfer in cavity by comparing the thermal parameters It showed that Bozinsk's approximation model provides more favorable and accurate results for investigating free convection heat transfer.

Mixed convection of Cu-Water nanofluid is studied numerically in a shallow inclined enclosure by applying lattice Boltzmann method. The D2Q9 lattice and internal energy distribution function based on the BGK collision operator are used in order to develop the thermal flow field. The enclosure's hot lid has the constant velocity of U0 while its cold lower wall has no motion. Moreover, sidewalls are taken in to account as adiabatic ones. At 3 modes of convection heat transfer (free convection, force convection and mixed convection), the effects of volume fraction and inclination angle of enclosure are studied for different values of Reynolds number as equal to 10 and 100. Comparison of achieved results as like the streamlines, isotherms and profiles of velocity and temperature versus pervious available ones, implies the appropriate agreement. It is seen that more amount of volume fraction and enclosure inclination angle at the state of free convection would correspond to higher Nusselt number. The incomes of present work show the suitable performance of lattice Boltzmann method in order to simulate the nanofluid mixed convection in an inclined enclosure.

Thermal instability in a low Prandtl number nanofluid in a porous medium is investigated by using Galerkin weighted residuals method for free-free boundaries. For porous medium, Brinkman-Darcy modelis applied. The model used for the nanofluid describes the effects of Brownian motion and thermophoresis. Linear stability theory based upon normal mode analysis is employed to find the expression for stationary and oscillatory convection. The effects of Prandtl- number, Darcy number, Lewis number and modified diffusivity ratio on the stationary convection are investigated both analytically and graphically. The results indicated that the Prandtl and Darcy numbers have a destabilizing effect while the Lewis number and modified diffusivity ratio have a stabilizing effect for the stationary convection.

In this article, the correlated free convection heat transfer in a rectangular cavity containing nanofluid and with a triangular solid area was investigated numerically.The governing equations written in terms of the primitive variables were solved numerically using the finite volume method while the velocity and pressure fields were coupled using the SIMPLER algorithm. Correlated characteristics such as the thickness of the triangular solid area (dimensions of the triangular solid area) and the ratio of the thermal conductivity coefficient of the triangular solid area to the nanofluid on the flow and free convection heat transfer cavity were investigated. Studies have been carried out for the Rayleigh number Ra  105, and constant volume fraction ϕ=0.02 for the ratio of thermal conductivity coefficients Kr = 0.1, Kr = 1 and Kr = 10,as well as for different dimensions of the triangular solid area.The results showed that with the increase in the ratio of the dimensions and thickness of the triangular solid region, as well as the ratio of the conductivity coefficient in a constant Rayleigh number, the temperature and velocity of the nanofluid increase. Also, with the increase in the ratio of the dimensions of the triangular solid area and the ratio of the conductivity coefficient, the values of the average Nusselt numbers increase along the walls, and more heat transfer passes through the solid-fluid interface.

In this research، validity of temperature-independent thermophysical properties assumption of water-Al203 nanofluid in natural convection problems within the enclosures is investigated. The numerical results are obtained utilizing an in-house finite volume code based on the SIMPLE algorithm. In order to do the validation the numerical results and those of existing correlations are compared. In order to evaluate the thermal performance of the enclosure، the average Nusselt number on the hot side wall in both temperature-independent and dependent cases is compared Results show that، in the all considered solid volume fractions، the difference in the Nusselt number in the case of temperature-independent properties is less than 10 percent in comparison with the case in which the properties are temperature-dependent when temperature difference is less than 5 ○C. As the temperature increases، the difference between Nusselt number in both cases increases and the effect of increase in solid volume fraction is to increase this difference. Results also show that the difference between these two cases is dependent solely on temperature differences between the hot and cold walls regardless of the temperature they have.

In this paper، the natural convection of water-Al2O3 nanofluid in a square enclosure exposed to a magnetic field is numerically investigated. The enclosure is bounded by two isothermal vertical walls at different temperaturesof Th and Tc. The two horizontals walls of the enclosure are thermally insulated. A vertical plate (membrane separator) with a negligible thickness and a variable height is located in the middle of the chamber. Discretization of the governing equations are achived through a finit method and are solved using the SIMPLE algorithm. Based on the results of the numerical solution، the effects of the relevant parameters such as the dimensionless height of the membrane separator، Rayleigh number، the solid volume fraction and the Hartmann number on the flow field and the heat transfer rate are investigated. The results show that the heat transfer rate decreases with an increase of the dimensionless height of the membrane separator and an increase of the Hartmann number. The heat transfer rate، however، increases as the Rayleigh number increases. Depending on the Rayleigh number، the thermal performance of the enclosure is either improved or deteriorated as the solid volume fraction is increased.

In this study the free convection heat transfer of a nanofluid, including water and nanoparticles suspended in a square cavity is simulated numerically for a laminar flow. Open source framework i.e. OpenFOAM was used to develop the equations and make changes in the desired terms such as relative velocity between the nanoparticles and the base fluid. To achieve the purpose of the research and to ensure the accuracy of the numerical algorithms used in this framework, at first the free convection inside the cavity was investigated using two-phase mixture model and the results of the present study were compared with the results presented in the literature. Then, with the help of existing mathematical equations, important parameters in simulating the forces acting on nanoparticles in the free convection inside the cavity were studied and as a result, the forces that had a significant impact were selected as the most important and corrected relative velocity was entered in the continuity, momentum, heat transfer and continuity equation of the second phase (nanoparticles) as a parameter called JP. This simulation was performed using the PIMPLE algorithm (SIMPLE + PIZO). To consider free convection, nanofluid’s density changes with Boussinesq relationship. The mixture two-phase model has used for modeling with higher speed and more accuracy and also effective thermophysical properties of nanofluid, related to JP parameter have been used in order to increase the accuracy of work. As a result, the effect of these forces on different conditions was investigated.

The fluid flow and heat transfer in lid-driven enclosures filled with Cu-water nanofluid is numerically investigated. The moving vertical walls of the enclosure are maintained in a constant temperature, while the horizontal walls are insulated. The hybrid scheme is usedto discretize the convection terms and SIMPLER algorithm is adopted to couple the velocity field and pressure in the momentum equations. The effect of moving direction of walls on mixed convection is studied for various Ri numbers, aspect ratios and volume fractions of nanoparticles. For this purpose, vertical walls are moved in two directions: one, force convection aids to free convection and two, it interacts to free convection. It is observed that the direction of moving wall mainly affected the flow field, temperature gradient and heat transfer. In addition, by increasing the volume fraction of nanoparticles, the variation of average Nusselt number on the hot wall, as an index of heat transfer rate, is linear in two cases.

In the present study , we have investigated the external free convection of a nanofluid near a vertical heated surface embedded in a saturated porous medium using the thermal non - equilibrium assumption. The vertical surface has a linear temperature distribution with a uniform mass suction or injection. Assuming the Brownian motion and thermophoresis as the primary driving mechanisms of free convection of the nanofluid , suitable volume averaged equations are employed. We have also followed similarity solution method for transforming the governing equations in to the ordinary differential equations. The new set of ordinary equations is solved numerically by the Shooting method and the flow and temperature fields are determined completely. The obtained numerical results are employed for calculating the Nusselt numbers for both the solid and liquid phases in the physical domain. Moreover , the Sherwood number for the nanoparticles is determined over a wide range of parameters.

This paper presents an insight into the boundary layer of free convection and heat transfer of nanofluids over a vertical plate at very low and high Prandtl number. Suitable similarity variables are used to convert the governing systems of nonlinear partial differential equations of the flow and heat transfer to systems of nonlinear ordinary differential equations which are solved using multi-step differential transformation method. The approximate analytical solutions are verified with numerical solutions. From the parametric studies, it is observed that the velocity and temperature of the nanofluid decreases and increases, respectively as the Prandtl number and volume-fraction of the nanoparticles in the base fluid increase. Also, the decrease in velocity and increase in temperature are highest in lamina shaped nanoparticle followed by platelets, cylinder, bricks and sphere shaped nanoparticles, respectively. Using a common base fluid to all the nanoparticle type, it is observed that the decrease in velocity and increase in temperature are highest TiO2 followed by CuO, Al2O3 and SWCNTs nanoparticles, in that order. The present study will enhance the understanding of free convection boundary-layer problems.