Heat flow visualization for natural convection in rhombic enclosures due to isothermal and non-isothermal heating at the bottom wall

Analysis has been carried out for the energy distribution and thermal mixing in steady laminar natural convective flow through the rhombic enclosures with various inclination angles, φ for various industrial applications. Simulations are carried out for various regimes of Prandtl (Pr) and Rayleigh (Ra) numbers. Dimensionless streamfunctions and heatfunctions are used to visualize the flow and energy distribution, respectively. Multiple flow circulations are observed at Pr = 0.015 and 0.7 for all φs at Ra = 10⁵. On the other hand, two asymmetric flow circulation cells are found to occupy the entire cavity for φ = 75° at higher Pr (Pr = 7.2 and 1000) and Ra (Ra = 10⁵). Heatlines are found to be parallel circular arcs connecting the cold and hot walls for the conduction dominant heat transfer at Ra = 10³. The enhanced convective heat transfer is explained with dense heatlines and convective loop of heatlines at Ra = 10⁵. Heatlines clearly demonstrate that the left wall receives heat from the bottom wall as heatlines directly connect both the walls whereas the convective heat circulation cells play lead role to distribute the heat along the right wall, especially for smaller φs. On the other hand, the heat flow is evenly distributed to both side walls at higher φs via convection as well as direct conductive transport. Significant convective heat transfer from the bottom hot wall to the left cold wall occurs for φ = 30° cavity whereas the heat transfer to the right cold wall is maximum for φ = 75° irrespective of Pr. Average Nusselt number studies also show that φ = 30° cavity gives maximum heat transfer rate from the bottom to left wall irrespective of Pr in isothermal heating case. On the other hand, enhanced thermal mixing occurs at φ = 75° for both isothermal and non-isothermal heating strategies except at Pr = 0.015 in isothermal heating case.     

Effects of thermal boundary conditions on natural convection flows within a square cavity

A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁵ and Prandtl number Pr, 0.7 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented.     

Heatlines based natural convection analysis in tilted isosceles triangular enclosures with linearly heated inclined walls: effect of various orientations

Natural convection in isosceles triangular enclosures with various configurations (case 1 — inverted, case 2 — straight and case 3 — tilted) is studied via heatline analysis for linear heating of inclined walls. Detailed analysis and comparison for various base angles (φ = 45°, 60°) of triangular enclosures have been carried out for a range of fluids (Pr = 0.015 − 1000) within Ra = 10³ − 10⁵ using Galerkin finite element method. The heat flow distributions indicate conduction dominant heat transfer at low Ra (Ra = 10³) for case 1 and case 2 whereas in case 3, convective heat flow is observed due to high buoyancy force. As Ra increases, enhanced thermal mixing is observed at the core of the cavity. Wall to wall heat transfer occurs at walls AB and AC due to linear heating boundary condition in all the cases. Although the distributions of fluid flow and heat flow are qualitatively similar for φ = 45° and 60°, the intensity of fluid flow and heat flow decreases as φ increases. Strength of fluid flow and heat flow circulation cells is found to be higher in case 3 for identical parameters. Results show that upper side wall (AC) for case 3 exhibits higher heat transfer rates whereas heat transfer rates for walls AB and AC are the same for case 1 and case 2. Also Nu_AB is higher for case 2 followed by case 1 and case 3 at the middle portion of wall AB. Thus to achieve high heat transfer from fluid to wall at the central region, case 2 and case 3 configurations may be recommended at high Ra (Ra = 10⁵) and Pr, irrespective of φ.     

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.     

Natural convection in a partially open square cavity with internal heat source: An analysis of the opening mass flow

A steady buoyancy-driven flow of air in a partially open square 2D cavity with internal heat source, adiabatic bottom and top walls, and vertical walls maintained at different constant temperatures is investigated numerically in this work. A heat source with 1% of the cavity volume is present in the center of the bottom wall. The cold right wall contains a partial opening occupying 25%, 50% or 75% of the wall. The influence of the temperature gradient between the verticals walls was analyzed for Ra_e = 10³–10⁵, while the influence of the heat source was evaluated through the relation R = Ra_i/Ra_e, investigated at between 400 and 2000. Interesting results were obtained. For a low Rayleigh number, it is found that the isotherm plots are smooth and follow a parabolic shape indicating the dominance of the heat source. But as the Ra_e increases, the flow slowly becomes dominated by the temperature difference between the walls. It is also observed that multiple strong secondary circulations are formed for fluids with a small Ra_e whereas these features are absent at higher Ra_e. The comprehensive analysis is concluded with horizontal air velocity and temperature plots for the opening. The numerical results show a significant influence of the opening on the heat transfer in the cavity.     

Analysis of Bejan’s heatlines on visualization of heat flow and thermal mixing in tilted square cavities

This article analyzes the detailed heat transfer phenomena during natural convection within tilted square cavities with isothermally cooled walls (BC and DA) and hot wall AB is parallel to the insulated wall CD. A penalty finite element analysis with bi-quadratic elements has been used to investigate the results in terms of streamlines, isotherms and heatlines. The present numerical procedure is performed over a wide range of parameters (10³ ? Ra ? 10⁵,0.015 ? Pr ? 1000,0° ? φ ? 90°). Secondary circulations cells are observed near corner regions of cavity for all φ’s at Pr = 0.015 with Ra = 10⁵. Two asymmetric flow circulation cells are found to occupy the entire cavity for φ = 15° at Pr = 0.7 and Pr = 1000 with Ra = 10⁵. Heatlines indicate that the cavity with inclination angle φ = 15° corresponds to large convective heat transfer from the wall AB to wall DA whereas the heat transfer to wall BC is maximum for φ = 75°. Heat transfer rates along the walls are obtained in terms of local and average Nusselt numbers and they are explained based on gradients of heatfunctions. Average Nusselt number distributions show that heat transfer rate along wall DA is larger for lower inclination angle (φ = 15°) whereas maximum heat transfer rate along wall BC occur for higher inclination angle (φ = 75°).     

Role of moving horizontal walls on entropy generation during mixed convection within entrapped triangular cavities

A comprehensive analysis based on the irreversibilities associated with the energy flow and entropy generation is highly essential for the optimization of thermal systems. Entropy generation during mixed convection process has been studied in entrapped triangular cavities for moving horizontal walls involving isothermally hot inclined walls and cold horizontal walls (case 1) or isothermally cold inclined walls and hot horizontal walls (case 2). Overall it is found that, Re = 100 may be preferred over Re → 0, Re = 1 and Re = 10 at Pr = 0.026 and 7.2, Gr = 10³ − 10⁵ within the cavities, irrespective of the cases. In addition to Re = 100, Re = 10 may be optimal for the upper cavity with case 1 and lower cavity with case 2 at Gr ≈ 10⁵ (higher Gr regime) and Pr = 7.2 based on moderate heat transfer rates.     

Boiling heat transfer and critical heat flux of ethanol–water mixtures flowing through a diverging microchannel with artificial cavities

This paper presents an experimental study on the convective boiling heat transfer and the critical heat flux (CHF) of ethanol–water mixtures in a diverging microchannel with artificial cavities. The results show that the boiling heat transfer and the CHF are significantly influenced by the molar fraction (x_m) as well as the mass flux. For the single-phase convection region except for the region near the onset of nucleate boiling with temperature overshoot, the single-phase heat transfer coefficient is independent of the wall superheat and increases with a decrease in the molar fraction. After boiling incipience, the two-phase heat transfer coefficient is much higher than that of single-phase convection. The two-phase heat transfer coefficient shows a maximum in the region of bubbly-elongated slug flow and deceases with a further increase in the wall superheat until approaching a condition of CHF, indicating that the heat transfer is mainly dominated by convective boiling. A flow-pattern-based empirical correlation for the two-phase heat transfer coefficient of the flow boiling of ethanol–water mixtures is developed. The overall mean absolute error of the proposed correlation is 15.5%, and more than 82.5% of the experimental data were predicted within a ±25% error band. The CHF increases from x_m = 0–0.1, and then decreases rapidly from x_m = 0.1–1 at a given mass flux of 175 kg/m² s. The maximum CHF is reached at x_m = 0.1 due to the Marangoni effect, indicating that small additions of ethanol into water could significantly increase the CHF. On the other hand, the CHF increases with increasing the mass flux at a given molar fraction of 0.1. Moreover, the experimental CHF results are compared with existing CHF correlations of flow boiling of the mixtures in a microchannel.     

Numerical simulation of turbulent fluid flow and heat transfer characteristics in heat exchangers fitted with porous media

Numerical simulations have been carried out to investigate the turbulent heat transfer enhancement in the pipe filled with porous media. Two-dimensional axisymmetric numerical simulations using the k–? turbulent model is used to calculate the fluid flow and heat transfer characteristics in a pipe filled with porous media. The parameters studied include the Reynolds number (Re = 5000–15,000), the Darcy number (Da = 10^?1–10^?6), and the porous radius ratio (e = 0.0–1.0). The numerical results show that the flow field can be adjusted and the thickness of boundary layer can be decreased by the inserted porous medium so that the heat transfer can be enhanced in the pipe. The local distributions of the Nusselt number along the flow direction increase with the increase of the Reynolds number and thickness of the porous layer, but increase with the decreasing Darcy number. For a porous radius ratio less than about 0.6, the effect of the Darcy number on the pressure drop is not that significant. The optimum porous radius ratio is around 0.8 for the range of the parameters investigated, which can be used to enhance heat transfer in heat exchangers.     

Effect of fin thickness on the air-side performance of wavy fin-and-tube heat exchangers under dehumidifying conditions

This study investigated the effect of fin thickness on the air-side performance of wavy fin-and-tube heat exchangers under dehumidifying conditions. A total of 10 samples were tested with associated fin thickness (δ_f) of 0.115 mm and 0.25 mm, respectively. For a heat exchanger with two rows (N = 2) and fin pitch F_p of 1.41 mm, the effect of fin thickness on the heat transfer coefficient is more pronounced. The heat transfer coefficients for δ_f = 0.25 mm is about 5–50% higher than those for δ_f = 0.115 mm whereas the pressure drop for δ_f = 0.25 mm is about 5–20% higher. The unexpected difference in heat transfer coefficient subject to fin thickness is attributable to better interactions between the directed main flow and the swirled flow caused by the condensate droplet for δ_f = 0.25 mm. The maximum difference in heat transfer coefficients for N = 2 and F_p = 2.54 mm subject to the influence of fin thickness is reduced to about 20%, and there is no difference in heat transfer coefficient when the frontal velocity is above 3 m/s. For N ⩾ 4 and F_p = 2.54 mm, the influence of fin thickness on the heat transfer coefficients diminishes considerably. This is because of the presence of tube row, and the unsteady/vortex shedding feature at the down stream of wavy channel. Based on the present test results, a correlation is proposed to describe the air-side performance for wavy fin configurations, the mean deviations of the proposed heat transfer and friction correlations are 7.9% and 7.7%, respectively.     

Hydrodynamics and heat transfer in swirl flow under conditions of one-side heating. Part 2: Boiling heat transfer. Critical heat fluxes

The paper gives the basic results of experimental investigation of boiling heat transfer in heat-absorbing devices of the ITER thermonuclear reactor, which are subjected to one-side heating. The experimental data on heat transfer at nucleate and film boiling and on critical heat fluxes are obtained in the following range of parameters of water flow: pressure p = 0.7–2.0 MPa, mass flux G = 340–25 000 kg/(m² s), and water temperature at the inlet T_in = 20–60 °C. A twisted tape is inserted in the circular channel in order to form swirling flow of water. The investigations are performed for tapes with different values of flow swirl coefficient, as well for test sections without a tape. Appropriate calculation formulas are derived, which reliably generalize the experimental data.     

Investigation of coated tubes in cross-flow boiling

The boiling in cross-flow is investigated for coated tubes (low-porosity, flame-sprayed) in this paper. The effect of surface roughness on flow boiling heat transfer for a horizontal tube surface in cross-flow is studied for saturated boiling of water at atmospheric pressure. The parameters varied were for flow velocity up to 3.24 kg/s (G = 258.49 kg/m² s), heat flux from 12 to 45 kW/m², surface roughness (Ra) from 0.3296 to 4.731 μm. Nominal enhancement in heat transfer coefficient at higher mass flux may be attributed to the continued nucleation at the uppermost surfaces (in the wake region of the flow) of the rougher tubes thereby increasing the overall heat transfer rate. The flow boiling data was found to best fit the Kutateladze asymptotic equation h = h_l[1 + (h_npb/h_l)ⁿ]^1/n with the value of n = 2.258 (which is close to the value of n = 2 suggested by Kutateladze).     

Critical heat flux on flow boiling of methanol–water mixtures in a diverging microchannel with artificial cavities

This study constitutes an experimental investigation into the convective boiling heat transfer and critical heat flux (CHF) of methanol–water mixtures in a diverging microchannel with artificial cavities. Flow visualization shows that bubbles are generally nucleated at both the artificial cavities and side walls of the channel. This confirms the proper functioning of such artificial cavities. Consequently, the wall superheat of the onset nucleate boiling is significantly reduced. Experimental results show that the boiling heat transfer and CHF are significantly influenced by the molar fraction (x_m) as well as the mass flux. The CHF increases with an increase in mass flux at the same molar fraction. On the other hand, the CHF increases slightly from x_m = 0 to 0.3, and then decreases rapidly from x_m = 0.3 to 1 at the same mass flux. The maximum CHF is reached at x_m = 0.3, particularly for a mass flux of 175 kg/m² s, due to the Marangoni effect. Flow visualization confirms that the Marangoni effect helps a region with a liquid film breakup persist to a higher heat flux, and therefore a higher CHF. Moreover, a new empirical correlation involving the Marangoni effect for the CHF on the flow boiling of methanol–water mixtures is developed. The present correlation prediction shows excellent agreement with the experimental data, and further confirms that the present correlation may predict the Marangoni effect on the CHF for the convective boiling heat transfer of binary mixtures.     

Hydrodynamics and heat transfer in swirl flow under conditions of one-side heating. Part 1: Pressure drop and single-phase heat transfer

The paper gives the basic results of experimental investigation of hydrodynamics and heat transfer in heat-absorbing devices of the ITER thermonuclear reactor, which are subjected to one-side heating. The entire array of experimental data is obtained in the following range of parameters of water flow: pressure p = 0.7–2.0 MPa, mass flux G = 340–25,000 kg/(m² s), inlet water temperature T_in = 15–60 °C. The experiments are performed with turbulent swirl flows of water for twisted tapes with the flow swirl coefficient k = 0.90, 0.66, 0.49, 0.39, 0.25, 0.19, and 0, as well for test sections without a tape. Given in the first part of the paper are the data on pressure drop and single-phase convective heat transfer. Appropriate calculation formulas are derived, which reliably generalize the experimental data.     

Experimental study of evaporation heat transfer of R-134a inside a corrugated tube with different tube inclinations

Experimental heat transfer studies during evaporation of R-134a inside a corrugated tube have been carried out. The corrugated tube has been provided with different tube inclination angles of the direction of fluid flow from horizontal, α. The experiments were performed for seven different tube inclinations, α, in a range of − 90° to + 90° and four mass velocities of 46, 81, 110 and 136 kg m^− 2 s^− 1 for each tube inclination angle during evaporation of R-134a. Data analysis demonstrate that the tube inclination angle, α, affects the boiling heat transfer coefficient in a significant manner. The effect of tube inclination angle, α, on heat transfer coefficient, h, is more prominent at low vapor quality and mass velocity. In the low vapor quality region, the heat transfer coefficient, h, for the + 90° inclined tube is about 62% more than that of the − 90° inclined tube. The results also showed that at all mass velocities, the highest average heat transfer coefficient were achieved for α = + 90°. An empirical correlation has also been developed to predict the heat transfer coefficient during flow boiling inside a corrugated tube with different tube inclinations.     

Natural convection heat transfer enhancement using adiabatic block: Optimal block size and Prandtl number effect

Numerical methods are used to solve the finite volume formulation of the two-dimensional mass, momentum and energy equations for steady-state natural convection inside a square enclosure. The enclosure consists of adiabatic horizontal walls and differentially heated vertical walls, but it also contains an adiabatic centrally-placed solid block. The aim of the study is to delineate the effect of such a block on the flow and temperature fields. The parametric study covers the range 10³ ⩽ Ra ⩽ 10⁶ and is done at three Pr namely, 0.071, 0.71 and 7.1. In addition the effect of increasing the size (characterized by the solidity Φ) of the adiabatic block is ascertained. It is found that the wall heat transfer increases, with increase in the Φ, until it reaches a critical value Φ = Φ_OPT, where the wall heat transfer attains its maximum. Further increases in the block size beyond Φ_OPT, reduces the wall heat transfer, for as the block size becomes larger than the conduction dominant core size it reduces the thermal mass of the convecting fluid. A steady-state heat transfer enhancement of 10% is observed for certain Ra and Pr values. Useful correlations predicting this optimum block size and the corresponding maximum heat transfer as a function of Ra and Pr are proposed; these predict within ±3%, the numerical results.     

Experimental study of R-134a evaporation heat transfer in a narrow annular duct

An experiment is carried out here to investigate the evaporation heat transfer and associated evaporating flow pattern for refrigerant R-134a flowing in a horizontal narrow annular duct. The gap of the duct is fixed at 1.0 and 2.0 mm. In the experiment, the effects of the duct gap, refrigerant vapor quality, mass flux and saturation temperature and imposed heat flux on the measured evaporation heat transfer coefficient h_r are examined in detail. For the duct gap of 2.0 mm, the refrigerant mass flux G is varied from 300 to 500 kg/m² s, imposed heat flux q from 5 to 15 kW/m², vapor quality x_m from 0.05 to 0.95, and refrigerant saturation temperature T_sat from 5 to 15 °C. While for the gap of 1.0 mm, G is varied from 500 to 700 kg/m² s with the other parameters varied in the same ranges as that for δ = 2.0 mm. The experimental data clearly show that the evaporation heat transfer coefficient increases almost linearly with the vapor quality of the refrigerant and the increase is more significant at a higher G. Besides, the evaporation heat transfer coefficient also rises substantially at increasing q. Moreover, a significant increase in the evaporation heat transfer coefficient results for a rise in T_sat, but the effects are less pronounced in the narrower duct at a low imposed heat flux and a high refrigerant mass flux. Furthermore, the evaporation heat transfer coefficient increases substantially with the refrigerant mass flux except at low vapor quality. We also note that reducing the duct gap causes a significant increase in h_r. In addition to the heat transfer data, photos of R-134a evaporating flow taken from the duct side show the change of the dominant two-phase flow pattern in the duct with the experimental parameters. Finally, an empirical correlation for the present measured heat transfer coefficient for the R-134a evaporation in the narrow annular ducts is proposed.     

Influence of the flashing phenomenon on the boiling curve of refrigerant R134a in minichannels

The results of experimental investigations of heat transfer during the flow of R134a in a minichannel are presented here. The experimental investigations were conducted using a minichannel with a total length of 500 mm and 1.68 mm internal diameter. The heated length of the minichannel was 200 mm, the total mass flow rate of the refrigerant (wρ) = 200–450 kg/m² s, the inlet subcooling ΔT_s = 5–15 K, and the heat flux density q = 1.7–60.3 kW/m². The results of experimental investigations are presented as a boiling curve. The phenomenon known as the zero boiling crisis and the influence of the flashing phenomenon on the boiling curve show the importance of these elements on heat transfer in single- and two-phase systems.     

Investigation of mixed convection heat transfer in a horizontal channel with discrete heat sources at the top and at the bottom

Mixed convection heat transfer from arrays of discrete heat sources inside a horizontal channel has been investigated experimentally. Each of the lower and upper surfaces of the channel was equipped with 8 × 4 flush mounted heat sources subjected to uniform heat flux. Sidewalls, lower and upper walls are insulated and adiabatic. The experimental parametric study was made for aspect ratios of AR = 2, 4 and 10, at various Reynolds and Grashof numbers. From the experimental measurements, row-average surface temperature and Nusselt number distributions of the discrete heat sources were obtained and effects of Reynolds and Grashof numbers on these numbers were investigated. From these results, the buoyancy affected secondary flow and the onset of instability have been discussed. Results show that top and bottom heater surface temperatures increase with increasing Grashof number. The top heater average-surface temperatures for AR = 2 are greater than those of bottom ones. For high values of Grashof numbers where natural convection is the dominant heat transfer regime (Gr¹/Re² ≫ 1), temperatures of top heaters can have much greater values. The variation of the row-average Nusselt numbers for the aspect ratio of AR = 4, show that with the increase in the buoyancy affected secondary flow and the onset of instability, values of Nusselt number level off and even rise as a result of heat transfer enhancement especially for low Reynolds numbers.     

Mixed convection flow and heat transfer across a square cylinder under the influence of aiding buoyancy at low Reynolds numbers

In this paper, mixed convection flow and heat transfer around a long cylinder of square cross-section under the influence of aiding buoyancy are investigated in the vertical unconfined configuration (Reynolds number, Re = 1–40 and Richardson number, Ri = 0–1). The semi-explicit finite volume method implemented on the collocated grid arrangement is used to solve the governing equations along with the appropriate boundary conditions. The onset of flow separation occurs between Re = 1–2, between Re = 2–3 and between Re = 3–4 for Ri = 0, 0.5 and 1, respectively. The flow is found to be steady for the range of conditions studied here. The friction, pressure and total drag coefficients are found to increase with Richardson number, i.e., as the influence of aiding buoyancy increases drag coefficients increase at the constant value of the Reynolds number. The temperature field around the obstacle is presented by isotherm contours at the Prandtl number of 0.7 (air). The local and average Nusselt numbers are calculated to give a detailed study of heat transfer over each surface of the square cylinder and an overall heat transfer rate and it is found that heat transfer increases with increase in Reynolds number and/or Richardson number. The simple expressions for the wake length and average cylinder Nusselt number are obtained for the range of conditions covered in this work.