This research presents a numerical investigation of the flow field and heat transfer of a Visco-plastic fluid, The Bingham-Papanastasiou model is used to examine the flow field and forced convection heat transfer of a Viscoplastic fluid between two concentric cylinders with a wavy inner surface. By focusing on this particular configuration (wavy inner cylinder shape), where the inner surface exhibits as the hot wall while the outer surface is considered as the cold wall. This investigation is numerically achieved by using the Comsol Multiphysics, which is based on the finite‐volume method, employing Galerkin’s method for solving the governing equations. The parameters studied in this research are expressed with the following values: r/ R=1/3, Reynolds number (Re=1, 10, 50), and undulation number (nu=0, 6, 12, 24). Increasing the inertia parameter results in a higher intensity of thermal buoyancy, positively influencing heat transfer, particularly at Re=50. Furthermore, the acceleration of flow within the investi-gated space improves the hydrodynamic behavior, facilitating the exchange of thermal energy between the hot and cold walls. Additionally, it has been discovered that an undulating shape with a specific number of undulations (nu=6) maximizes hydrothermal performance within the investigated volume. The presence of these undulations enhances fluid mixing and dis-rupts the formation of stagnant regions ,which leading to improved heat transfer.

In process engineering as chemical and biotechnological industry, agitated vessels are commonly used for various applications; mechanical agitation and mixing are performed to enhance heat transfer and improve specific Physico-chemical characteristics inside a heated tank. The research subject of this work is a numerical investigation of the thermo-hydrodynamic behavior of viscoplastic fluid (Casson–Papanastasiou model) in a stirred tank, with introducing a new anchor impeller design by conducting some modifications to the standard anchor impeller shape. Four geometry cases have been presented for achieving the mixing process inside the stirred vessel, CAI; classical anchor impeller, AI1; anchor impeller with added horizontal arm blade, AI2 and AI3 anchor impeller with two and three added arm blades, respectively. The investigation is focused on the effect of inertia and plasticity on the thermo-hydrodynamic behavior (flow pattern, power consumption, and heat transfer) by varying the Reynolds number (Re = 1, 10, 100, 200), Bingham number (Bn = 1, 10, 50), in addition to the effect of geometry design in the overall stirred system parameters. The findings revealed an excellent enhancement of flow pattern and heat transfer in the stirred system relatively to the increase of inertia values. Also, an energy reduction has been remarked and the effect of anchor impeller shape. AI3 geometry design significantly improves the flow pattern and enhances heat transfer by an increased rate of 10.46% over the other cases.

The fluid flows and power consumption in a vessel stirred by anchor impellers are investigated in this paper. The case of rheologically complex fluids modeled by the Bingham-Papanastasiou model is considered. New modifications in the design of the classical anchor impeller are introduced. A horizontal blade is added to the standard geometry of the anchor, and the effect of its inclination angle (α) is explored. Four geometrical configurations are realized, namely: α = 0°, 20°, 40°, and 60°. The effects of the number of added horizontal blades, Reynolds number, and Bingham number are also examined. The obtained findings reveal that the most efficient impeller design is that with (case 4) arm blades inclined by 60°.This case allowed the most expansive cavern size with enhanced shearing in the whole vessel volume. The effect of adding second horizontal arm blades (with 60°) gave better hydrodynamic performance only with a slight increase in power consumption. A significant impact of Bingham number (Bn) was observed, where Bn = 5 allowed obtaining the lowest power input and most expansive well-stirred region.

Several industrial fields require mixing and mechanical agitation processes. This operation is mainly used to enhance heat and mass transfer inside stirred tank systems and improve the degree of homogeneity to obtain a high-quality final product. The main goal of this research paper is to analyze the thermal and hydrodynamic behavior of non-Newtonian nanofluid (Bingham–Papanastasiou–Al₂O₃) inside a symmetrically stirred tank. A 3D numerical study has been conducted for a stationary laminar flow inside a symmetric cylindrical vessel under influencing parameters, including the inertia parameter ($Re=1, 20, 100$) and the volume fraction of nanoparticles ($\mathsf{Ø}=0.02, 0.06, 0.1$) with different geometric configurations, has been introduced into the stirring system. According to the findings, with high inertia ($Re=100$), the heat transfer inside the stirred tank is enhanced. Furthermore, increasing the nanoparticle fraction volume had a significant impact on the acceleration of heat transfer along the stirred vessel. It has been also found that the geometric configuration of an anchor with added arm blade (Case 2) is more efficient compared with the rest of the anchor agitator.

Numerical investigation of mixed convective in a vented square cavity with fin. The horizontal walls are adiabatic, while the left and right walls are at hot and cold temperatures, respectively. The fluid inlet to the cavity from the lower left open area, and exit from the upper right open area. In this study, a finite element scheme is employed. The analysis is done for specific Prandtl number, Reynolds number, fin length, Richardson number, and the location of the fin. The finding indicates that the increases when high the location of the fin is, the increase at the maximum height of this fin location is estimated to be 17% due to an increase in the area of fluid flow on the hot wall caused by rising convective. The highest heat transfer occurs when the fin length is equal to 0.6 at the location.