Increasing Rayleigh Number Research Articles

Wall-attached convection under strong inclined magnetic fields

We employ a linear stability analysis and direct numerical simulations to study the characteristics of wall modes in thermal convection in a rectangular box under strong and inclined magnetic fields. The walls of the convection cell are electrically insulated. The stability analysis assumes periodicity in the spanwise direction perpendicular to the plane of a homogeneous magnetic field. Our study shows that for a fixed vertical magnetic field, the imposition of horizontal magnetic fields results in an increase of the critical Rayleigh number along with a decrease in the wavelength of the wall modes. The wall modes become tilted along the direction of the resulting magnetic fields and therefore extend further into the bulk as the horizontal magnetic field is increased. Once the modes localized on the opposite walls interact, the critical Rayleigh number decreases again and eventually drops below the value for onset with a purely vertical field. We find that for sufficiently strong horizontal magnetic fields, the steady wall modes occupy the entire bulk and therefore convection is no longer restricted to the sidewalls. The aforementioned results are confirmed by direct numerical simulations of the nonlinear evolution of magnetoconvection. The direct numerical simulation results also reveal that at least for large values of horizontal magnetic field, the wall-mode structures and the resulting heat transfer are dependent on the initial conditions.

Numerical Analysis of Laminar Natural Convection Inside Enclosed Squared and Trapezoidal Cavities at Different Inclination Angles

The effects of cavity shape by inclination angle on laminar natural convection inside trapezoidal and square-shaped cavities have been numerically investigated in this work. Several simulations had been conducted for various inclinations of the trapezoidal cavity at Rayleigh numbers (Ra) =105 to 106 in a laminar flow regime. The walls at the left and right sides of the cavities were heated isothermally, while the walls at the top and bottom sides were adiabatic. The problem was assumed to be 2-D and solved using the software package ANSYS Fluent 16.2. Cavity filled with air is examined in two distinct instances; varying boundary layers and the flow generated for the natural convection. This numerical study analyzed the flow characteristics, temperature distribution, and Nusselt number. The analysis reveals that as the Rayleigh number increases, the Nusselt number also increases, with a more pronounced effect at higher Rayleigh numbers. It has been observed that there is a substantial effect of cavity shapes on the Nusselt number. The presence of an angled wall inhibits convection resulting in stronger flow in the squared cavity compared to the trapezoidal cavity. From numerical results, it is also found that the temperature distribution at Ra = 105 is wider than the temperature distribution at Ra= 106.

Combining neutral scalar and isothermal Shan-Chen lattice Boltzmann method to simulate droplet placement on a wall in isothermal and non-isothermal states

BackgroundIn the current article, two-phase thermal fluxes are created by combining the thermal model of the neutral scalar model with the two-phase Shan-Chen model of the lattice Boltzmann method (LBM). MethodsThe different intermolecular powers for the isothermal Shan-Chen model show how a droplet would be placed on a wall. By raising the droplet intermolecular power parameter, the surface area increases and becomes wet. Next, the isothermal Shan-Chen method and the neutral scalar method are combined to investigate multi-phase thermal problems. The droplet placement on the hot wall is therefore done at relatively high Rayleigh numbers. By raising the Rayleigh number, the isothermal lines within the droplet's interior gradually become less ascending and less descending until they eventually achieve a uniform state when it is placed against a hot wall. Additionally, the channel's Rayleigh-Bénard convective heat transfer is enhanced by increasing the Rayleigh number. Significant findingsNatural convection in the enclosures can be used in solar collectors. As the Rayleigh number increases, the average Nusselt number (Nuavg) rises as would be expected. The results demonstrate that LBM is a practical method for simulating multi-phase thermal flows.

Rayleigh–Bénard convection with an immersed floating body

The paper presents the results of an experimental and numerical study of turbulent thermal convection in a rectangular box containing an extended immersed free-floating plate. Varying the values of control parameters, such as Rayleigh number, aspect ratio and vertical position of the plate, provides a wide range of possible modes, from immobile and purely periodic to stochastic. We have shown that stable periodic motions occur when the plate floats close to one of the heat exchangers. An increase in the distance between the plate and the heat exchanger breaks the periodic motion and (at moderate Rayleigh numbers) leads to a pronounced asymmetry, when the plate stays close to one of the walls most of the time, makes rare excursions to the opposite wall and immediately returns. As the Rayleigh number increases, the plate motions from one edge of the box to the other reappear, but always have an irregular character. Regarding the dependence of the system behaviour on the geometry of the box, both lower and upper limits of periodic plate motions were found in the experiments. In the numerical simulations, the upper limit was not achieved – the plate moves quasi-periodically through the chain of vortices of different signs even at the largest aspect ratio being considered. The heat-insulating floating plate provides the spatial and temporal variation of the heat flux and reduces the integral heat flux, but the reduction in heat flux depends significantly on the vertical position of the plate.

Fixed-flux Rayleigh–Bénard convection in doubly periodic domains: generation of large-scale shear

This work studies two-dimensional fixed-flux Rayleigh–Bénard convection with periodic boundary conditions in both horizontal and vertical directions and analyses its dynamics using numerical continuation, secondary instability analysis and direct numerical simulation. The fixed-flux constraint leads to time-independent elevator modes with a well-defined amplitude. Secondary instability of these modes leads to tilted elevator modes accompanied by horizontal shear flow. For $Pr=1$ , where $Pr$ is the Prandtl number, a subsequent subcritical Hopf bifurcation leads to hysteresis behaviour between this state and a time-dependent direction-reversing state, followed by a global bifurcation leading to modulated travelling waves without flow reversal. Single-mode equations reproduce this moderate Rayleigh number behaviour well. At high Rayleigh numbers, chaotic behaviour dominated by modulated travelling waves appears. These transitions are characteristic of high wavenumber elevator modes since the vertical wavenumber of the secondary instability is linearly proportional to the horizontal wavenumber of the elevator mode. At a low $Pr$ , relaxation oscillations between the conduction state and the elevator mode appear, followed by quasi-periodic and chaotic behaviour as the Rayleigh number increases. In the high $Pr$ regime, the large-scale shear weakens, and the flow shows bursting behaviour that can lead to significantly increased heat transport or even intermittent stable stratification.

Highly resolved LES and URANS computations of a differentially heated square cavity

This investigation focusses on the use of two wall-resolved LES approaches for the simulation of the buoyancy driven flow in a differentially heated square cavity, aiming to advance understanding of the flow phenomena involved. The study also assesses the predictive accuracy and cost-effectiveness of LES for natural convection flows. This assessment is pursued through comparisons of the resulting predictions, and also of their computational requirements, with those for DNS, produced in an earlier study, and those of a number of URANS models produced during the current investigation. URANS models tested here include both high- and low-Reynolds-number schemes. In the case of the high-Reynolds-number models a recently developed numerical variant of the Analytical Wall Function (AWF) has been employed to account for the effects of near-wall turbulence. Both LES approaches result in predictions that are close to those of the DNS but have considerably more modest resource requirements. The URANS approaches, which have the lowest resource requirements, for key parameters such as the local Nusselt number are not as accurate as the LES approaches and their performance is highly dependent on the turbulence model employed. Surprisingly, the simplest of the low-Re models employed, the Launder–Sharma two-equation model, is reasonably close to the DNS data. The approach that requires the least computational resource, the high-Re model with the recent version of the AWF, also offers a promising URANS route. Simulations were also conducted to investigate the flow behaviour at a Rayleigh number that is an order of magnitude higher than that of the available DNS. At such high Rayleigh number, at which the phenomena are of close relevance to cooling loops of nuclear reactors, comparisons are performed between the LES and the high-Re AWF combination. The findings show that as the Rayleigh number increases, the turbulence levels become stronger, but these are confined to more refined structures within the thinner near-wall boundary layers.

Time-periodic natural convection in a pentagonal house with pitched roof during one day

A numerical investigation of unsteady natural convective flow and heat transfer in a pentagonal house is performed. We set a sinusoidal periodic heat flux boundary condition for the pitched roof. Local radial basis function method and Fourier spectral method are adopted to solve the governing equations. The Rayleigh number varies from 103 to 105, the period of the roof heat flux ranges from 10 to 1,000, and the amplitude is set as 0.1, 0.3, and 0.5, respectively. It is found that all the control parameters significantly impact the fluid flow and heat transfer. The temperature and flow fields exhibit periodic behavior due to the sinusoidal heat source. The increasing Rayleigh number leads to a larger periodic average Nusselt number of the top and right walls and a smaller value of the bottom wall. Moreover, an obvious hysteresis phenomenon of heat transfer occurs especially for high Rayleigh number and large period.

Effect of Uniform and Space-Dependent Heat Source on the Onset of Buoyancy-Driven Convection in Viscosity Fuels: A Linear Theory

The viscosity of fuel oil is significantly influenced by temperature, with higher temperatures leading to lower viscosity. To ensure optimal combustion, it's crucial to maintain the fuel's viscosity within a specific range. With regard to variable, spacedependent and uniform heat sources, the impact of variable viscosity on the stability of Buoyancy Rayleigh-Bénard convection is demonstrated. The impact of non-inertial acceleration on natural convection is also studied in the problem. The Fourier series representation of stream function, temperature distribution describes how to derive an analytical expression for the thermal Rayleigh number. Here we noticed that the heat source parameter, the viscosity parameter, and the Taylor number effect the stability of the fluid system. Also, it is demonstrated here the impact of rotational strength accompanied with the stabilized system, where as an increase in the internal Rayleigh number and thermorheological parameter is to destabilize the same. It is also observed that, it is possible to control convection by proper tuning these parameters. A comparative study of external Rayleigh number and stability analysis for the onset of instability is presented in the problem. Some of the important new results have been revealed in the context of heat sources

Effects of an Inclined Cente red Conductor on MHD Natural and Forced Convection Within a Heated Wavy Chamber

The study of the effect of hall and ion slip on an inclined conductor on MHD natural and forced convection in a heated wavy chamber with a constant transversal magnetic field applied. The governing momentum and energy equation were solved by applying finite central scheme approximation and the resulting partial difference equations were solved by MATLAB software. The study showed that an increase heat absorption coefficient lowers the surface heat transfer thus lowering flow rate. An increase in Rayleigh number increases the flow rate while an increase in the angle of inclination of the conductor increases the buoyancy force component thereby increasing the flow rate. The results further showed that flow rate became higher at an inclination angle of 90º. In addition, the results also showed that an increase in Hartmann increases the flow rate. The Hartmann number, Rayleigh number and Absorption coefficient are analytically discussed and represented in tables and graphical profiles with respect to flow velocity and temperature profile due to engineering demand. This current study a direct application in the development of MHD propelled vessels in the marine and space-craft department.

Role of applying PCMs on thermal behavior of innovative unit roof enclosure

As a technical approach, using Phase Change Materials (PCM) can be an effective method to prevent energy losses through building enclosures. In the present paper, different roof structures containing PCM have been examined to analyze their thermal behavior. The governing equations were developed and solved for a sample unit extracted from a typical roof. The control volume based finite element method has been applied for solving coupled equations governing heat transfer through the roof and flow of melted PCM. The effect of key parameters including thermal diffusivity of the PCM and the wall, Prandtl number (Pr), Rayleigh number (Ra) and solid wall thickness to total thickness has been examined. The main results indicate an enhancement of heat transfer through the increase of the thermal diffusivity of the PCM with respect to the building material. Increasing the thermal diffusivity ratio from 1 to 25 doubles the heat transfer rate and decreases the full melting time by 80% for high Rayleigh. Pr affects the mode of heat transfer but has little impact on PCM melting rate. Raising Ra improves heat transfer under the condition of high thermal diffusivity in the PCM. Increasing Rayleigh number from 104 to 106 doubles the heat transfer rate and reduces the melting by 67% for high thermal diffusivity ratio. Finally, increasing the size of the wall thickness does not affect the fraction of melted PCM but reduces the heat transfer rate. The heat transfer rate can be increased by up to 75% when the non-dimensional thickness of the solid layer is reduced from 0.5 to 0.005.

Energy Efficiency Analysis of Natural Convection Heat Transfer in Concentric Annulus with Interior and Exterior Grooves

This study is a numerical investigation of the convective heat transfer in motionless concentric annulus composed of two horizontal cylinders, one of which is grooved. The inner cylinder is kept at hot temperature Th and the outer one is kept at cold temperature Tc. The aim of this paper is to analyze the effect of the groove on thermal and dynamic behavior in the annulus when the groove is located on the hot cylinder (inner groove), and when it is located on the cold cylinder (exterior groove). To observe the effect the inner and outer groove on the flow structure and on the heat transfer rate, the groove is positioned at ϕ0=-90̊, -45̊, 0 ̊, 45 ̊, and 90̊. Moreover, the groove size (f) and the radius ratio (e) of the annulus have been changed to investigate their effects on heat transfer rate as well as on the energy efficiency of the process. The results show that the heat transfer rate rises up with the increase of Rayleigh number. It is seen that; in the case of the inner groove; the heat transfer rate reaches a maximum at ϕ0=40̊, whatever the groove size. Furthermore, the energy efficiency of the process is maximum when the inner groove is positioned at ϕ0=90̊, and it increases well with the increase of f. On the other hand, in the case of the exterior groove, the heat transfer rate is practically close to that of non-grooved annulus for f<0.7. A decrease of 34% of the energy efficiency is noticed with the increase of the size of the groove to f=0.7. Our results would be very useful for manufacturers who are looking for increasing the energy efficiency of their process, or also who need to boost or decrease the heat transfer rate depending on the objective of their process.

Numerical Investigation of Fin Shape Optimization and Entropy of Magnetohydrodynamics Natural Convection Nanofluid Flow in a Cavity

The purpose of the investigation is to analyze the effect of fin length and position in terms of rotational angle on heat transmission and entropy generation. Different parameters such as Prandtl numbers, Hartmann numbers, Rayleigh numbers, and particle volume fractions are used to analyze nanofluid laminar flow behavior and temperature distribution. The fin has a significant impact on both the isotherm and the streamlines. Findings revealed that increasing the rotational angle of a spinning heat exchanger might result in more consistent temperature distribution along isotherms; larger fins, on the other hand, frequently provide greater heat dissipation due to increased surface area. Furthermore, when Rayleigh numbers increase, so does the temperature distribution between the fins and the surrounding fluid. The presence of a magnetic field affects fluid dynamics and contributes to the generation of entropy. Higher Prandtl numbers can result in the enhancement heat transfer phenomena and the generation of entropy.

Numerical investigation of steady state, laminar, natural convection of Bingham fluids in a trapezoidal enclosure heated from the bottom and cooled from the sides

Laminar, steady-state, natural convection of Bingham fluids in trapezoidal enclosures with a heated bottom wall, cooled inclined sidewalls and an adiabatic top wall has been studied based on numerical simulations for a range of values of nominal Bingham numbers, Rayleigh numbers (i.e., 103 ≤ Ra ≤ 105), and sidewall inclination angles (i.e., 30° ≤ φ ≤ 60°) for a representative nominal Prandtl number (i.e., Pr = 103). It has been found that the mean Nusselt number Nu‾ increases with increasing Rayleigh number Ra due to the strengthening of advective transport. An increase in the sidewall inclination angle φ leads to a decrease in the mean Nusselt number Nu‾ due to an increase in the area for heat loss from the trapezoidal enclosure. The value of the mean Nusselt number Nu‾ was found to decrease with increasing Bingham number Bn. At high values of Bingham number Bn, the fluid flow essentially stops within the enclosure and the heat transfer takes place primarily due to conduction and, accordingly, the mean Nusselt number Nu‾ settles to a constant value, for a given value of sidewall inclination angle φ, irrespective of the value of nominal Rayleigh number Ra. Furthermore, a correlation for the mean Nusselt number Nu‾ in trapezoidal enclosures with a heated bottom wall, an adiabatic top wall, and cooled inclined sidewalls accounting for the range of Rayleigh numbers Ra, Bingham numbers Bn and inclined wall angles φ considered which provides adequate approximation of the corresponding values obtained from the numerical simulations has been identified.

Experimental Investigation into Natural Convection Heat Transfer inside Triangular Enclosure with Internal Hot Cylinder

Natural convection air heat transfer and fluid movement currents around a hot circular cylinder inside an inclined triangular enclosure has been analyzed experimentally. Three different sizes of an enclosure with a long side of 20, 25, and 30 cm, the thickness of 1 mm, and depth of 50 cm were used in the present work to give three radius ratios. The effect of Rayleigh number, radius ratio, the rotation angle of triangle enclosure, and the inclination angle of the apparatus with horizontal axis ? on the heat transfer process was investigated. The ranges of these parameters were: Rayleigh number from 5×106 to 2.5×108, radius ratio (0.345, 0.455, and 0.618), rotation angle (0o, 45o, and 90o), and inclination angle (0o, 45o and 90o). The results show that the heat transfer rates increase with increase in Rayleigh number and as the rotation angle of enclosure is changed from 0o to 90o. Moreover, the heat transfer rate increases linearly with Rayleigh number at higher radius at rotation angle 0o, 90o only. While, it increases slightly with Rayleigh number at rotation angle 45o. Additionally, the higher heat transfer rates occur at vertical position of enclosure inclination angle 90o and rotation angle 0o (the base of triangle at the bottom) and it decreases as inclination angle deviates from 90o to 0o. This behavior is reverse completely at higher radius ratio 0.618. Empirical correlations for the average Nusselt number has been found to depend on Rayleigh number., radius ratio, rotation angle and inclination angle.

Heat transfer in a quasi-one-dimensional Rayleigh–Bénard convection cell

We report an experimental and numerical study on Rayleigh–Bénard convection in a slender rectangular geometry with the aspect ratio $\varGamma$ varying from 0.05 to 0.3 and a Rayleigh number range of $10^5\leqslant Ra\leqslant 3\times 10^9$ . The Prandtl number is fixed at $Pr=4.38$ . It is found that the onset of convection is postponed when the convection domain approaches the quasi-one-dimensional limit. The onset Rayleigh number shows a $Ra_c=328\varGamma ^{-4.18}$ scaling for the experiment and a $Ra_c=810\varGamma ^{-3.95}$ scaling for the simulation, both consistent with a theoretical prediction of $Ra_c\sim \varGamma ^{-4}$ . Moreover, the effective Nusselt–Rayleigh scaling exponent $\beta =\partial (\log Nu)/\partial (\log Ra)$ near the onset of convection also shows a rapid increase with decreasing $\varGamma$ . Power-law fits to the experimental and numerical data yield $\beta =0.290\varGamma ^{-0.90}$ and $\beta =0.564\varGamma ^{-0.92}$ , respectively. Near onset, the flow shows a stretched cell structure. In this regime, the velocity and temperature variations in a horizontal cross-section are found to be almost invariant with height in the core region of a slender domain. As the Rayleigh number increases, the system evolves from the viscous dominant regime to a plume-controlled one, a feature of which is enhancement in the heat transport efficiency. Upon further increase of $Ra$ , the flow comes back to the classical boundary-layer-controlled regime, in which the quasi-one-dimensional geometry has no apparent effect on the global heat transfer.

Instability thresholds for penetrative porous convection with variable viscosity fluids

A comprehensive investigation discerning different viscosity-temperature variations on the onset of porous penetrative convection modeled through quadratic density-temperature law is undertaken. The fluid viscosity is assumed to vary linearly, quadratically and exponentially with temperature. The variable viscosity results in a coupling between stream function and temperature in the Darcy momentum balance equation. The linear instability of the basic state is analyzed numerically by examining small-amplitude disturbances in velocity and temperature fields. By carrying out numerical computations for a wide range of parametric regimes, it is established that the principle of exchange of stabilities (PES) is valid. The critical values of the Darcy-Rayleigh number and of the wave number are obtained. The analysis reveals that the combined influence of variable viscosity and the density-maximum characteristic is to expedite the onset of porous convection much faster compared to their isolation presence. The size of the convection cell decreases with an increase in the Darcy-modified Rayleigh number linked to the quadratic density variant. The outcomes obtained under the limiting cases are shown to exhibit consistency with previously published findings.

Fluid Structure Interaction Analysis of Natural Convective Flow and Heat Transfer in an L-Shaped Cavity

The primary objective of this research work is to perform a numerical study on the fluid-structure interaction (FSI) of flow and heat transfer characteristics within an L-shaped cavity. The investigation will focus on analyzing the effects of various key variables, namely the Rayleigh number and wall elasticity, on the observed results. To accomplish this, the COMSOL software, which utilizes the finite element method, will be employed as the numerical simulation tool. To ensure the reliability and credibility of the obtained results, the findings of this research were rigorously validated against previously published data available in the literature. The outcomes of this investigation were presented using various visualization techniques. Streamlines, temperature contours, and heat transfer enhancement will be among the visual representations used to illustrate the flow and temperature distribution within the L-shaped cavity. Anticipated results indicated that the calculations of the average Nusselt number exhibited a strong dependency on the Rayleigh number and the wall elasticity. As such, the average Nusselt number was higher for flexible wall compared to rigid wall model. Moreover, the average Nusselt number was found to increase with an increase in Rayleigh number. Young’s modulus was found to have a profound effect on the patterns of the streamlines. The average Nusselt number was found to decrease with an increase in the Young’s modulus. This study may provide valuable insights into optimizing heat transfer and designing efficient thermal management systems for various practical applications.

Heat Transfer Investigation in Plus-Shaped Enclosure Using Power Law Fluid: A Finite Element Approach

The main purpose of this study is to investigate the thermal behavior of power law fluid within a plus-shaped cavity under the influence of natural convection, also taking into account the Darcy number and magnetohydrodynamics (MHD). The problem is formulated as a system of partial differential equations considering the power law fluid’s rheological behavior. The left-side walls are maintained at a specific low temperature while the lower and the right-side walls have uniform maximum temperatures. The boundary condition is designed to enhance heat transfer efficiency within the cavity, utilizing advanced thermal insulation methodologies. Finite element method (FEM) simulations are conducted, and a grid independence test is performed to validate the results. The impact of relevant parameters on the variation in momentum and thermal distributions is investigated using streamline and isothermal contour plots. The results indicate that as the Rayleigh number increases, the kinetic energy also increases, whereas the viscosity and circulation zones expand with an increase in the power law index. The Nusselt number exhibits a higher value in the shear-thinning case (n = 0.7) compared to the Newtonian (n = 1) and shear-thickening (n = 1.2) cases. This empirical observation underscores the vital role that fluid rheology plays in molding the overall heat transfer performance within the cavity. The study concludes that there is a distinct correlation between the heat transfer rate and the Rayleigh number (Ra). As Ra increases, there is a significant improvement in the heat transfer rate within the flow domain. Furthermore, the fluid behavior and heat transfer performance within the cavity are significantly influenced by the presence of magnetohydrodynamics (MHD) and the Darcy effect.

An experimental and numerical analysis of natural convection in a partially open cuboid enclosure with a cylindrical obstacle

Natural convection in partially open enclosures has been area of intensive research in the past. However, a dearth of experimental or numerical studies has been found on the effect of cylindrical obstacle size on natural convection in such an enclosure. To address this gap, this study employs real-time experimental analysis using a non-invasive technique (Mach-Zehnder interferometry), that provides temperature distribution of flowing fluid in the investigating domain. The experiments are conducted in a partially open cuboid enclosure with an internal heat source on the bottom wall and a centrally placed cylindrical obstacle. The partial opening occupies 50% of the height of the left vertical wall. The study investigates the effect of obstacle diameter and Rayleigh number on natural convection through experimentation and numerical simulations using ANSYS Fluent 2020. An air velocity transducer is used to measure velocity at the opening. The interferograms obtained from the experiment are used to characterize the natural convection and compared with the results obtained from the numerical investigation. Fringes intensify at higher Rayleigh number, and the temperature gradient near the heat source increases with increase in obstacle diameter. The average Nusselt number and average exit velocity of flowing fluid increase with increase in obstacle diameter and Rayleigh number. For Rayleigh numbers in the range of 107 to 108, a threefold increase in the obstacle diameter results in an average increment in Nusselt number by 22% and an increment in the average exit velocity by 25%.

Laminar Natural Convection of Water-Based Alumina Nanofluids in a Square Enclosure

Steady-state, laminar, natural convection of water-based alumina nanofluids in a square enclosure with partial heating from the bottom and symmetrical cooling from the sides has been investigated based on numerical simulations. The effects of Rayleigh number, normalized heat source length and nanoparticle volume fraction on the heat transfer behavior have been investigated. An increase in Rayleigh number, for given values of normalized heat source length and nanoparticle volume fraction, leads to an increase in Nusselt number. For a given set of values of Rayleigh number based on base-fluid properties and normalized heat source length, the Nusselt number does not vary significantly with increasing nanoparticle volume fraction because the strengthening viscous effects with increasing volume fraction for water-based alumina nanofluids counteracts the enhanced thermal diffusion in nanofluids. However, when effective Rayleigh number is based on nanofluid properties, Nusselt number decreases with increasing nanoparticle volume fraction. For a given set of values of Rayleigh number and nanoparticle volume fraction, the Nusselt number increases with increasing normalized heat source length due to the strengthening of advective transport. A correlation for mean Nusselt number is proposed which adequately captures qualitative and quantitative behavior obtained from the simulations across the considered parameter range.