The Brownian motion of the nanoparticles in nanofluid is one of the potential contributors to enhance effective thermal conductivity and the mechanisms that might contribute to this enhancement are the subject of considerable discussion and debate. In this paper, the mixing effect of the base fluid in the immediate vicinity of the nanoparticles caused by the Brownian motion was analyzed, modeled, and compared with existing experimental data available in the literature. CFD was developed to study the effect of wall/nanoparticle interaction on forced convective heat transfer in a tube under constant wall temperature condition. The results showed that the motion of the particle near the wall which can decrease boundary layer and the hydrodynamics effects associated with the Brownian motion have a significant effect on the convection heat transfer of nanofluid.
Fluid heating and cooling play significant roles in a lot of industrial processes such as refinery, petrochemical, power stations, and electronics [
Because of these suitable properties and the excellent stability of these fluids, nanofluids present a promising alternative to traditional heat transfer fluids in a wide range of applications. However, the precise mechanisms that contribute to the observed enhancement are not currently well understood and no widely accepted explanations have been identified. As a result, in order to fully understand the mechanisms that govern the enhancement of these nanofluids and optimize the thermophysical properties, the mixing effect of the base fluid in the immediate vicinity of the nanoparticles caused by the Brownian motion of the nanoparticles was analyzed, modeled, and compared with existing experimental data available in the literature. Due to the lack of experimental tools required to isolate the effect of each mechanisms, many investigations have focused only on the Brownian motion effects of the nanoparticles, using either numerical simulation or experimental techniques [
In this research, the convective heat transfer near the wall region of the tube flow containing water and Al2O3 nanofluid under a constant temperature was simulated using the Computational Fluid Dynamics (CFD) tools. Al2O3 nanoparticle with average diameters of 27 nm was used. The effects of the nanoparticle Brownian motion on the convective heat transfer coefficient were investigated near the wall.
Visual observations of Brownian motion indicate that each nanoparticle can be modeled as having a local periodic motion within the suspension, as shown in Figure
Trajectory of nanoparticle.
The influence range for this local periodic motion model can be calculated by solving the governing equations of the convection caused by the motion of Al2O3 nanoparticles in three dimensions. Figure
Geometry and boundary condition of system.
The surface of nanoparticles was assumed to be adiabatic, and wall 2 was supposed to be a heated surface, with a constant temperature of 24.1°C, as shown in Figure
To model fluids and heat transfer, the two-dimensional computational grids consisting unstructured cells were used separately in some cases. It has been proven that the unstructured cell technology is a significant improvement in terms of meshing flexibility and simulation time to perform a complete simulation. The mesh size surrounding the particle is too fine to predict the variation of pressure, velocity, and temperature with high accuracy, but it has normal size near the walls to increase the calculation speed (Figure
Mesh model of base case.
In Figure
Transient CFD code was prepared based on the SIMPLE algorithm and second order upwind method allows calculating with Cartesian and cylindrical coordinates. Modeling of the Brownian motion via CFD requires geometry specification through identifying the computational grid, numerical solution strategy, and specification conditions.
The base fluid phase considered here was assumed to be Newtonian with laminar flow and to have constant physical properties except heat capacity and conductivity coefficient. Nanoparticle periodic motion model and the governing equations (continuity, momentum, and energy) for the convection caused by nanoparticles motion in two-dimensional form can be determined as shown below:
In the first case, To show the effect of nanoparticle interaction with wall in fluid flow, first the model was performing without nanoparticle and then the nanopartical interaction effect was studied. The boundary condition was defined as mentioned above. Figure
Case 1, temperature gradient (time = 0.001 S).
In this case, a nanoparticle was located near wall 2 at the same distance from the inlet and outlet. The particle moves through fluid in
Case 2, velocity, temperature and pressure gradient, and mesh model (time = 0.001 S).
The pressure field at the top of Figure
Figure
Case 2, convective heat transfer coefficient on walls 1 and 2.
Increase in convective heat transfer coefficient near the wall 2 shows the effect of nanoparticle Brownian motion. This motion causes reduction in heat and fluid boundary layer near the wall. Furthermore, the microconvection of vibration motion leads to increasing the convective heat transfer coefficient, as obviously seen in the figure.
In this case, the effect of two adjacent nanoparticles, instead of one nanoparticle was studied. The distance between two particles is 30 nm. The boundary and initial conditions are the same as Case 1.
Figure
Case 3, velocity, temperature, pressure gradient, and mesh model (time = 0.001 S).
Compared with the results and heat transfer rate related to the model of Figures
The model of two adjacent nanoparticles clarifies how the induced microconvection influences the convective heat transfer coefficient of base fluid. Also, the modeling of two adjacent nanoparticles clarifies how the induced microconvection effects the heat transfer capability.
Figure
Case 3, convective heat transfer coefficient on walls 1 and 2.
When two nanoparticles are close to each other, the influence on the area will be more than twice due to the hydrodynamic interaction. This, in turn, increases the heat transfer capacity of the nanofluid at macroscale.
This paper discussed the Brownian motion effect as one of the main factors for enhancing forced convective heat transfer coefficient of nanofluids. The corresponding temperature, pressure, and velocity fields were simulated using CFD model and a finite-difference algorithm. The simulations for single and adjacent nanoparticles were discussed in detail. The results clearly indicated that microconvection/mixing induced by the Brownian motion of nanoparticles could significantly affect the macroconvective heat transfer capability of the nanofluids. This information is especially interesting when accompanied with other works on the variation of the viscosity of nanofluids, due to the Brownian motion and hydrodynamic interaction between nanoparticles [
Mass, kg
Displacement, m
Time, s
Angular velocity, m/s
Initial location, m
Density, kg/m3
Velocity components, m/s
External forces, N
Static pressure, N/m2
Specific heat capacity
Expansion coefficient
Viscosity
Diffusion matrix
Temperature, k
Thermal conductivity, W/m·k
Heat flux, W/m2.