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7. Conclusions

Figure 16 7. Conclusions

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In the above equations, the following dimensionless parameters are used [24, 22]: 2. Governing equations for laminar nanofluids
In the above equations, the following dimensionless parameters are used [24, 22]: 2. Governing equations for laminar nanofluids
To calculate the local Nusselt number along the lower wall, the following relation is used [22]:
To calculate the local Nusselt number along the lower wall, the following relation is used [22]:
Total Nusselt number on the surface of each rib is calculated by To calculate the local friction factor along the lower wall, the following relation is used:
Total Nusselt number on the surface of each rib is calculated by To calculate the local friction factor along the lower wall, the following relation is used:
The average friction factor along each horizontal part of the lower wall can be calculated as
The average friction factor along each horizontal part of the lower wall can be calculated as
A2-D microchannel with four same rectangular ribs was selected for the analysis. Investigation of heat transfer and fluid dynamics, including the study of velocity, thermal field, and friction effects, was performed in different angles of inclination. The schematic of the investigated microchannel is illustrated in Figure 1. The microchannel is 1350 um long and 90 um high. The length of the lower wall of the microchannel was divided into three parts. The temperature of 290.5 K was set at the inlet. The temperature of 305.5 K was considered in the middle part of the microchannel with the length of 450 um, consisting of four ribs. The channel was insulated on the total length of the upper wall (L,) as well as on the length of 450 um of both left and right sides of the lower wall. Rectangular ribs in all the studied cases were considered to have a pitch, width, and height of 90, 15, and 30 um (one-third of the microchannel’s height), The thermal expansion coefficient can be obtained from the suggested formula by Khanafer et al. [32] and Abouali and Ahmadi [33]:
A2-D microchannel with four same rectangular ribs was selected for the analysis. Investigation of heat transfer and fluid dynamics, including the study of velocity, thermal field, and friction effects, was performed in different angles of inclination. The schematic of the investigated microchannel is illustrated in Figure 1. The microchannel is 1350 um long and 90 um high. The length of the lower wall of the microchannel was divided into three parts. The temperature of 290.5 K was set at the inlet. The temperature of 305.5 K was considered in the middle part of the microchannel with the length of 450 um, consisting of four ribs. The channel was insulated on the total length of the upper wall (L,) as well as on the length of 450 um of both left and right sides of the lower wall. Rectangular ribs in all the studied cases were considered to have a pitch, width, and height of 90, 15, and 30 um (one-third of the microchannel’s height), The thermal expansion coefficient can be obtained from the suggested formula by Khanafer et al. [32] and Abouali and Ahmadi [33]:
The FLUENT commercial code was used to solve the partial differential equations that govern to the flow. The software applies the finite volume method, which is a particular case of the residual weighting method. This procedure is based on dividing the computational domain respectively. In all cases, inclination angle between the microchannel and the horizon line was changed from 0° (horizontal case) to 90° (vertical case). A Reynolds number equal to 50 was selected to investigate the laminar flow, and Richardson number was varied between 0.1 and 10. Water as the base fluid was mixed with 0, 2, and 4% volume fractions of Cu nanoparticles (y = 0.00, 0.02, and 0.04).
The FLUENT commercial code was used to solve the partial differential equations that govern to the flow. The software applies the finite volume method, which is a particular case of the residual weighting method. This procedure is based on dividing the computational domain respectively. In all cases, inclination angle between the microchannel and the horizon line was changed from 0° (horizontal case) to 90° (vertical case). A Reynolds number equal to 50 was selected to investigate the laminar flow, and Richardson number was varied between 0.1 and 10. Water as the base fluid was mixed with 0, 2, and 4% volume fractions of Cu nanoparticles (y = 0.00, 0.02, and 0.04).
Figure 2. Local Nusselt number variation—comparison with the work of Salman et al. [38]. 5.2. Comparison with numerical study of nanofluid
Figure 2. Local Nusselt number variation—comparison with the work of Salman et al. [38]. 5.2. Comparison with numerical study of nanofluid
A structured, nonuniform grid has been chosen for the discretization of the computational domain. A more refined grid was applied near the walls, where temperature and velocity eradients are sensitive. Grid independency of the computational domain was tested by using various grid distributions. Average Nusselt number and dimensionless pressure drop for each number of grids are shown in Figure 4(A, B) , from which a grid of 60 x 900 was chosen for all the simulation cases.
A structured, nonuniform grid has been chosen for the discretization of the computational domain. A more refined grid was applied near the walls, where temperature and velocity eradients are sensitive. Grid independency of the computational domain was tested by using various grid distributions. Average Nusselt number and dimensionless pressure drop for each number of grids are shown in Figure 4(A, B) , from which a grid of 60 x 900 was chosen for all the simulation cases.
Figure 5. (A) Streamlines and (B) Isotherm contours for 4% volume fraction and y = 90°. The isotherm contours and streamlines for y = 90°, Re =50, different Richardson numbers, and volume fraction of 4% are shown in Figure 5 (A, B). After the microchannel’s entry, the flow attains a fully developed hydrodynamic regime. When the fluid reaches the ribs, its direction is diverted and will result in an increased vertical component of the velocity. Yet, increased Richardson number does not lead to any change in the streamlines’ variations. In case of isotherms’ illustrations along the microchannel, once fluid with temperature of T,, arrives in the rib-roughened areas with T,(surface temperature), temperature of fluid decreases, and heat is transferred between the rib-roughened surfaces and fluid. Along the microchannel, ribs function as a mixer and reduce the temperature gradient between the surface and the fluid, and afterwards, the rate of heat transfer increases. These variations in heat transfer improve as the inclination angle (y) or Richardson number increases. The first influential factor is the resultant from the gravity and variations in its components—perpendicular to and in line with the flow fluid—along the microchannel. Once y increases from 0 to 90°, the terms of diffusion and advection in natural convection heat transfer strengthen, which leads to isothermal line variations.
Figure 5. (A) Streamlines and (B) Isotherm contours for 4% volume fraction and y = 90°. The isotherm contours and streamlines for y = 90°, Re =50, different Richardson numbers, and volume fraction of 4% are shown in Figure 5 (A, B). After the microchannel’s entry, the flow attains a fully developed hydrodynamic regime. When the fluid reaches the ribs, its direction is diverted and will result in an increased vertical component of the velocity. Yet, increased Richardson number does not lead to any change in the streamlines’ variations. In case of isotherms’ illustrations along the microchannel, once fluid with temperature of T,, arrives in the rib-roughened areas with T,(surface temperature), temperature of fluid decreases, and heat is transferred between the rib-roughened surfaces and fluid. Along the microchannel, ribs function as a mixer and reduce the temperature gradient between the surface and the fluid, and afterwards, the rate of heat transfer increases. These variations in heat transfer improve as the inclination angle (y) or Richardson number increases. The first influential factor is the resultant from the gravity and variations in its components—perpendicular to and in line with the flow fluid—along the microchannel. Once y increases from 0 to 90°, the terms of diffusion and advection in natural convection heat transfer strengthen, which leads to isothermal line variations.
Figure 6. Dimensionless velocity contours for 2% volume fraction, different inclination angles, and Ri = 10: (A) along the flow and (B) perpendicular to the flow. 6 (A, B). The increasing y exerts a significant effect on fluid flow behavior and heat transfer The velocity components (perpendicular to and along with the flow) vary by flowing the fluid along the microchannel, because of the ribs. Increased inclination angle intensifies these variations. The outcomes showed that the perpendicular velocity component exhibited more variation, which causes vortexes and reverse flows in the flow field. Consequently, this velocity component is deemed more effective, because its intensification can improve flow mixing and rate of heat transfer.
Figure 6. Dimensionless velocity contours for 2% volume fraction, different inclination angles, and Ri = 10: (A) along the flow and (B) perpendicular to the flow. 6 (A, B). The increasing y exerts a significant effect on fluid flow behavior and heat transfer The velocity components (perpendicular to and along with the flow) vary by flowing the fluid along the microchannel, because of the ribs. Increased inclination angle intensifies these variations. The outcomes showed that the perpendicular velocity component exhibited more variation, which causes vortexes and reverse flows in the flow field. Consequently, this velocity component is deemed more effective, because its intensification can improve flow mixing and rate of heat transfer.
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Finite Volume MethodsModeling and SimulationNanotechnologyComputational Fluid Dynamics (CFD) modelling and simulationElectronic Cooling SystemElectronics CoolingElectronic cooling
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