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.     

Non-Darcian effects on natural convection heat transfer in a wavy porous enclosure

A numerical investigation is carried out to analyze natural convection heat transfer inside a cavity with a sinusoidal vertical wavy wall and filled with a porous medium. The vertical walls are isothermal while the top and bottom horizontal straight walls are kept adiabatic. 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 importance of non-Darcian effects on convection in a wavy porous cavity is analyzed in this work. Different flow models for porous media such, as Brinkman-extended Darcy, Forchheimer-extended Darcy, and the generalized flow models, are considered. Results are presented in terms of streamlines, isotherms, and local heat transfer. The implications of Rayleigh 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.     

Natural convection heat transfer in a circular enclosure

Natural convection heat transfer in a circular enclosure, one half of which was heated and the other half of which was cooled, was investigated experimentally, focusing on the effect of the inclination angle. The experiments were carried out with water. Flow and temperature field were visualized by using the aluminum and liquid-crystal suspension method. The results show that with downward heating the heat transfer coefficient increased as the inclination angle of the boundary between the heating wall and the cooling wall approached the vertical. But with upward heating, the heat transfer coefficient showed minimal change, exhibiting a small peak value when the inclination angle was γ ˜ –45°. The heat transfer coefficient of a flat circular enclosure was estimated from the circular enclosure's heat transfer coefficient. These results can be explained by the obtained flow and temperature fields. © 1999 Scripta Technica, Heat Trans Asian Res, 28(2): 152–163, 1999     

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.     

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.     

Mixed convection heat transfer in a lid-driven cavity with a rotating circular cylinder

Mixed convection heat transfer in a lid-driven cavity with a rotating cylinder was analyzed numerically for two important parameters - Richardson number, the non-dimensional angular velocity of the cylinder, and the direction of rotation using the commercial software, ADINA. The results from these simulations were validated using an open-source spectral element code, Nek5000. The results of this investigation were presented in terms of streamlines, isotherms, and average and local Nusselt numbers. The present results illustrated that the average Nusselt number was found to depend on the direction of the angular velocity. The average Nusselt number increased with an increase in the clockwise angular velocity of the cylinder for various Richardson numbers. However, it decreased with an increase in the counterclockwise until reached a critical velocity where average Nusselt number increased with an increase in the angular velocity. This study illustrated that the maximum heat transfer can be achieved when placing a rotating cylinder inside a cavity compared with non-rotating cylinder.     

Natural convection heat transfer in a nanofluid-filled trapezoidal enclosure

Heat transfer enhancement utilizing nanofluids in a trapezoidal enclosure is investigated for various pertinent parameters. Transport equations are modelled by a stream-vorticity formulation and solved numerically by finite difference approach. The inclined sloping boundaries is treated by adopting staircase-like zigzag lines. Based upon the numerical predictions, the effects of Grashof number, inclination angle of the sloping wall, volume fraction of nanoparticles on flow and temperature patterns as well as the heat transfer rate within the enclosure are presented. Water–Cu and water–Al₂O₃ nanofluids were tested. We found that acute sloping wall and Cu nanoparticles with high concentration are effective to enhance the rate of heat transfer. We also developed a new correlation for the average Nusselt number as a function of the angle of the sloping wall, effective thermal conductivity and viscosity as well as Grashof number.     

A penalty finite element method for natural convection heat transfer in a partially divided enclosure

Theoretical study of natural convection has been performed in a square enclosure partitioned by a single adiabatic baffle protruding from the ceiling. A penalty finite element method with 9-node quadrilateral element and Newton-Raphson scheme are adopted in this study to solve the heat transfer coefficients of three different baffle locations and two different baffle heights. During the calculating process, an out-of-core skyline method is utilized to reduce computer memory. The fluid in the enclosure is air; Rayleigh number of 10⁴ and 10⁵ are calculated. The results show that heat transfer coefficients are influenced by the baffle height and baffle location.     

Numerical simulation of double-diffusive mixed convection and entropy generation in a lid-driven trapezoidal enclosure with a heat source

In this study, entropy generation of double-diffusive mixed convection is investigated inside a right-angled trapezoidal cavity with a partially heated and salted bottom wall. Similar to the approach that assigns color to streamlines, a new coloring scheme is employed to visualize heatlines and masslines in a more meaningful manner. In addition, various consequential parameters, namely the Lewis and Richardson numbers, the buoyancy ratio, the direction of lid movement, and the heat source location, have been analyzed. According to the results, as the Lewis number increases, the average Nusselt number declines, while the total entropy generation augments. Furthermore, for Le?=?0.1, the conduction mass transfer dominates the mass transfer field; hence, the masslines are virtually perpendicular to the isoconcentration lines.     

Natural convection heat transfer in a nanofluid filled semi-annulus enclosure

To investigate natural convection heat transfer in a semi-annulus enclosure filled with nanofluid, the Control Volume based Finite Element Method (CVFEM) is used. The fluid in the enclosure is Cu–water nanofluid. The inner and outer semi circular walls are maintained at constant temperatures while the two other walls are thermally insulated. The Navier Stokes equations in their vorticity-stream function form are used to simulate the flow pattern and isotherms. The numerical investigation is carried out for different governing parameters namely; the Rayleigh number, nanoparticle volume fraction and the angle of turn for the enclosure. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. The results reveal that there is an optimum angle of turn in which the average Nusselt number is maximum for each Rayleigh number. Moreover, the angle of turn has an important effect on the streamlines, isotherms and maximum or minimum values of local Nusselt number.     

Conjugate natural convection in an enclosure with a heat source of constant heat transfer rate

A numerical study of two-dimensional transient natural convection in a rectangular enclosure having finite thickness heat-conducting walls with a heat source of constant heat transfer rate located on the inner side of the left wall in conditions of convection–radiation heat exchange with an environment on one of the external boundaries has been performed. Mathematical simulation has been carried out in terms of the dimensionless variables such as stream function – vorticity – temperature. Stream function, vorticity and energy equations have been solved by finite difference numerical method. The relevant governing parameters were: the Grashof number from 10⁶ to 10⁸, the Prandtl number, Pr = 0.7 and the conductivity ratio. Detailed results including streamlines and temperature profiles have been obtained.     

Mixed convection with viscous dissipation and pressure work in a lid-driven square enclosure

Buoyant laminar flow in a square lid-driven enclosure is analysed. The vertical sides are kept isothermal at different temperatures, while the horizontal sides are insulated. Assisting mixed convection flow due to uniform motion of the top side is considered. The governing balance equations are solved numerically by employing a Galerkin finite element method. The effects of viscous dissipation and pressure work are taken into account. In order to investigate the influence of these effects, the Nusselt number is evaluated with respect to the heat fluxes at both vertical sides, for different values of the Rayleigh number and of the Péclet number based on the lid velocity. Two sample fluids are considered: a gas and a highly viscous liquid. In the framework of the Oberbeck–Boussinesq approximation, a comparison is made between three different energy balance models: (A) enthalpy formulation (pressure work and viscous dissipation are included); (B) internal-energy formulation (viscous dissipation is included); (C) both pressure work and viscous dissipation are neglected. It is shown that, in the absence of a lid motion, the three models yield substantially the same predictions. On the other hand, when the forced flow induced by the lid motion becomes sufficiently large, the three models yield discrepant results, thus implying that pressure work and viscous dissipation are not negligible. Moreover, it is shown that, in this case, model (A) yields unphysical results, while model (B) leads to reasonable predictions.     

Experimental study of natural convection heat transfer in a semicircular enclosure

An experimental study of natural convection heat transfer in a differentially heated semicircular enclosure was carried out. The flat surface was heated and the radial surface was cooled isothermally. The effects of angle of enclosure inclination on the heat transfer across semicircular regions of several radii were measured for Rayleigh numbers Ra_R ranging from 6.72 × 10⁶ to 2.33 × 10⁸, using water as the working fluid. The angle of inclination varied from −90 degrees to 90 degrees with radii R of 50, 40, and 30 mm. The flow patterns were sketched from the results of a visualization experiment using aluminum powder. The temperature measurements in the enclosure were carried out using liquid crystals and thermocouples. The results indicate that different flow patterns were encountered as the angle of inclination varied, and the heat transfer rate was largely dependent on the flow pattern. In particular, enhanced heat transfer rates can be obtained when plume-like flow occurs along both hot and cold walls in the case of an upward-facing hot wall. Heat transfer for the inclined enclosure can be predicted using the equation for a vertical enclosure presented in this paper. © 1998 Scripta Technica, Inc. Heat Trans Jpn Res, 26(2): 131–142, 1997     

Effects of the inclination angle on natural convection heat transfer and entropy generation in a square porous enclosure

ABSTRACT

In this paper, we analyze numerically the effects of the inclination angle on natural convection heat transfer and entropy generation characteristics in a two-dimensional square enclosure saturated with a porous medium. There is a significant alteration in Nusselt number with the orientation of the enclosure at higher values of Rayleigh number. It reveals that the variation of entropy generation rate with the inclination angle is significant for higher values of Darcy number. The dominant source of irreversibility is due to heat transfer at low values of Darcy number, whereas entropy generation due to fluid flow dominates over that due to heat transfer for larger values of Darcy number.     

Free convection heat transfer in a partially divided vertical enclosure with conducting end walls

A numerical study has been made of natural convection in an enclosure with perfectly conducting horizontal end walls and finitely conducting baffles. Results obtained using the Boussinesq model for density variation show good agreement with reported measurements of natural convection in a partitioned enclosure. Except at low Rayleigh numbers, a separation bubble is observed behind the baffle. The strength of the separation bubble increases while the strength of the main flow (moving up the hot wall and down the cold one) decreases with increasing baffle conductivity. The average Nusselt number for the enclosure is significantly smaller in the presence of the baffles. Except at low Rayleigh numbers (where baffle conductivity has little influence) the Nusselt number values decrease with increasing baffle conductivity.     

Natural convection and fluid flow in inclined enclosure with a corner heater

The phenomena of natural convection in an inclined square enclosure heated via corner heater have been studied numerically. Finite difference method is used for solving momentum and energy equations in the form of stream function–vorticity. One wall of the enclosure is isothermal but its temperature is colder than that of heaters while the remaining walls are adiabatic. The numerical procedure adopted in this analysis yields consistent performance over a wide range of parameters; Rayleigh number, Ra (10³ ? Ra ? 10⁶); Prandtl number, Pr (0.07 ? Pr ? 70); dimensionless lengths of heater in x and y directions (0.25 ? hx ? 0.75, 0.25 ? hy ? 0.75); and inclination angle, ? (0° ? ? ? 270°). It is observed that heat transfer is maximum or minimum depending on the inclination angle and depending on the length of the corner heaters. The effect of Prandtl number on mean Nusselt number is more significant for Pr < 1.     

Natural convection heat transfer by heated partitions within enclosure

In this study, natural convection heat transfer and fluid flow of two heated partitions. within an enclosure have been analysed numerically. The right side wall and the bottom wall of the enclosure were insulated perfectly while the left side wall and top wall were maintained at the same uniform temperature. The partitions were placed on the bottom of the enclosure and their temperatures were kept higher than the non-isolated walls. The effects of position and heights of the partitions on heat transfer and flow field have been investigated. Computations for Rayleigh number in the range of 10⁴ and 10⁶ have been conducted. Using the control volume approach, finite difference equations are obtained with non-staggered grid arrangement, a computer program based on the SIMPLEM algorithm was developed. The finite difference equations were solved iteratively with a line-by-line Thomas algorithm.     

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.