Range Of Rayleigh Numbers Research Articles

Heat transfer in a conical gap using H2O–Cu nanofluid and porous media. Effects of the main physical parameters

Heat transfer around a conical antenna is quantified in this work. Cooling of this active electronic component is ensured by a medium of high porosity saturated by a H2O–Cu nanofluid with a volume fraction varying between 0% and 5%. The ratio between the thermal conductivity of the porous materials and that of the water (base fluid) ranges from 4 to 41.2, the null value corresponding to a heat transfer without porous media (only nanofluid). The conical enclosure's aspect ratio varies in the 0.2–0.6 range, being its base inclined between 0° (horizontal base with cone's top oriented upwards) and 180° range (horizontal base with cone's top oriented downwards). The associated Rayleigh number varies within the 3.32x105-6.74x107 range. Heat transfer by natural convection is quantified for any configuration combining these five parameters and presented via a correlation allowing determination of the average Nusselt number. This study shows that heat transfer increases when the cone is tilted. For a given aspect ratio, the maximum is reached when the cone is vertical with the top pointing down. This observation remains valid in the overall Rayleigh number range. The average Nusselt number enhancement varies between 20 and 70%, according on the considered cavity's aspect ratio. This study complements a recent one restricted to the case of a cone whose horizontal base is located at the bottom, being 0.2 the aspect ratio of the enclosure.

Natural convection heat transfer from a ribbed vertical plate: Effect of rib size, pitch, and truncation

Buoyancy-induced flows over ribbed vertical surfaces involve complex thermal and dynamic interactions between the mainstream and the surface texture, yielding contrasting effects on the heat transfer performance of the heated plate; proper analysis of the overall effect on the heat transfer rate is essential for efficient operation and optimization purposes. The present work pursues an insight into the different factors controlling this problem. Natural convection heat transfer from a vertical plate of 0.5 m height, regularly roughened with wooden transverse square ribs, is experimentally investigated. The surface temperature of the baseplate is varied so that a range of the plate Rayleigh number (Ra) from 3.4 × 108 to 4.9 × 108 is covered. The density of the roughness pattern and the rib pitch-to-height ratio (P/e) are varied by changing the number of ribs attached to the surface (from 10 to 40 rib rows) and using three different square cross-sections (of side lengths 2, 3, or 5 mm). The experimental work relies on the schlieren optical technique, through which the thermal boundary layer is visualized and the Nusselt number distribution is acquired. Analysis of the results reveals that enhancement of the local Nusselt number, relative to a corresponding smooth surface, may be attained only at the central part of the inter-rib region; this occurs exclusively for relatively large values of P/e. At a later stage, the effectiveness of rib truncation in enhancing the heat transfer from the baseplate is explored. Three staggered arrangements are considered, by varying the number of rib segments per row, and heat transfer enhancement, sensitive to the number of rib segments per row, is found. This paper also provides insight into the role of thermal-field disturbances close to turbulent transition, and sheds light on the potential of truncated ribs to amplify such perturbations.

Heat transfer modulation in Rayleigh–Bénard convection by an oscillatory bottom plate

In this paper, we consider a heat transfer modulation in Rayleigh–Bénard convection by imposing a periodic sinusoidal oscillation to the bottom hot plate parallel to itself. Two-dimensional numerical simulations are carried out under lateral periodic conditions, over a Rayleigh number range of 106≤Ra≤109 and for a fixed Prandtl number of Pr = 7.1. For a given Rayleigh number, it is found that the Nusselt number, characterizing the global heat transfer efficiency of the system, shows a counter-intuitive initial drop and subsequent rise behavior, as the characteristic oscillatory velocity Vosc increases. Accordingly, taking the classical Rayleigh–Bénard convection as a reference, a heat transfer reduction regime for low Vosc and a heat transfer enhancement regime for high Vosc are recognized. The reduction regime is resulted from the thickening of the thermal boundary layer due to the amplified viscous effect by the oscillation, which increases the thermal resistance of the system. In addition to thickening the thermal boundary layer, a stronger oscillation could also trigger a thermal boundary layer instability, inducing massive emission of the thermal plumes and eventually giving rise to a significant global heat transfer enhancement. Moreover, the combined effect of thickening and destabilizing of the thermal boundary layer leads to a temporal periodic evolution of the Nusselt number at the bottom plate in the enhancement regime. A critical oscillatory velocity Vc is selected at the crossover between two regimes, and it is found decreasing with an increasing Ra as Vc∼Ra−0.2. Through dimensional analysis, we provide a physical explanation for this dependence.

Natural Convection Heat Transfer from an Isothermal Plate

Using boundary-layer theory, natural convection heat transfer formulas that are accurate over a wide range of Rayleigh numbers (Ra) were developed in the 1970s and 1980s for vertical and downward-facing plates. A comprehensive formula for upward-facing plates remained unsolved because they do not form conventional boundary-layers. From the thermodynamic constraints on heat-engine efficiency, the novel approach presented here derives formulas for natural convection heat transfer from isothermal plates. The union of four peer-reviewed data-sets spanning 1<Ra<1012 has 5.4% root-mean-squared relative error (RMSRE) from the new upward-facing heat transfer formula. Applied to downward-facing plates, this novel approach outperforms the Schulenberg (1985) formula’s 4.6% RMSRE with 3.8% on four peer-reviewed data-sets spanning 106<Ra<1012. The introduction of the harmonic mean as the characteristic length metric for vertical and downward-facing plates extends those rectangular plate formulas to other convex shapes, achieving 3.8% RMSRE on vertical disk convection from Hassani and Hollands (1987) and 3.2% from Kobus and Wedekind (1995).

Regimes of successive and spontaneous double-diffusive layering and their merger

A recent observation revealed that alternating layers of milk and coffee-enriched regions are formed when espresso is poured into steamed milk Xue et al. This is generally known as double-diffusive convection (DDC), often seen in oceans, solidifying mixtures, etc. Inspired by this observation, we report an extensive numerical investigation of DDC, for a system having a linearly stable solute stratification of an aqueous solution exposed to lateral thermal cooling from a sidewall. The phenomenon is analyzed with the help of finite-volume-based numerical solutions of the conservation equations (continuity, momentum, energy, and species) for two-dimensional, unsteady, laminar convection. A large number of simulations, covering a wide range of thermal Rayleigh numbers (105≤RaT≤108) and solutal Rayleigh numbers(106≤RaS≤108), revealed the transitions between four different flow regimes in the form of correlations of the two Rayleigh numbers. The analysis of the overall time of survival of double-diffusive layers (DDLs) for a wide range of RaS&RaT established that the time of survival follows the same proportionality with RaS&RaT as the curve of onset of the spontaneous layered regime. In addition to the transient evolution of flow and transport variables (composition, temperature and density fields), the heat transfer coefficients at the sidewalls were obtained for the whole life-span of DDLs. While the influence of DDLs in rendering an alternating high and low wall heat transfer was evident, the overall heat transfer was also found to be significantly lower when compared with the absence of DDC. These findings explain why a layered latte remains hotter for a larger duration.

Fluid Flow and Heat Transfer Characteristics of Clerestory-Shaped Attics Heated from Below

In this study, a finite volume analysis of the aerodynamics and heat transfer in attics of a clerestory roof design with pitch angles 14o, 18o, 30o and 45o and Rayleigh number range 3 x 105≤ Ra ≤ 2 x 107 is carried out. The shape of the enclosure has strong influence on the structure of the flow and temperature fields. The flow field is characterised by counter-rotating vortices enclosed by aerodynamic boundary layers. The size, strength and direction of rotation of the cells are controlled by the forces propelling the thermal plumes and the cold jets. The reduction of the number and size of the counter-rotating cells and their formation within the enclosures provide an analogous reduction of the total heat transfer rate as the roof pitch angle increases. The velocity and temperature profiles across midheight and midlength of the enclosures enable the prediction of appropriate position in the attic with the right condition to place sensitive items. On the heat transfer, the relationship between the mean Nusselt number and the Rayleigh number is presented in form of a correlation. Results obtained in the study are of significance to building engineers engaged in the analysis and design of building attics and tropical agriculturalists for the control of produce drying rates. Keywords: Heat transfer, heated below, natural convection, pitch roof, clerestory-shaped

INFLUENCE OF THE ASPECT RATIO AND LOCATION OF AN ISOTHERMAL BLOCK ON THE BUOYANCY-INDUCED HEAT TRANSFER IN AN ENCLOSURE

The objective of the current study's numerical analysis is to find the effect of the aspect ratio and placement of an isothermal block on fluid flow and heat transfer within an air-filled square cavity and having a Prandtl number of 0.71. The flow is considered to be taking place by natural convection and Rayleigh's numbers range between 10<sup>3</sup> and 10<sup>6</sup>. Between 1.00 and 2.00, the block's aspect ratio is evaluated. In a cavity with a centrally positioned hot block, the impact of Rayleigh's number and block aspect ratio on heat and fluid transport is evaluated. The effect of the location of the block is examined at three different locations as the top wall, center, and bottom wall of the cavity, respectively. A finite-difference-based stream function vorticity formulation is considered for the computation. The findings indicate that Rayleigh's number is a positive function of the heat-transfer rate and fluid velocity which shows that increase in Ra enhances buoyancy. The increase in the aspect ratio of the internal block enhances the area of hydrodynamic blockage, which modifies the rate of convection and flow velocity of the fluid within the cavity. The results also show that shifting the block's location has a significant impact on the buoyancy force generated inside the enclosure. A higher total heat transmission rate is produced by the bottom and center-placed blocks.

Scaling transition of thermal dissipation in turbulent convection

Direct numerical simulation (DNS) of non-slip two dimensional (2D) Rayleigh–Benard convection (RBC) is conducted for a wide range of Rayleigh number (Ra up to 1013) at Prandtl number Pr = 0.7 and aspect ratio Γ = 1. The thermal dissipation rate is shown to display an evident scaling transition through the compensated plot, i.e., ⟨εθ⟩∝Raγ with γ≈−0.17 for 106≤Ra≤109, while γ≈−0.19 for Ra=109≤Ra≤1013. To track the transition, separate contributions from the thermal boundary layer (BL) and the bulk flow region are examined, incorporated also with the mean and fluctuation decomposition. It turns out that the mean temperature gradient in the BL is the dominant contribution, and together with other parts (i.e., fluctuations in the BL and bulk, and the mean gradient in the bulk), they all exhibit an obvious transition at Ra≈109. We have further checked the Nusselt number (Nu), which also shows the transition at Ra≈109. Interestingly, Nu∝Ra0.33 is observed for small Ra, while Nu∝Ra2/7 is absent in 2D RBC cases. To understand the physical origin of transition, spatial distributions and probability density functions of thermal dissipation rate are finally discussed, with notable statistical features changed at Ra≈109.

Temperature response to periodic modulation in internal heating convection

Thermal convection in nature and industrial applications usually encounters time-varying internal heating (IH); however, the effect of temporal modulation on temperature responses and heat fluxes of the system has been rarely explored. Here, we numerically studied the IH convection with a temporally periodic heating source. We conducted direct numerical simulations over Rayleigh number (Ra) range 105≤Ra≤109 at fixed Prandtl number Pr = 1 with dimensionless modulation frequency 4×10−5≤f≤10−1 and amplitude fixed at Ω = 1. We first find that the introduction of periodic modulation has a slight effect on the heat transport over the individual plates and flow strength except for the lowest Ra. We then focus on the characteristics of the amplitude A and phase lag Δϕ of the globally averaged temperature response to the periodic modulation. Three regimes of the phase response are identified: (i) in-phase regime, where synchronous response is found at small frequencies with the vanished phase lag Δϕ and A keeping at constant value; (ii) transition regime, where both Δϕ and A decrease with increasing f for moderate frequencies; and (iii) half anti-phase regime, where Δϕ attains the minimal value −π/2. We also find that the transition behavior between three regimes can be well described using the normalization of the Ra-dependent critical frequency with the scaling Ra−0.30. To explain the regime transition, we further theoretically deduce an analytical solution for A and Δϕ, which agrees well with the numerical results. This solution can explain why fRa0.30 gives a good description of the transition behavior. Our present findings provide a fundamental understanding of the underlying mechanism of temporal modulation on IH systems and have substantial implications for the investigation of convective system with periodic heating source.

Heat flux enhancement by regular surface protrusion in partitioned thermal convection

We investigate the influence of the regular roughness of heated and cooled plates and adiabatic partition boards on the mean heat transport in a square Rayleigh–Bénard (RB) convection enclosure by two-dimensional direct numerical simulations. The roughness is in the form of isothermal protrusions with a rectangular base and triangular tip. The protrusion height varies from 10% to 25% of enclosure height. With increased protrusion height, the large-scale circulation cannot wash out the cavity between two consecutive protrusions. Thus, the overall heat transport of the enclosure impedes. We have inserted the partition boards between two successive protrusions with a gap between the conduction plate and the partition board to wash out the cavity. The partition board height varies from 20% to 99.8% of enclosure height. We have performed the simulations for the range of Rayleigh number 106–108 and at a fixed Prandtl number of 1. The tip of the triangular protrusion acts as an active plume-emitting spot. We observe a single large-scale elliptical roll with counter-rotating corner rolls for small partition board height. With an increase in partition board height, an elliptical large-scale roll breaks down into the number of large-scale rolls horizontally placed one beside the other. Finally, we observe multiple rolls stacked vertically when the partition boards almost touch the conduction walls. Heat flux enhancement strongly depends on large-scale flow structures. We found a maximum heat flux enhancement in protrusion with partitioned RB case approximately up to 4.7 times the classical square RB for an optimal gap between conduction plate and partition board. The maximum heat transport enhancement is due to the strong horizontal flow through the gap between the conduction plate and partition board, which locally reduces the thermal boundary layer's thickness. The interaction between the horizontal jets and the thermal boundary layers enhances heat transport.

COMPARATIVE NUMERICAL STUDY OF NATURAL CONVECTION IN SQUARE AND TRIANGULAR CAVITY

This paper is based on the numerical investigation of natural convection of two vertical enclosure of square and triangular cavity with air filled. The vertical cavity consist of adiabatic and hot and cold wall with wide range of Rayleigh number from 103 to 106 with aspect ratio from 1 to 10 at the interval of 2.5. Flow patterns and isotherm plots were used to display the results, and for every case, local and mean Nusselt values were also produced. The results show that an increase in Rayleigh numbers greatly increases heat transfer, natural convection intensity, and average Nusselt number at a particular aspect ratio. Keyword: ANN (average Nusselt number), AR (aspect ratio), LNN (local Nusselt number), Nu (Nusselt number), Pr (Prandtl number), Ra (Rayleigh number).

Study of combined effect of natural convection and radiation heat transfer from annular finned vertical cylinder

AbstractThe present numerical study reports the combined effect of natural convection and radiation heat from a vertical cylinder with annular fins. The study involves simulation for laminar as well as turbulent regimes. For the present study, Rayleigh's number is varied in the range , emissivity in the range , and the fin spacing ratio (s/d) in the range . The radiation heat transfer has been found to share a considerable amount in the total heat transfer of the system for the laminar regime, but in the turbulent regime, its effect is minimal and can be neglected. When the fin spacing ratio is reduced, the total heat transfer increases for both the turbulent and laminar flow conditions. But the radiation heat increases with a reduction in fin spacing ratio for laminar and in case of turbulent flow radiation heat rate reduces with a reduction in s/d ratio. For the range of Rayleigh numbers considered in the present study, the Nusselt number increases with the increment of the fin spacing ratio. Thus, it can be concluded that there is a remarkable enhancement in the heat transfer rate in laminar cases with the fins. For turbulent cases, the fin efficiency lies between 40% and 50%.

Numerically investigation of Flow and Heat Transfer in differentially heated enclosures

In this research work natural convection in two dimensional cavity is studied numerically for differently heated air filled square and rectangular cavity. Vertical cavity with two adiabatic and hot and cold wall with different aspect ratio of 1, 2.5, 5, 7.5 and 10 has taken for investigation. the heat transfer was investigated over the wide range of Rayleigh number from 103 to 106 . Solutions are obtained for several Rayleigh numbers with Prandtl number Pr = 0.70 and aspect ratio 1, 2.5, 5, 7.5 and 10. The Pressure-Velocity Coupling Method used with Non-Iterative Time Advancement (NITA) scheme used to solve the problem. Flow patterns and isotherm plots were used to display the results, and for every case, local and mean Nusselt values were also produced. The results show that an increase in Rayleigh numbers greatly increases heat transfer, natural convection intensity, and average Nusselt number at a particular aspect ratio. The distribution of temperature and stream function are taken as a function of thermal and geometrical output parameter for given problem. Two stage investigations have been performed to find out the variation in the result between different approaches. Keyword: ANN (average Nusselt number), AR (aspect ratio), LNN (local Nusselt number), Nu (Nusselt number), Pr (Prandtl number), Ra (Rayleigh number).

Flow states and heat transport in liquid metal convection

We present an experimental study of Rayleigh–Bénard convection using liquid metal alloy gallium-indium-tin as the working fluid with a Prandtl number of $Pr=0.029$ . The flow state and the heat transport were measured in a Rayleigh number range of $1.2\times 10^{4} \le Ra \le 1.3\times 10^{7}$ . The temperature fluctuation at the cell centre is used as a proxy for the flow state. It is found that, as $Ra$ increases from the lower end of the parameter range, the flow evolves from a convection state to an oscillation state, a chaotic state and finally a turbulent state for $Ra>10^5$ . The study suggests that the large-scale circulation in the turbulent state is a residual of the cell structure near the onset of convection, which is in contrast with the case of $Pr\sim 1$ , where the cell structure is transiently replaced by high order flow modes before the emergence of the large-scale circulation in the turbulent state. The evolution of the flow state is also reflected by the heat transport characterised by the Nusselt number $Nu$ and the probability density function (p.d.f.) of the temperature fluctuation at the cell centre. It is found that the effective local heat transport scaling exponent $\gamma$ , i.e. $Nu\sim Ra^{\gamma }$ , changes continuously from $\gamma =0.49$ at $Ra\sim 10^4$ to $\gamma =0.25$ for $Ra>10^6$ . Meanwhile, the p.d.f. at the cell centre gradually evolves from a Gaussian-like shape before the transition to turbulence to an exponential-like shape in the turbulent state. For $Ra>10^6$ , the flow shows self-similar behaviour, which is revealed by the universal shape of the p.d.f. of the temperature fluctuation at the cell centre and a $Nu=0.19Ra^{0.25}$ scaling for the heat transport.

Experimental investigation of natural convection Al2O3-MWCNT/water hybrid nanofluids inside a square cavity

ABSTRACT The use of nanofluids for convectional heat transfer has become a spry area of research in recent years with the aim of improving heat transfer efficiency. Hybrid nanofluids have attracted significant attention and are advancing research and industrial applications since they involve employing more than one type of nanoparticle(s) in a base fluid. They enhance heat transfer by combining the chemical and physical properties of several nanoparticles concurrently and providing the properties in a homogeneous state. However, few experimental studies have focused on natural convective heat transfer using hybrid nanofluids. In this study, the natural convection of alumina – multiwalled carbon nanotube/water hybrid nanofluids formulated using a two-step method at a percentage weight ratio of 10:90 Al2O3: MWCNT at various nanoparticles volume concentrations of 0.00, 0.05, 0.10, 0.15, and 0.20 vol% was studied inside a square cavity (AR = 1) with two vertical walls which are isothermal, aimed at the Rayleigh number (Ra) range of 2.81 × 108 to 8.58 × 108. The average Nusselt number (Nuav), heat transfer coefficient (hav ), heat transfer (Qav ), and Rayleigh number (Ra) were considered at varying temperature gradients of 20°C – 50°C. Al2O3-MWCNT/water hybrid nanofluid with 0.10 vol% volume concentration was discovered to have the maximum value for hav,Qav , and Nu av. However, it was also observed that a further increase in the hybrid nanoparticles’ volume concentration led to their deterioration at various temperature gradients. The maximum enhancements of 44%, 49%, and 42% were noted for hav,Qav , and Nuav , respectively, at ∆T = 50 °C, in comparison with the base fluid. Al2O3-MWCNT/water hybrid nanofluids application in a square cavity demonstrated enhanced natural convection. This present study concluded that hybrid nanofluids as heat transfer fluid significantly improved heat transfer performance compared to the base fluid.

Effect of inclination angle on heat transport properties in two-dimensional Rayleigh–Bénard convection with smooth and rough boundaries

Using direct numerical simulations, two-dimensional tilted Rayleigh–Bénard convection (RBC) is studied in both smooth and roughness-facilitated convection cells of double aspect ratio ( $\varGamma =2$ ) for air as a working fluid. We investigate the effect of inclination angle ( $0^{\circ } \leq \phi \leq 90^{\circ }$ ) on heat flux ( $Nu$ ), Reynolds number ( $Re$ ) and flow structures. In a Rayleigh number range $10^{6}\leq Ra\leq 10^{9}$ , we address the $Ra$ dependence of $Nu(\phi )$ trend. In the smooth case, while greater tilt results in highest heat flux below $Ra=10^{8}$ , $Nu$ drops with $\phi$ monotonically above it (RBC transports heat most efficiently), which explains the different $Nu(\phi )$ trend observed in the previous studies due to $Ra$ dependence (Guo et al., J. Fluid Mech., vol. 762, 2015, pp. 273–287; Shishkina & Horn, J. Fluid Mech., vol. 790, 2016, R3; Khalilov et al., Phys. Rev. Fluids, vol. 3, 2018, 043503). For the smooth case, we identify the control parameters ( $\phi =75^{\circ }$ and $Ra=10^{7}$ ) that yield maximum heat flux (an increment of $18\,\%$ with respect to the level case). On the other hand, among the three roughness set-ups used in the present study, the tallest roughness configuration yields the maximum increment in heat flux ( $25\,\%$ ) in vertical convection ( $\phi =90^{\circ }$ ) at $Ra=10^{6}$ . With increase in $Ra$ , $Re$ changes with $\phi$ marginally in the smooth case, whereas it shows notable changes in its roughness counterpart. We find that the weakening of thermal stratification is related directly to the height of roughness peaks. While $Ra$ delays the onset of thermal stratification (in terms of inclination angle) in the smooth case, an increase in roughness height plays the same role in roughness-facilitated convection cells.

An Experimental Investigation of Increasing the Thermal Efficiency of a Finned Tube Heat Exchanger by Using the Chimney Effect

In the paper, experimental analyses of the free convection heating transfer in a flat wavy-fin heat exchanger with the dimensions of 500 × 500 mm were investigated. The experimental reserch mainly included determining the average heat flux and heat-transfer coefficient for two selected types of finned heat exchangers. First, tests were conducted for exchangers without considering the so-called ’chimney’ effect; these tests will be treated as reference studies. Then, experiments for specially designed ’chimneys’ over the exchanger with heights of 350, 850, and 1350 mm, respectively, were carried out again. The analyses were performed for an average temperature difference between the heat-exchange surface and the environment in the range of 18 to 55 K. The experimental results demonstrated that, compared to the exchanger without a chimney, the addition of a chimney significantly affects the improvement in the thermal performance of the heat exchanger under natural convection conditions. Regarding the variant without a chimney, when a chimney is used with the highest height of 1350 mm and a maximum temperature difference of 55 K, the average heat flux increases by approximately 450% and the average heat-transfer coefficient is approximately 10 times higher. The heat exchanger characterised by lower airflow resistance showed higher values of average heat flux of 5 to 45% in the Rayleigh number range of 25 to 180. Studies have indicated that in some cases, a simple modification of the geometry of the heat exchanger leads to significant improvements in thermal performance and, in extreme cases, to the elimination of supporting equipment such as fans.

Effect of slip length on flow dynamics and heat transport in two-dimensional Rayleigh–Bénard convection

We report a direct numerical simulation (DNS) study of the heat transport and temperature profiles of the plume ejecting and impacting regions in the two-dimensional turbulent Rayleigh–Bénard (RB) convection with slippery plates and horizontally periodic boundary conditions. The numerical study is conducted in the parameter range of Rayleigh number from to and the slip length b from 0 (NS) to ∞ (FS) for the top and bottom plates. Two distinct flow patterns can be seen depending on b, namely convection roll state and zonal flow, which affect the Nusselt number and the Reynolds number . We show that the zonal flow occurs when the normalised slip length , where is the thermal boundary layer thickness for the no-slip (NS) plates. and increase with increasing , and can reach the optimum before the generation of the zonal flow. It is observed that with the effective scaling exponent for the convection roll state, and for the zonal flow. Furthermore, for the convection roll state, the power-law scaling of the local heat flux is in the plume ejecting region, while in the plume impacting region, for varying slip length . The DNS data with different slippery plates for both plume ejecting and impacting regions agree well with the predicted temperature profiles by Huang et al. (J Fluid Mech. 2022;943:A2).

Thermo-fluid characteristics and second law analysis of an inclined two-fluid system with variable surface roughness

The present numerical study focuses on the analysis of thermodynamic characteristics of an inclined two-fluid system (Al2O3-water and CuO-water nanofluids) having a heat conducting partition wall of variable surface roughness with constant geometric orientation. A further level of thermal control that results in an optimum system orientation for greater thermo-physical transport along with less entropy generation and thermal optimization is explored by examining the effect of system inclination. Based on the second law of thermodynamics, the quantitative results include the variation of average Nusselt number, average fluid temperature, average entropy generation, and average Bejan number for a wide range of Rayleigh number and inclination angle. Current study realizes that the mean quantitative properties of the system are significantly affected by the change of Rayleigh number and inclination angle, despite having a weak dependency on the partition roughness. The variation of average Bejan number with Rayleigh number assumes a reverse trend compared to the same for average Nusselt number and entropy generation and decreases continuously as the flow circulation strengthens. The rate of thermal transport is significantly regulated by the system orientation. Each Rayleigh number conforms to a critical angle of the system inclination for highest thermal transport and entropy generation.

Competition between Rayleigh–Bénard and horizontal convection

We investigate the dynamics of a fluid layer subject to a bottom heat flux and a top monotonically increasing temperature profile driving horizontal convection (HC). We use direct numerical simulations and consider a large range of flux-based Rayleigh numbers $10^6 \leq Ra_F \leq 10^9$ and imposed top horizontal to bottom vertical heat flux ratios $0 \leq \varLambda \leq 1$ . The fluid domain is a closed two-dimensional box with aspect ratio $4\leq \varGamma \leq 16$ and we consider no-slip boundaries and adiabatic side walls. We demonstrate a regime transition from Rayleigh–Bénard (RB) convection to HC at $\varLambda \approx 10^{-2}$ , which is independent of $Ra_F$ and $\varGamma$ . At small $\varLambda$ , the flow is organised in multiple overturning cells with approximately unit aspect ratio, whereas at large $\varLambda$ a single cell is obtained. The RB-relevant Nusselt number scaling with $Ra_F$ and the HC-relevant Nusselt number scaling with the horizontal Rayleigh number $Ra_L=Ra_F\varLambda \varGamma ^4$ are in good agreement with previous results from classical RB convection and HC studies in the limit $\varLambda \ll 10^{-2}$ and $\varLambda \gg 10^{-2}$ , respectively. We demonstrate that the system is multi-stable near the transition $\varLambda \approx 10^{-2}$ , i.e. the exact number of cells not only depends on $\varLambda$ but also on the system's history. Our results suggest that subglacial lakes, which motivated this study, are likely to be dominated by RB convection, unless the slope of the ice–water interface, which controls the horizontal temperature gradient via the pressure-dependence of the freezing point, is greater than unity.