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.     

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 and entropy generation inside porous quadrantal enclosure with nonisothermal heating at the bottom wall

In this work, we study numerically the natural convection heat transfer and entropy generation characteristics inside a two-dimensional porous quadrantal enclosure heated nonuniformly from the bottom wall. The effect of Darcy number is significant in dictating the Nusselt number only for higher values of Rayleigh number and the variation is more profound for larger values of Darcy number. The variation of entropy generation rate is significant with the Darcy number only for higher values of Rayleigh number. The entropy generation due to heat transfer is the significant contributor of irreversibility at low values of Darcy number, while for larger values of Darcy number and Rayleigh number entropy generation due to fluid friction becomes dominant.     

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.     

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     

Numerical simulation on enhancement of natural convection heat transfer by acoustic cavitation in a square enclosure

Natural convection heat transfer of liquid in a square enclosure with and without acoustic cavitation is numerically investigated. In order to model the effect of sound field, a prescribed periodic change pressure is imposed on liquid in the region with ultrasonic beam. The cavitation model which takes into consideration such effects as phase change, bubble dynamics, and noncondensable gases is established. In order to capture the cavitation phenomenon and obtain a realistic pressure field and cavitation zones, the time step is set to quarter period of sound pressure and a relatively small relaxation factor for momentum equation and near zero relaxation factors for vaporization mass and density are used. The simulation results show that both liquid temperature uniformity and heat transfer coefficient of heating surface are greatly improved by means of acoustic cavitation. This phenomenon can be explained by jet-flow bundle formed by the asymmetry collapse of cavitation bubbles on the heating surface. The jet-flow bundle cannot only enhance fluid mixing around the heating surface and thus improve the uniformity of liquid temperature in the square enclosure, but also directly impact the heating surface and thus make thermal boundary layer become thin. The field synergy principle is introduced to analyze the heat transfer enhancement by acoustic cavitation.     

Numerical investigation of natural convection in a square enclosure partially filled with horizontal layers of a porous medium

Two-dimensional buoyancy-induced flow and heat transfer inside a square enclosure partially occupied by copper metallic foam subjected to a symmetric side cooling and constant heat flux bottom heating was tested numerically. Finite Element Method was employed to solve the governing partial differential equations of the flow field and the Local Thermal Equilibrium model was used for the energy equation. The system boundaries were defined as lower heated wall by constant heat flux, cooled lateral walls, and insulated top wall. The three parameters elected to conduct the study are heater length (7 ≤ ζ ≤ 20 cm), constant heat flux (150 ≤ q″ ≤ 600 W m⁻²), and porous material thickness (5 ≤ H ≤ 20 cm). The porous material used was the copper metal foam of porosity = 0.9 and pore density PPI = 10, and saturated with a fluid of Prandtl number = 0.7. On the basis of the results obtained, it was concluded that at the porous layer thickness = 5 cm, the rate of heat transferred was (74.6%) higher than when the layer height was 20 cm (the cavity is fully filled) and at the same thickness it was found that the heat rate is (51.4%) higher than when using the half filling (H = 10 cm). Further, the local and mean Nusselt number is maximum when using the largest heater size and smallest porous layer thickness. Finally, better circulation and convective modes were observed at high values of heat flux.     

Maximum heat transfer density rate enhancement from cylinders rotating in natural convection

In this paper we investigate the thermal behaviour of an assembly of consecutive cylinders in a counter-rotating configuration cooled by natural convection with the objective of maximizing the heat transfer density rate (heat transfer rate per unit volume). A numerical model is used to solve the governing equations that describe the temperature and flow fields. The spacing between the consecutive cylinders is optimised for each flow regime (Rayleigh number) and cylinder rotation speed. It was found that the optimized spacing decreases as the Rayleigh number increases and the heat transfer density rate increases, for the optimized structure, as the cylinder rotation speed is increased. Results further shows that there is an increase in the heat transfer density rate of the rotating cylinders over stationary cylinders.     

Numerical prediction of entropy generation due to natural convection from a horizontal cylinder

Entropy generation due to natural convection has been calculated for three radii and a wide range of Rayleigh numbers for an isothermal cylinder. It was predominantly caused by conduction. The viscous contribution was negligible. Locations of high local entropy generation were identified for different configurations. The total entropy generation decreased with increasing cylinder size for a given value of the Rayleigh number.     

Numerical investigation of natural convection in an inclined enclosure filled with porous medium under magnetic field

In the present study, natural convection of fluid in an inclined enclosure filled with porous medium is numerically investigated in a strong magnetic field. The physical model is heated from left-hand side vertical wall and cooled from opposing wall. Above this enclosure an electric coil is set to generate a magnetic field. The Brinkman–Forchheimer extended Darcy model is used to solve the momentum equations, and the energy equations for fluid and solid are solved with the local thermal non-equilibrium (LTNE) models. Computations are performed for a range of the Darcy number from 10⁻⁵ to 10⁻¹, the inclination angle from 0 to π/2, and magnetic force parameter γ from 0 to 100. The results show that both the magnetic force and the inclination angle have significant effect on the flow field and heat transfer in porous medium.     

A review on entropy generation in natural and mixed convection heat transfer for energy systems

This paper reviews the second law analysis of thermodynamics in enclosures due to buoyancy-induced flow for energy systems. It defines entropy generation minimization or thermodynamic optimization. In addition, the article summarizes the recent works on entropy generation in buoyancy-induced flows in cavity and channels. Studies on mixed convection were also included in the study. Presentation was performed for flow in porous media and viscous fluid filled media at different shaped enclosures and duct under buoyancy-induced force.     

Numerical analysis of the longitudinal size of the partition on natural convection heat transfer and fluid flow within a differentially heated porous enclosure

The article deals with the effect of longitudinal size and shape partition embedded within a differentially heated porous enclosure. The objective is to curtail the heat transfer rate across such porous enclosures by means of partitions embedded within. The partition shapes under consideration are straight vertical left-inclined, right-inclined, L-shaped, wavy, corrugated, and square-wave. It is sought to find the most effective combination of partition length and shape that could serve the required objective. Also, many times, due to the constructional constraints of the porous enclosure or cavity, using full-length partitions may not be feasible. In this regard, it is also sought to find the partition length that is to be maintained for achieving a significant reduction in heat transfer without much compromise. The results of the current study are useful for thermal design engineers particularly in the field of thermal insulation, solar heating application, and packed bed energy storage systems where the major challenge is to reduce the heat transfer across the system. The parameters under consideration are the longitudinal length L and Rayleigh number Ra. All the partitions under study are evaluated for bottom-wall and top-wall attached conditions. Some of the notable findings are that for smaller-sized partitions (B < 0.5), L-shaped partitions are most effective in controlling the convection heat transfer rate across the enclosure while for larger-sized partitions (L > 0.5), square-wave-shaped partitions should be preferred for effective reduction in the rate of convection heat transfer.     

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.     

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     

Numerical investigation of laminar natural convective heat transfer from a horizontal triangular cylinder to its concentric cylindrical enclosure

A numerical simulation was conducted to investigate the steady laminar natural convective heat transfer for air within the horizontal annulus between a heated triangular cylinder and its circular cylindrical enclosure. The Boussinesq approximation was applied to model the buoyancy-driven effect and the governing equations were solved using the finite volume method. Four different Rayleigh numbers and four different radius ratios were considered, and four different inclination angles for the inner triangular cylinder were investigated as well. The computed flow and temperature fields were demonstrated in the form of streamlines and isotherms. Variations of the maximum stream function and the local and average Nusselt numbers were displayed as functions of the above-mentioned parameters. Correlations of the average Nusselt number were proposed based on curve fitting. At constant radius ratio, inclination angles of the inner triangular cylinder are found to have negligible effects on the average Nusselt number.     

双绝热圆柱对水平三角腔内自然对流影响的数值研究

针对含双绝热圆柱的底部加热水平等腰三角腔内空气的稳态层流自然对流开展研究.通过有限容积法对控制方程进行了数值求解,其中瑞利数的变化范围为104 ～106,圆柱体的尺寸比则分别为0（无圆柱体）、1/8和1/4.基于计算结果对自然对流的流动与传热特性随瑞利数和尺寸比的变化规律进行了分析和讨论.结果表明,双绝热圆柱的存在较大程度上改变了三角腔内自然对流的流型和温度场分布,但对整体传热影响较小,仅略微提高了平均努赛尔数,强化传热的效果在尺寸比为1/8时较为明显.     

Suppression of natural convection heat transfer coefficients in an attic shaped enclosure

The use of convection suppression devices has been widely discussed in the literature as a means of reducing natural convection heat loss from enclosed spaces. In this study the use of a single baffle was examined as a possible low cost means of suppressing heat loss by natural convection in an attic shaped enclosure.     

Conjugate natural convection around a finned pipe in a square enclosure with internal heat generation

This work is focused on the numerical study of steady, laminar, conjugate natural convection around a finned pipe placed in the center of a square enclosure with uniform internal heat generation. Four perpendicular thin fins of arbitrary and equal dimensions are attached to the pipe whose internal surface is isothermally cooled. The sides of the enclosure are considered to have finite and equal thicknesses and their external sides are isothermally heated. The problem is put into dimensionless formulation and solved numerically by means of the finite-volume method. Representative results illustrating the effects of the finned pipe inclination angle and fins length on the streamlines and temperature contours within the enclosure are reported. In addition, results for the local and average Nusselt numbers are presented and discussed for various parametric conditions.