Numerical study on mixed convection in a lid-driven cavity with non-uniform heating on both sidewalls

A numerical study has been performed on mixed convection in a lid-driven cavity. The vertical sidewalls of the cavity are maintained with sinusoidal temperature distribution. A finite volume method is used to solve numerically the non-dimensional governing equations. Results are analyzed over a range of the Richardson numbers, amplitude ratios and phase deviations. The results show that heat transfer rate is increased on increasing amplitude ratio. It is observed that average Nusselt numbers are increased first and then decreased when increasing the phase deviation from 0 to π. The non-uniform heating on both walls provides higher heat transfer rate than non-uniform heating of one wall.     

Hydromagnetic effect on mixed convection in a lid-driven cavity with sinusoidal corrugated bottom surface

The present numerical simulation is conducted to analyze the mixed convection flow and heat transfer in a lid-driven cavity with sinusoidal wavy bottom surface in presence of transverse magnetic field. The enclosure is saturated with electrically conducting fluid. The cavity vertical walls are insulated while the wavy bottom surface is maintained at a uniform temperature higher than the top lid. In addition, the transport equations are solved by using the finite element formulation based on the Galerkin method of weighted residuals. The implications of Reynolds number (Re), Hartmann number (Ha) and number of undulations (λ) on the flow structure and heat transfer characteristics are investigated in detail while, Prandtl number (Pr) and Rayleigh number (Ra) are considered fixed. The trend of the local heat transfer is found to follow a wavy pattern. The results of this investigation illustrate that the average Nusselt number (Nu) at the heated surface increases with an increase of the number of waves as well as the Reynolds number, while decreases with increasing Hartmann number.     

Effect of sinusoidal wavy bottom surface on mixed convection heat transfer in a lid-driven cavity

The current numerical study is conducted to analyze mixed convection heat transfer in lid-driven cavity with a sinusoidal wavy bottom surface. The cavity vertical walls are insulated while the wavy bottom surface is maintained at a uniform temperature higher than the top lid. In addition, the transport equations are solved using the finite element formulation based on the Galerkin method of weighted residuals. The validity of the numerical code used is ascertained by comparing our results with previously published results. The implications of Richardson number, number of wavy surface undulation and amplitude of the wavy surface on the flow structure and heat transfer characteristics are investigated in detail while the Prandtl number is considered equal to unity. The trend of the local heat transfer is found to follow a wavy pattern. The results of this investigation illustrate that the average Nusselt number increases with an increase in both the amplitude of the wavy surface and Reynolds number. Furthermore, optimum heat transfer is achieved when the wavy surface is designated with two undulations while subjected to low Richardson numbers.     

MHD mixed convection in a lid-driven cavity with corner heater

Laminar mixed convection flow in the presence of magnetic field in a top sided lid-driven cavity heated by a corner heater was considered. The corner heater is under isothermal boundary conditions with different length in bottom and right vertical walls. Finite volume technique was used to solve governing equations. The temperature of the lid is lower than that of heater. The study is performed for different Grashof and Hartmann numbers at Re = 100. The obtained results showed some very interesting results.     

Numerical study of mixed convection flows in a square lid-driven cavity utilizing nanofluid

A numerical investigation of laminar mixed convection flows through a copper–water nanofluid in a square lid-driven cavity has been executed. In the present study, the top and bottom horizontal walls are insulated while the vertical walls are maintained at constant but different temperatures. The study has been carried out for the Rayleigh number 10⁴ to 10⁶, Reynolds number 1 to 100 and the solid volume fraction 0 to 0.05. The thermal conductivity and effective viscosity of nanofluid have been calculated by Patel and Brinkman models, respectively. The effects of solid volume fraction of nanofluids on hydrodynamic and thermal characteristics have been investigated and discussed. It is found that at the fixed Reynolds number, the solid concentration affects on the flow pattern and thermal behavior particularly for a higher Rayleigh number. In addition it is observed that the effect of solid concentration decreases by the increase of Reynolds number.     

Magnetohydrodynamic natural convection in a vertical cylindrical cavity with sinusoidal upper wall temperature

A series of numerical simulations were performed in order to study liquid metal MHD natural convection in a vertical cylindrical container with a sinusoidal temperature distribution at the upper wall and the other surfaces being adiabatic. Starting from the basic hydrodynamic case, the effect of vertical (axial) and horizontal magnetic fields is assessed. Depending on the magnitude of the Rayleigh and Hartmann numbers, both turbulent and laminar (azimuthally symmetric or not) flows are observed. The results show that the increase of Rayleigh number promotes heat transfer by convection while the increase of Hartmann number favors heat conduction. The vertical magnetic field reduces the Nusselt number more than the horizontal. The circulation patterns for the most convective cases are confined close to the top corner of the container with the simultaneous formation of a secondary flow pattern at the bottom corner, while for the more conductive cases only one circulation pattern exists covering the entire domain.     

Natural convection in porous cavity with sinusoidal bottom wall temperature variation

Numerical study of natural convection in a porous cavity is carried out in the present paper. Natural convection is induced when the bottom wall is heated and the top wall is cooled while the vertical walls are adiabatic. The heated wall is assumed to have spatial sinusoidal temperature variation about a constant mean value which is higher than the cold top wall temperature. The non-dimensional governing equations are derived based on the Darcy model. The effects of the amplitude of the bottom wall temperature variation and the heat source length on the natural convection in the cavity are investigated for Rayleigh number range 20–500. It is found that the average Nusselt number increases when the length of the heat source or the amplitude of the temperature variation increases. It is observed that the heat transfer per unit area of the heat source decreases by increasing the length of the heated segment.     

Experimental and numerical studies on periodic convection flow and heat transfer in a lid-driven arc-shape cavity

This paper presents experimental and numerical studies on periodic convection flow and heat transfer in a lid-driven arc-shape cavity with temperature differential. Three cases were considered: Gr = 2 × 10⁵, 5 × 10⁵ and 1.2 × 10⁶ at Re = 100 (Gr = Grashof number; Re = Reynolds number). The mathematical model was proposed in our previous study. The current study performs an experiment to validate this model, to corroborate the existence of the periodic flow, and to more deeply probe the internal flow and temperature characteristics. The experimental setup primarily comprised an arc-shape cavity, a moving lid, a thermo-system, a smoke generator and an image acquisition system. The periodic convection flow in the cavity was visualized using kerosene smoke. The numerical and experimental results consistently reveal that the periodic flow pattern was observed in the case with Gr = 5 × 10⁵, whereas the steady-state flow pattern took place in the other two cases (Gr = 2 × 10⁵ and Gr = 1.2 × 10⁶). The numerical simulation produced reasonable and satisfactory agreement with the experiment for the periodic flow pattern and period. The difference between the predicted and measured periods is less than 5%. The transport properties, such as average kinetic energy, overall Nusselt number, stream function, phase space trajectory, local kinetic energy, velocity history and temperature distribution, were further analyzed and discussed in this paper. The proposed numerical simulation not only confirms the experimental observation, but also enhances the understanding of periodic convection in an arc-shape cavity subjected to a moving lid and temperature differential.     

Mixed convection in a lid-driven triangular enclosure filled with nanofluids

This paper presents the results of a numerical study on the mixed convection in a lid-driven triangular enclosure filled with a water–Al₂O₃ nanofluid. A comparison study between two different scenarios of upward and downward left sliding walls is presented. The effects of parameters such as Richardson number, solid volume fraction and the direction of the sliding wall motion on the flow and temperature fields as well as the heat transfer rate are examined. The results show that the addition of Al₂O₃ nanoparticles enhances the heat transfer rate for all values of Richardson number and for each direction of the sliding wall motion. However, the downward sliding wall motion results in a stronger flow circulation within the enclosure and hence, a higher heat transfer rate.     

Accurate numerical simulation for non-Darcy double-diffusive mixed convection in a double lid-driven porous cavity using SEM

The non-Darcy double-diffusive mixed convection in a double lid-driven porous cavity with two thermosolutal sources is numerically investigated in this article, depicting the effects of different physical parameters on heat and mass transfer in the drying chamber. The flow is generated due to the motion of the horizontal moving lids and the buoyancy produced by the temperature and concentration gradients. The governing equations are discretized by the Legendre spectral element method (SEM) with high accuracy, and an improved time-splitting method is developed to deal with the coupled pressure and velocity in the Brinkman-Forchheimer extended Darcy model. The effects of Darcy number (Da?=?10^?5～10^?1), Richardson number (Ri?=?10^?2～10¹), and buoyancy ratio (Br = ?5?～?5) are investigated, and numerical results are analyzed by contours of streamline, isotherm, heatline, isoconcentration, and massline in detail. Results reveal the pattern of heat and mass transfer with the variation on significant parameters by the average Nusselt and Sherwood numbers on the moving lids of the cavity.     

Finite element based heatline approach to study mixed convection in a porous square cavity with various wall thermal boundary conditions

A penalty finite element method based simulation is performed to analyze the influence of various walls thermal boundary conditions on mixed convection lid driven flows in a square cavity filled with porous medium. The relevant parameters in the present study are Darcy number (Da = 10^?5 ? 10^?3), Grashof number (Gr = 10³ ? 10⁵), Prandtl number (Pr = 0.7–7.2), and Reynolds number (Re = 1–10²). Heatline approach of visualizing heat flow is implemented to gain a complete understanding of complex heat flow patterns. Patterns of heatlines and streamlines are qualitatively similar near the core for convection dominant flow for Da = 10^?3. Symmetric distribution in heatlines, similar to streamlines is observed irrespective of Da at higher Gr in natural convection dominant regime corresponding to smaller values of Re. A single circulation cell in heatlines, similar to streamlines is observed at Da = 10^?3 for forced convection dominance and heatlines are found to emanate from a large portion on the bottom wall illustrating enhanced heat flow for Re = 100. Multiple circulation cells in heatlines are observed at higher Da and Gr for Pr = 0.7 and 7.2. The heat transfer rates along the walls are illustrated by the local Nusselt number distribution based on gradients of heatfunctions. Wavy distribution in heat transfer rates is observed with Da ? 10^?4 for non-uniformly heated walls primarily in natural convection dominant regime. In general, exponential variation of average Nusselt numbers with Grashof number is found except the cases where the side walls are linearly heated. Overall, heatlines are found to be a powerful tool to analyze heat transport within the cavity and also a suitable guideline on explaining the Nusselt number variations.     

Computational study of unsteady mixed convection heat transfer of nanofluids in a 3D closed lid-driven cavity

Mixed heat convection of three-dimensional unsteady flow of four different types of fluids in a double lid-driven enclosure is simulated by a two-phase mixture model in this project. The cubic cavity with moving isothermal sidewalls has uniform heat flux on the middle part of the bottom wall, and the other remaining walls forming the enclosure are adiabatic and stationary. The relevant parameters in the present research include Reynolds number Re (5000–30,000), nanoparticle diameter (25 nm–85 nm), and nanoparticle volume fraction (0.00–0.08). In general, remarkable effects on the heat transfer and fluid patterns are observed by using nanofluids in comparison to the conventional fluid. Different types of nanofluids or different diameters of nanoparticles can make pronounced changes in the heat convection ratio. In addition, increasing in either volume fraction of nanoparticles or Reynolds number leads to increasing in the Nusselt number, fluctuation kinetic energy and root mean square velocity of the fluid in the domain. It is also found that both URANS and LES methods have shown good performance in dealing with unsteady flow conducted in this project. However, the comparisons have elucidated clearly the advantages of the LES approach in predicting more detailed heat and flow structures.     

Numerical simulation of mixed convection flows in a square lid-driven cavity partially heated from below using nanofluid

The present numerical study deals with mixed convection in a square lid-driven cavity partially heated from below and filled with water-base nanofluid containing various volume fractions of Cu, Ag, Al₂O₃ and TiO₂. Finite difference method was employed to solve the dimensionless governing equations of the problem. The effects of governing parameters, namely, Reynolds number, solid volume fraction, different values of the heat source length and different locations of the heat source on the streamlines and isotherms contours as well as Nusselt number and average Nusselt number along the heat source were considered. The present results are validated by favorable comparisons with previously published results. The results of the problem are presented in graphical and tabular forms and discussed.     

Numerical analysis of fluid flow due to mixed convection in a lid-driven cavity having a heated circular hollow cylinder

Mixed convection heat transfer in a lid-driven cavity along with a heated circular hollow cylinder positioned at the center of the cavity has been analyzed numerically. The present study simulates a realistic system such as air-cooled electronic equipment with a heat component or an oven with heater. A Galerkin weighted residual finite element method with a Newton–Raphson iterative algorithm is adopted to solve the governing equations. The computation is carried out for wide ranges of the Richardson numbers, cylinder diameter and solid fluid thermal conductivity ratio. Results are presented in the form of streamlines, isothermal lines, average Nusselt number at the heated surface and fluid temperature in the cavity for the mentioned parameters. It is found that the flow field and temperature distribution strongly depend on the cylinder diameter and also the solid–fluid thermal conductivity ratio at the three convective regimes.     

Analysis of mixed convection of nanofluid in a 3D lid-driven trapezoidal cavity with flexible side surfaces and inner cylinder

Numerical study of mixed convection in a lid-driven 3D flexible walled trapezoidal cavity with nanofluids was performed by using Galerkin weighted residual finite element method. Effects of various pertinent parameters such as Richardson number (between 0.05 and 50), elastic modulus of the side surfaces (between 1000 and 10⁵), side wall inclination angle (between 0° and 20°) and solid particle volume fraction (between 0 and 0.04) on the fluid flow and heat transfer characteristics in a 3D lid-driven-trapezoidal cavity were numerically examined. It was observed that these characteristics are influenced when the pertinent parameters change. Flexible side surface can be used as control element for heat transfer rate. Increment and reduction in the space which are provided by the flexible side walls result in heat transfer enhancement and deterioration for side wall inclination angle of 0° and 10°. Average Nusselt number enhances by about 9.80% when the value of the elastic modulus is increased from 1000 to 10⁵ for side wall inclination angles of θ = 0°. Adding nanoparticles to the base fluid results in linear increment of heat transfer and at the highest volume fraction, 25.30% of heat transfer enhancement is obtained. A polynomial type correlation for the average Nusselt number along the hot wall was proposed and it has a fourth order polynomial dependence upon the Richardson number and first order dependence upon the solid particle volume fraction.     

Conjugate-mixed convection heat transfer in a lid-driven enclosure with thick bottom wall

Conjugate heat transfer by mixed convection and conduction in lid-driven enclosures with thick bottom wall has been studied by a numerical method. The enclosure is heated from the bottom wall isothermally. Temperature of the top moving wall, which has constant flow speed, is lower than that of the outside of bottom wall. Vertical walls of the enclosure are adiabatic. Governing parameters are solved for a wide range of Richardson numbers (0.1 ≤ Ri ≤ 10), ratio of height of bottom wall to enclosure height (0.1 ≤ h/H ≤ 0.5) and thermal conductivity ratio (0.01 ≤ λ_f/λ_s ≤ 10). Obtained results showed that heat transfer decreases with increasing of λ_f/λ_s ratio, Richardson number and thickness ratio of the wall. Flow strength is affected for only higher values of λ_f/λ_s ratio.     

Second law analysis in a three dimensional lid-driven cavity

Three dimensional analyses of laminar mixed convection and entropy generation in a cubic lid-driven cavity have been performed numerically. Left side of cavity moves in + y (Case I) or −y (Case II) direction. The cavity is heated from left side and cooled from right while other surfaces are adiabatic. Richardson number is the main parameter which changes from 0.01 to 100. Prandtl number is fixed at Pr = 0.71. Results are presented by isotherms, local and mean Nusselt number, entropy generation due to heat transfer and fluid friction, velocity vectors and Bejan number. Total entropy generation contours are also presented. It is found that direction of lid is an effective parameter on both entropy generation and heat and fluid flow for low values of Richardson number but it becomes insignificant at high Richardson number.