Increasing Richardson Number Research Articles

Lid driven flow and heat transfer due to various positions of slit in a square cavity: FEM approach

A detailed analysis of flow and heat transfer due to moving slit within the various positions of the square cavity is discussed. The slit is strategically positioned and examined at three distinct locations within the square cavity i.e. left, middle and right. Constraints of the square cavity are defined for horizontal and vertical walls. The top horizontal wall is considered to be adiabatic while the other three walls of the cavity are cold. The upper surface of slit is heated and movable towards the left side of the square cavity while the other three walls are immovable and cold. The fluid flow dynamics and heat transfer within the enclosed cavity are governed by fundamental principles of mass, momentum and energy conservation. These governing principles manifest as intricate mathematical equations, specifically nonlinear partial differential equations accompanied with boundary conditions. The key parameters under consideration include the Reynolds number (250≤Re≤1500) and Richardson number (0.01≤Ri≤5) at a fixed Prandtl number (Pr=6.2). These parameters are analysed through variations in velocities, temperature profiles, isotherms and streamlines. In the computational framework, the momentum and temperature equations are addressed through quadratic interpolation, while linear interpolation is applied to handle the pressure equation. The numerical solution, utilizing Newton's technique and the PARADISO solver, is rigorously validated against existing research methodologies, establishing its methodological reliability. Higher Reynolds numbers shift the primary vortex towards the middle and create corner recirculation zones, more uniform heat distribution, while higher Richardson numbers increase buoyancy forces, reducing isotherm contours and affecting heat distribution. The local Nusselt number increases with the increase in Reynolds numbers but shows small changes with the increase in Richardson number. The value of Nusselt number decreases as the position of slit changes from left to right.

Influence of solid cylinders on fluid flow and thermal analysis in a curved channel with constant magnetic field

The current study explores the numerical simulation of constant mixed convection heat transfer and fluid flow within a channel, driven by the inlet velocity. The investigation focuses on a curved irregular channel where the presence of three differently sized circular obstacles introduces an unpredictable element to the heat transfer process. For the two-dimensional physical scenario, mathematical equations are formulated to analyze velocity and temperature. Employing appropriate dimensional variables, the coupled partial differential equations are transformed into dimensionless form. Subsequently, the Finite Element Method (FEM) is employed to simulate the results for non-dimensional physical parameters such as Reynolds number, Richardson number, Hartmann number, nanoparticles' volume fraction, and various states of the circular obstacles on heated lines, flow structure, velocities, and temperatures at mean positions generating isotherms, streamlines, velocity, and temperature profiles for various parameter increments. The analysis reveals significant influences of Reynolds number (Re) and heated circular obstacles on the temperature profile, manifesting as heated lines within the system. The analysis brings to light the substantial impacts of nanoparticles on the temperature profile at both the vertical and horizontal mean positions. An elevated Hartmann number signifies a more robust magnetic field than viscous forces. A heightened magnetic field can hinder fluid movement and modify the patterns of heat transfer. Based on the graphical results, we infer that temperature differences tend to arise between strata as the Richardson number increases, leading to a heightened and more evident stratification.

Multigrid simulations of non-Newtonian fluid flow and heat transfer in a ventilated square cavity with mixed convection and baffles

The impact of baffles on a convective heat transfer of a non-Newtonian fluid is experimentally studied within a square cavity. The non-Newtonian fluid is pumped into the cavity through the inlet and subsequently departs from the cavity via the outlet. Given the inherent non-linearity of the model, a numerical technique has been selected as the method for obtaining the outcomes. Primarily, the governing equations within the two-dimensional domain have been discretized using the finite element method. For approximating velocity and pressure, we have employed the reliable P2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb{P}}_{2}$$\\end{document}–P1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb{P}}_{1}$$\\end{document} finite element pair, while for temperature, we have opted for the quadratic basis. To enhance convergence speed and accuracy, we employ the powerful multigrid approach. This study investigates how key parameters like Richardson number (Ri), Reynolds number (Re), and baffle gap bg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\ ext{b}}}_{{\ ext{g}}}$$\\end{document} influence heat transfer within a cavity comprising a non-Newtonian fluid. The baffle gap (bg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${b}_{g}$$\\end{document}) has been systematically altered within the range of 0.2–0.6, and for this research, three distinct power law indices have been selected namely: 0.5, 1.0, and 1.5. The primary outcomes of the investigation are illustrated through velocity profiles, streamlines, and isotherm visualizations. Furthermore, the study includes the computation of the Nuavg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${Nu}_{avg}$$\\end{document}(average Nusselt number) across a range of parameter values. As the Richardson number (Ri) increases, Nuavg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${Nu}_{avg}$$\\end{document} also rises, indicating that an increase in Ri results in augmented average heat transfer. Making the space between the baffles wider makes heat flow more intense. This, in turn, heats up more fluid within the cavity.

Effect of Prandtl number and free-stream orientation on global parameters for flow past a heated square cylinder

In this study, an in-depth examination of the aerodynamic parameters involving forced and mixed convection around a heated square cylinder is presented. The ranges of Prandtl number (Pr), Richardson number (Ri), and flow orientation (α) are kept as 0.71 ≤ Pr ≤ 1000, 0 ≤ Ri ≤ 1.6, 0° ≤ α ≤ 90°, while the Reynolds number (Re) and the cylinder orientation (ϕ) are kept fixed as Re = 100 and ϕ = 0°, respectively. The flow is considered as two-dimensional (2D), steady, laminar, incompressible, and viscous. The buoyancy effects are taken into account through the Boussinesq approximation. At lower Pr, the flow shifts from unsteady to steady with increasing Ri. This transition persists at higher Ri with increasing Prandtl values. The flow remains consistently unsteady at α = 90°. Isotherm crowding intensifies with higher Pr and/or Ri across all flow inclinations. Across the complete spectrum of flow angles, it is noted that the mean lift coefficient rises as the Richardson number increases. Additionally, the mean drag coefficient reaches its peak at Ri = 1.6 when Pr = 0.71. The findings reveal that the Strouhal number (St) rises as the Richardson number (Ri) increases, and it decreases as the Prandtl number (Pr) increases. The mean Nusselt number (Nu¯) demonstrates an upward trend as the Prandtl number increases, with Ri held constant. It is also observed that Nu¯ is more sensitive to the Prandtl number than the Richardson number and is maximum at Pr = 1000 for the selected range of flow orientations.

Numerical Investigation of Nanofluids Mixed Convection in a Lid-Driven Cavity with Two Heat Sources

Heat transfer enhancement through using nanofluids improves energy efficiency and enables energy savings. In this paper, a nanofluids flow and heat transfer are numerically investigated in a cavity. Four nanoparticle types (CuO, Al2O3, ZnO and SiO2) dispersed in the base liquid (water) are considered. The cavity is partially heated by two identical sources placed on the vertical walls. Partial differential equations (PDEs) are solved using (ANSYS R2 (2020) software). The Maxwell physical model and the Brownian motion effect are used to calculate the thermal conductivity and dynamic viscosity considering the diameter of the nanoparticles. Numerical simulations are performed for various parameters including nanoparticle type, nanoparticle volume fraction (0 ≤ Φ ≤ 0.06), nanoparticle diameter (29 nm, 49 nm and 69 nm) and Richardson number (0.1 ≤ Ri ≤ 10). The streamlines, isotherms, and average Nusselt number are analyzed. The results of this study showed that the average Nusselt number increases with increasing the volume fraction of nanoparticles, and decreases with incrementing the nanoparticle diameter. The heat transfer increases as the Richardson number increases. The nanofluid SiO2-water is suggested as it showed the highest heat transfer rate among the investigated nanofluids. Using Φ = 6% nanoparticles with a diameter of 29 nm improves the average Nusselt number by 6.81%, 2.43% and 0.96% for SiO2, Al2O3, ZnO, respectively, when compared to CuO, for the right-wall (Nuaverage(1)), and 6.70%, 2.40% and 0.84% for the left wall (Nuaverage(2)).

Vertical Exchange Induced by Mixed Layer Instabilities

Abstract Submesoscale turbulence in the upper ocean consists of fronts, filaments, and vortices that have horizontal scales on the order of 100 m to 10 km. High-resolution numerical simulations have suggested that submesoscale turbulence is associated with strong vertical motion that could substantially enhance the vertical exchange between the thermocline and mixed layer, which may have an impact on marine ecosystems and climate. Theoretical, numerical, and observational work indicates that submesoscale turbulence is energized primarily by baroclinic instability in the mixed layer, which is most vigorous in winter. This study demonstrates how such mixed layer baroclinic instabilities induce vertical exchange by drawing filaments of thermocline water into the mixed layer. A scaling law is proposed for the dependence of the exchange on environmental parameters. Linear stability analysis and nonlinear simulations indicate that the exchange, quantified by how much thermocline water is entrained into the mixed layer, is proportional to the mixed layer depth, is inversely proportional to the Richardson number of the thermocline, and increases with increasing Richardson number of the mixed layer. The results imply that the tracer exchange between the thermocline and mixed layer is more efficient when the mixed layer is thicker, when the mixed layer stratification is stronger, when the lateral buoyancy gradient is stronger, and when the thermocline stratification is weaker. The scaling suggests vigorous exchange between the permanent thermocline and deep mixed layers in winter, especially in mode water formation regions. Significance Statement This study examines how instabilities in the surface layer of the ocean bring interior water up from below. This interior–surface exchange can be important for dissolved gases such as carbon dioxide and oxygen as well as nutrients fueling biological growth in the surface ocean. A scaling law is proposed for the dependence of the exchange on environmental parameters. The results of this study imply that the exchange is particularly strong if the well-mixed surface layer is thick, lateral density gradients are strong (such as at fronts), and the stratification below the surface layer is weak. These theoretical findings can be implemented in boundary layer parameterization schemes in global ocean models and improve our understanding of the marine ecosystem and how the ocean mediates climate change.

Cross-Diffusion and Higher-Order Chemical Reaction Effects on Hydromagnetic Copper–Water Nanofluid Flow Over a Rotating Cone in a Porous Medium

Spin coating of engineering components with advanced functional nanomaterials which respond to magnetic fields is growing. Motivated by exploring the fluid dynamics of such processes, a mathematical model is developed for chemically reactive Cu–H2O magnetohydrodynamic (MHD) nanofluid swirl coating flow on a revolving vertical electrically insulated cone adjacent to a porous medium under a radial static magnetic field. Heat and mass transfer is included and Dufour and Soret cross-diffusion effects are also incorporated in the model. Thermal and solutal buoyancy forces are additionally included. To simulate chemical reaction of the diffusing species encountered in manufacturing processes, a higher-order chemical reaction formulation is also featured. Via suitable scaling transformations, the governing nonlinear coupled partial differential conservation equations and associated boundary conditions are reformulated as a nonlinear ordinary differential boundary value problem. MATLAB-based shooting quadrature with a Runge–Kutta method is deployed to solve the emerging system. Concentration, temperature and velocity variations for various nondimensional flow parameters have been visualized and analyzed. In addition, key wall characteristics, i.e., radial and circumferential skin friction, Nusselt number and Sherwood number, have also been computed. Validation with earlier studies is also included. The simulations indicate that when compared to a lower-order chemical reaction, a higher-order chemical reaction allows a greater rate of heat and mass transfer at the cone surface. Increasing Dufour (diffuso-thermal) and Soret numbers generally reduces radial and circumferential skin friction and also Nusselt number, whereas it elevates the Sherwood number. Both skin friction components are also suppressed with increasing Richardson number. Strong deceleration in the tangential and circumferential velocity components is induced with greater magnetic field.

NUMERICAL study of MAGNETO convective Buongiorno nanofluid flow in a rectangular enclosure under oblique magnetic field with heat generation/absorption and complex wall conditions

A mathematical model is presented to analyze the magnetohydrodynamic (MHD) convective flow in a rectangular enclosure. Earlier studies on the Tiwai-Das volume fraction nanofluid model did not consider the Buongiorno nanofluid model. This is the focus of the present analysis which examines the laminar mixed convection magnetohydrodynamic flow of a nanofluid in a differentially heated rectangular enclosure with complex boundary conditions under an inclined magnetic field. Buongiorno's two-component nanofluid model is employed, which incorporates the effects of Brownian motion and thermophoretic diffusion of nanoparticles. Magnetic nanofluids have considerable potential for enhancing transport processes in energy systems such as hybrid fuel cells. The study is essential with heat generation/absorption effects. Additionally, the work is highlighted by the general case of an oblique (inclined) magnetic field. The conservation equations for mass, primary and secondary momentum, energy, and nanoparticle concentration with wall boundary conditions are dimensionless using appropriate scaling transformations. A finite-difference computational scheme known as the Harlow-Welch Marker and Cell (MAC) method is employed to solve the dimensionless nonlinear coupled boundary value problem. A mesh independence study is included. Graphical plots are presented for the impact of key control parameters on streamline contours, isotherm contours, iso-concentration (nanoparticle mass) contours, and local Nusselt number. With heat sink (absorption), the Nusselt number is enhanced in magnitude whereas it is suppressed with heat generation since there is a heat reduction transmitted to the boundary. The configurations of streamlines, isotherms, and iso-concentrations are mostly invariant to magnetic field direction changes. The obtained results show interesting behaviors of the flow and thermal fields, which mainly involve the effect of Brownian motion and thermophoresis parameters, as well as unsteady regimes, depending on specific values of the Schmidt number, Richardson number, and Prandtl numbers. Increasing the Schmidt number induces a contraction in the central cooler zone in the enclosure and also reduces the iso-concentration magnitudes in the central region across the enclosure. The core region of the enclosure heats up as the thermophoresis and Brownian motion parameters rise, pushing the previously cooler top and bottom wall zones further away from the center. There is also a decrease in iso-concentration magnitudes in particular at the upper and lower boundaries at higher values of Brownian motion and thermophoresis parameters. At decreasing buoyancy ratios, the left vortex cell first decelerates while the right vortex cell accelerates. However, when the buoyancy ratio increases, the left vortex cell streamlines magnitudes increase with a contraction in vortex size, while the right cell develops. A Very minor alteration is observed in the isotherm and iso-concentration contours with an increasing buoyancy ratio. When the Richardson number increases, the vortex cell structures shift from a strong circulation cell on the left to a weaker cell on the right, resulting in reverse distribution. With the rising Richardson number, significant cooling is also caused in the core zone, as well as a drop in iso-concentrations, with the original dual low-concentration upper and lower zones merging into a single center zone. The original symmetric left and right vortex cells are gradually twisted diagonally towards the right wall as the magnetic field increases, yet the stronger right cell and the weaker left cell are maintained.

Fluid-structure interaction of a thin flexible heater inside a lid-driven cavity

The purpose of this study is to explore the characteristics of fluid-structure interaction and heat transfer enhancement from a hot flexible thin plate during mixed convection. The mixed convection condition of the plate heater is assumed by placing it inside a lid driven cavity with top and bottom cavity walls being fixed and insulated while left and right cavity walls maintained at constant low temperature move in downward and upward direction respectively. The Galerkin Finite Element Approach has been used to numerically solve equations describing unsteady flow, thermal and stress fields in the Arbitrary Lagrangian-Eularian (ALE) framework. Key parameters include Reynolds number ( Re) and Richardson number ( Ri), and Cauchy number ( Ca) which are varied in the range of 100 ≤ Re ≤ 500, 0.1 ≤ Ri ≤10, and 10−4 ≤ Ca ≤ 10−7 respectively. To investigate the effect of the heater’s geometry, the plate length ( l) has been varied within 0.1 ≤ l ≤ 0.7. The results have been presented in terms of the distribution of streamline and isotherm, heat transfer rate from the flexible heater as well as its deformation. The outcomes reveal that heat transfer enhances with the increase in Reynolds number and Richardson number while it degrades with the extension of the heater. Moreover, thermal frequency obtained by Fast Fourier Transform (FFT) indicates dominant peaks at higher Reynolds number and Richardson number although these become insignificant as the plate becomes rigid.

Vortex-induced vibration and heat dissipation of multiple cylinders under opposed thermal buoyancy

The vortex-induced vibration of three cylinders in an equilateral triangular arrangement with opposed thermal buoyancy are studied by numerical method. The cylinders are uniformly elastic and can freely vibrate in the transverse flow direction. The temperature of cylinders is higher than free stream. The incoming flow is in the same direction as gravity and opposite to thermal buoyancy. The ranges of Richardson number and reduced velocity considered in this work are −1≤Ri ≤ 0 and 3 ≤ U*≤12. The maximum amplitude of each cylinder rises significantly under opposed thermal buoyancy, and the maximum amplitude of cylinder 1, cylinder 2, and cylinder 3 increased by 206%, 174%, and 172%, respectively. When U*>8, the vibrations of cylinder 2 and cylinder 3 are close to the same phase. The opposed thermal buoyancy hinders the separation of flow boundary layer, resulting in thickening of thermal boundary layer and deterioration of heat transfer. The deterioration of heat transfer can be alleviated at high reduced velocity (U*≥10). The increase of Richardson number will lead to the weakening of heat transfer at up-flow surface of cylinder and enhancement of heat dissipation near the back stagnation point. The local Nusselt number distribution around cylinder is affected by vortex-induced vibration, vortex shedding, and the interaction of shear layers from each cylinder.

Fluid Flow and Mixed Heat Transfer in a Horizontal Channel with an Open Cavity and Wavy Wall

Heat exchangers are utilized extensively in different industries and technologies. Consequently, optimizing heat exchangers has been a major concern among researchers. Although various studies have been conducted to improve the heat transfer rate, the use of a wavy wall in the presence of different types of heat transfer mechanisms has not been investigated. This study thus investigates the mixed heat transmission behavior of fluid in a horizontal channel with a cavity and a hot, wavy wall. The fluid flow in the channel is considered laminar, and the governing equations including continuity, momentum, and energy are all solved numerically. The numerical solution is stabilized by using a first-order multi-dimensional characteristic-based scheme in combination with a fifth-order Runge-Kutta method. The flow and heat transfer effects of varying Richardson numbers, Reynolds numbers, wave amplitude, wavelength, channel height, and cavity width are examined. The results indicate that the mean Nusselt number increases with an increase in Reynolds number, wave amplitude, and cavity width, while it decreases with an increase in Richardson number, wavelength, and channel height. The minimum Nusselt number is calculated to be 0.7, whereas the maximum Nusselt number is 27.09. The Nusselt number has only increased by 40% in the higher depths of the cavity, despite the Richardson number being 10,000 times larger. But this figure increases to 130% at lower depths. The mean Nusselt number is thus significantly influenced by channel height and cavity width. The influence of wave amplitude on the mean Nusselt number is twice that of wavelength.

NUMERICAL STUDY OF FREE CONVECTION Ag-WATER NANOFLUID FLOW IN A SQUARE ENCLOSURE WITH VISCOUS DISSIPATION AND HEAT GENERATION/ABSORPTION EFFECTS IN A POROUS MEDIUM WITH COMPLEX WALL CONDITIONS

Nanofluids hold great promise in improving transport processes in energy systems including hybrid fuel cells. In this present work, a mathematical model is developed for laminar free convection flow of Ag-water nano-additives in an enclosure in a porous medium with complex boundary conditions. Additionally, heat generation/absorption and viscous dissipation effects are included. Via appropriate scaling transformations, the conservation equations for mass, primary and secondary momentum, energy, and nanoiparticle vorticity with wall boundary conditions are rendered dimensionless. A finite-difference computational scheme known as the marker and cell (MAC) method, developed by Harlow and Welch, is occupied to solve the dimensionless, nonlinear coupled boundary value problem. A mesh independence study is included. The impact of parameters such as Eckert number (Ec), Darcy number (Da), Grashof number (Gr), Prandtl number (Pr), Reynolds number (Re), and Richardson number (Ri) are observed with physical framework. Graphical plots are presented for the impact of key control parameters on streamline contours, isotherm contours, and local Nusselt number. By heat sink (absorption), the Nusselt number is increased, whereas by heat generation it is reduced since there is a decrease in heat transferred to the boundary. The presence of viscous dissipation effects moves the streamlines toward the blue core and allows the temperature to increase in the neighborhood of the hot wall of the envelope. An increase in Richardson number induces a flip in vortex cell structures from an initially strong circulation cell on the left and weaker cell on the right, to the opposite distribution. Significant cooling is also induced in the core zone with an increasing Richardson number, and a decrease in vorticity is observed.

Mixed Convection Heat Transfer of a Hybrid Nanofluid in a Trapezoidal Prism with an Adiabatic Circular Cylinder

This communication presents the mixed convection flow of hybrid nanofluid flow in a trapezoidal prism cavity. The cavity contains an adiabatic circular cylinder filled with A g − M g O water hybrid nanofluid. The top surface of a prism cavity is heated to a uniform temperature of T h , and the bottom surface of the prism is cooled to a temperature of T c . The other surfaces of a prism are thermally insulated. The equations governing the flow problem are obtained using conservation principles and nondimensionalized with the help of nondimensional variables. Then, with the help of the Galerkin finite element method algorithm embedded in COMSOL Multiphysics® software, the numerical simulation was performed. The streamlines and isotherms on the surfaces of the cavity have been plotted and thoroughly discussed. The results reveal that buoyant convection distorts the isothermal fields as the Richardson number increases, so does fluid flow penetration in the cavity. The results also reveal that as the Richardson number and volume fraction of hybrid nanoparticles increase, the average Nusselt number diminishes.

Double-Diffusive Mixed Convection and Radionuclides Removals from the Tail Gas Treatment Unit in Nuclear Medicine Building: Multiple Sifting Structures and Porous Medium

This paper investigates the effect of porous-media arrangement, hot-plate arrangement, heat flux, and inlet flow on the mixed convection heat transfer, and uniformity of temperature and concentration in an open enclosure. This model is considered for use as an adsorption treatment unit for radioactive waste gas in a nuclear medicine building. The radioactive waste gas flows through the cavity from bottom to top. The two-dimensional governing equations have been solved using the finite volume method. The Prandtl number and aspect ratio of the cavity are fixed at 0.71 and 1, respectively. The problem has been governed by five parameters: −10 ≤ Br ≤ 10, 10−6 ≤ Da ≤ 102, 0.1 ≤ Kc ≤ 10, 10−2 ≤ Ri ≤ 10, and 0.1 ≤ Kr ≤ 10, and the layouts of the porous layer and hot plates. The simulation results indicate that the Type C (polymeric porous media) has excellent heat transfer characteristics with a 10% increase in the Nusselt number (Nu). The contours of streamlines, isotherms and heatlines indicate that, with the increase of Richardson number (Ri), the trend of Nu varies for different arrangements of hot plates. It is interesting to note that the convective heat transfer of Type F (surrounded arrangement) was found to have the lowest Nu number for the same Ri number. The convective heat transfer is more pronounced for Type E (symmetrical arrangement). The Nu number of Type E (symmetrical arrangement) is about 110% higher than that of Type F (surrounded arrangement) and it is about 35% higher than that of Type D (centralized arrangement). This type also has a more uniform temperature distribution, as indicated by the temperature variance. The findings of this study can guide preheating system optimization.

Buoyancy-driven mixed convection flow of FENE-P fluids over a flat plate

The primary purpose of this study is to investigate the buoyancy mixed convection flow of non-Newtonian fluid over a flat plate. The addition of a small amount of polymers into a Newtonian solvent raises the viscosity and generates elastic properties in the resulting solution. To study the behavior of these viscoelastic fluids, finite extensible nonlinear elastic constitutive equations along with Peterlin’s closure (FENE-P model) are used. Along with mass, momentum and energy equations, viscoelastic constitutive equations are also used to examine the rheology of the resulting polymer solution. Similarity transformations are introduced to convert the governing equations into nondimensional forms. The nondimensional equations are solved using the fourth-order boundary value solver in MATLAB. The distribution of the velocity and temperature fields is displayed graphically under the impact of various involved parameters like Eckert number (Ec), Richardson number (Ri), Prandtl number (Pr). The addition of polymers increases the friction among the different fluid layers, leading to viscous dissipation in the fluid. The presented model’s validation is done with the Newtonian fluid to verify the results. The Nusselt number is also computed and analyzed to study the heat transfer rate. The effects of viscoelastic parameters like Weissenberg number (W[Formula: see text]), polymer viscosity ratio ([Formula: see text]) and polymer extensibility parameter ([Formula: see text]) on heat transfer rate are also shown graphically. Buoyancy parameter (Richardson number, [Formula: see text]) represents the dominance of natural convection relative to that of forced convection. The temperature of the resulting fluid falls with the increase in the value of Ri. The Nusselt number tends to decrease with increasing Richardson number when viscous dissipation effects are active.

Impacts of a floating photovoltaic system on temperature and water quality in a shallow tropical reservoir

A three-dimensional hydrodynamic-ecological lake model combined with field measurements and sampling was applied to investigate the impacts of floating photovoltaic (PV) systems on hydrodynamics and water quality in a shallow tropical reservoir in Singapore. The model was validated using field data and subsequently applied to predict temperature and water quality changes for a hypothetical 42 ha placement of floating photovoltaic panels, covering about 30% of the water surface and capable of generating up to 50 MW of energy. The impact of the panel placement was studied numerically. The area of the reservoir where panels are placed experiences both light limiting and reduced wind stress conditions. The model indicated an average water temperature increase of 0.3 °C beneath the panels, consistent with the field observation from a 1 ha demonstration installation. Comparisons of model results between the uncovered and covered areas reveal greater stability of the water column (increase in Richardson number from 2.3 to 3.3) and reduction in mixing energy (from 9 × 10–7 to 7 × 10–7 W/kg) under the PV panels. Furthermore, the model predicted that chlorophyll a, total organic carbon and dissolved oxygen concentrations would decline by up to 30%, 15% and 50%, respectively, under the photovoltaic panels. Total nitrogen and total phosphorus, averaged over the water column, increased by 10% and 30%, respectively, under the panels. Distant from the floating solar panels, temperature, stability and water quality were unaffected.

Direct numerical simulation of turbulent heat transfer in liquid metals in buoyancy-affected vertical channel

This article investigates the impact of buoyancy force in a vertical channel with combined natural and forced convection liquid metal flow using direct numerical simulation (DNS). In particular, a liquid metal with Pr = 0.025 and Re = 4667 is considered in the combined natural and forced convection regime (Ri = 0, 0.25, 0.50 and 1.00). The liquid metal is driven upward while buoyancy aids the flow close to the hot wall and opposes the flow close to the cold wall. The influence of buoyancy on turbulent heat transfer and mean flow are analyzed. Turbulent transport is enhanced in aiding flow and weakened in opposing flow with increasing Richardson number for low-Prandtl-number fluids. The enhancement of normalized Reynolds stresses is more significant in the opposing flow compared to the aiding flow. Turbulent heat flux also increases and, consequently, enhances heat transfer. Besides, the budgets of streamwise and wall-normal turbulent heat flux, temperature variance, Reynolds shear stress and turbulent kinetic energy are investigated and related to the variations of the quantities in mean fields. The budgets of temperature variance and turbulent kinetic energy are nearly balanced by shear production and dissipation. As for the budget of Reynolds shear stress, streamwise and wall-normal turbulent heat flux, temperature pressure-gradient correlation contributes to the budget significantly in addition to production and dissipation. The DNS results can not only shed light on the heat transfer mechanism of turbulence in liquid metal flows, but also be used for validating and improving turbulent models for low-Prandtl-number fluids, which could be useful for developing Gen IV liquid-metal-cooled fast reactors.

Counter-rotating Taylor-Couette flows with radial temperature gradient

In the present work, counter-rotating turbulent Taylor-Couette flows with radial temperature gradient have been studied as an extension of previously studied simple-rotating turbulent Taylor-Couette flows. The rotation axis is orthogonal to the gravity vector. Direct Numerical Simulations (DNS) have been carried out for Reynolds number ranging from 1000 to 5000 and Richardson number varying from 0 to 0.4. The effect of variation of Reynolds number and Richardson number on the flow statistics, flow dynamics, and near-wall coherent structures are studied. For neutrally buoyant cases, near-wall coherent structures exist near the inner and the outer wall, with the core being almost vortex-free. With an increase in Richardson number, more dense and finer vortical structures spread out in the core in half the circumferential domain only. This behavior is due to the spatial stable or unstable stratification in the azimuthal direction, leading to the generation of turbulence in the lower half of the domain and mitigation of turbulence in the upper half of the domain. Further, the turbulent kinetic energy (TKE) budget analysis reveals an increase in turbulence on heating the outer cylinder wall due to an increase in the production term. Heating the outer cylinder wall leads to a slight decrease in skin friction for the inner cylinder.

Mixed Convection inside a Duct with an Open Trapezoidal Cavity Equipped with Two Discrete Heat Sources and Moving Walls

The current research presents a numerical investigation of the mixed convection inside a horizontal rectangular duct combined with an open trapezoidal cavity. The region in the bottom wall of the cavity is heated by using two discrete heat sources. The cold airflow enters the duct horizontally at a fixed velocity and a constant temperature. All the other walls of the duct and the cavity are adiabatic. Throughout this study, four various cases were investigated depending on the driven walls. The effects of the Richardson number and Reynolds number ratio are studied under various cases related to the lid-driven sidewalls. The results are presented in terms of the flow and thermal fields and the average Nusselt number. The yielded data show that the average Nusselt number rises as the Richardson number and Reynolds number ratio increases. Furthermore, the Reynolds number ratio and the movement of the cavity sidewall(s) have a significant effect on the velocity and temperature contours. By the end of the study, it is shown that the maximum rates of heat transfer are related to Case 1 where the left sidewall moves downward and heater 2, which is placed near the left sidewall.

Numerical study of mixed convection and entropy generation of Water-Ag nanofluid filled semi-elliptic lid-driven cavity

In this study, laminar mixed convection of water/Ag nanofluid with volume fraction of nanoparticles φ = 0, 2, 4, and 6% and Grashof numbers Gr = 50,000, 150,000, 250,000 and 400,000 and Richardson numbers Ri = 0.1, 1, and 10 are simulated using finite volume method. Obtained results indicate that adding a higher volume fraction of nanoparticles at lower Richardson numbers leads to the enhancement of heat transfer and Nusselt number. Streamlines behavior in the cavity is under the influence of two main factors including lid-driven motion (which is the basic factor) and the viscosity of fluid (which transfers the fluid motion to bottom layers and affects the flow domain). Every factor stimulating the flow domain causes uniform temperature distribution in the cavity. The increase of Richardson number leads to the enhancement of lid-driven velocity, temperature penetration and a better mixture of fluid layers, and by increasing Grashof number; this issue can have a great effect on uniform temperature distribution.