No abstract

The mixed convection from a heated sphere for an arbitrary flow incident angle (θ) at low to moderate Reynolds numbers () and Richardson numbers () is studied by an immersed boundary method, thereby investigating the influence of different flow incident angles () on the buoyancy flow and heat transfer. The numerical method is validated by comparing the results with the simulation results of pure forced convection as well as those of mixed convection with assisting flow (0 o flow incident angle) published in the literature. Extensive simulations for a wide range of different incident flow angles have been performed. New correlations are obtained for the overall Nusselt number (Nu) in terms of θ and Ri, and Re, showing a quadratic decrease in Nu with respect to θ only for (aiding and cross flow) and a half bell-shaped decrease in Nu for (opposed flow). The combined treatment of mixed convection for the completely upward flow, cross flow, and completely downward flow (i.e. at incident angle 0°, 90° and 180°, respectively) was achieved showing almost linear relationships between the heat transfer rates and Ri for .

A three-dimensional immersed boundary method (IBM) is applied for the solution of the thermal interactions between spherical particles in a viscous Newtonian fluid. At first, the free convection of an isolated isothermal sphere immersed in a viscous fluid is analyzed as a function of the Grashof number. A new correlation for the heat transfer rate from a single sphere is obtained, which is valid in the ranges 0.5 ≤ Pr ≤ 200 and 0 ≤ Gr ≤ 500. Second, the free convection heat transfer rate from pairs of spheres (bispheres) and from small spherical clusters immersed in air (Pr = 0.72) is investigated using this numerical technique. For bispheres, their orientation and the thermal plume interactions within a range of interparticle distances may cause the enhancement of the heat transfer rate above the values observed for two isolated spheres. For the simple triangular particle clusters, where the particles are in contact, it was observed that the average heat transfer rate per sphere decreases with the increased number of spheres in the cluster.

The understanding of its shape on the movement of microparticles and nanoparticles is crucial to the development of technologies of using these particles in drug delivery systems. The effect of shape on nanoparticles used in drug delivery, in particular, is a very active area of experimental investigation. Also, the determination of the drag force on nanoparticles of different shapes is very important in designing effective nanoparticle-mediated therapies. One of the common shapes of nanoparticles is rod. In this study we present a resolved discrete particle method (RDPM), which is also called the Direct Numerical Simulation (DNS), to investigate the effect of rod shapes on the drag force in a vicious fluid as compared to other particle shapes such as a sphere and a cone. These particles are assigned the same volume and placed in contact with the bottom wall in a simple shear flow. Their drag forces are computed numerically; it is found that the particle shape has a significant effect on the drag forces. In the case of a spherical particle, our results agree very well with the analytical results found in the literature. The drag force on a rod at different orientations and the motion of two rod-shaped particles of identical volume are in a shear flow are also examined. The motion of a rod-shaped particle and a cone-shaped particle in a shear flow at low Reynolds number is also compared.

A novel numerical technique that utilizes a three-dimensional Immersed Boundary Method (IBM) to solve the thermal interactions between spherical particles in a fluid is developed. At first, the natural convection of an isolated isothermal sphere immersed in a viscous fluid is analyzed and a new correlation for the heat transfer rate from a single sphere is obtained for 0.5≤Pr≤200 and 0 ≤ Gr ≤500. Secondly, the free convection heat transfer rate of a pair of spheres (bi-sphere) and spherical clusters immersed in air (Pr=0.72) were investigated using this numerical technique. The interactions depend on the separation distance between the spheres. It was observed that an increase in the separation of two spheres in tandem or side-by-side within a certain range may enhance the average heat transfer rate, when the interparticle distance is more than five radii. The average heat transfer rate of a cluster of touching, identical spheres with the same Grashof number was found to decrease as the number of spheres increased in the cluster.