It is a common practice to use ideal thermal boundary conditions to investigate natural convection. These correspond to very good conducting walls and to very bad conducting walls. In particular, this has been the case in natural convection of viscoelastic fluids. In this paper, these conditions are generalized by taking into account the finite thermal conductivities and thicknesses of the walls in the natural convection of a viscoelastic Jeffreys fluid heated from below. The goal is to present more realistic results related to experimental conditions. The critical Rayleigh number R c , the frequency of oscillation ω c , and the wavenumber k c have been plotted varying the properties of the walls from the case of very good thermal conductivity to very poor thermal conductivity. In order to understand the convective phenomena, two parameters are fixed and the other one varied among the nondimensional relaxation time F, the relative retardation time E, and the Prandtl number Pr of the viscoelastic fluid. The role of the relative retardation time E on the thermal instability is discussed in detail.

This paper is a numerical study conducted to investigate the conjugate flow and heat transfer occurring in three-dimensional (3D) natural convection. A cubical enclosure partially filled with porous block (central cubic) and considered in local thermal equilibrium with the fluid. The physical case considered concerns the existence of a horizontal temperature difference across the enclosure, between the left and the right wall, with the other external surfaces being adiabatic. Under these conditions, flow inside the enclosure is generated by the density (temperature) difference across the enclosure and the interaction between the solid porous blocks and the fluid. The Nusselt number on the hot and cold walls is presented to illustrate the overall characteristics of heat transfer consequence of the constrained flow inside the enclosure. The study focuses on the fluid flow and heat transfer evolution versus the dimensionless thickness of the inserted porous layer (0% ≤ η ≤ 100%) and the relative thermal conductivity of the solid matrix to that of the fluid ( 10 − 3 ≤ λ ̃ ≤ 10 3 ) . The obtained complex flow structure and the corresponding heat transfer (velocity, temperature profiles) are discussed in a steady-state situation. The numerical results are illustrated in terms of isotherms, velocity, streamlines fields, and averaged Nusselt number. Thus, the results of this work can help developing new tools and to optimize the overall heat transfer rate, which is important in many electronic energy components and other energy recovering systems.

Natural convective heat transfer in a concentric and a highly eccentric, vertical, open ended, annular channel has been investigated numerically. The inner to outer diameter ratio was 0.61, and the height to hydraulic diameter ratio was 18:1. Three heating modes were considered, all having uniform heat flux applied to one or both of the two walls, while the unheated wall was kept adiabatic. The wall temperature distribution, mass flow rate, and midchannel Nusselt number for the case with both walls heated were found to be in excellent agreement with available experimental results. For the same heating conditions, the heat transfer rate in the concentric annular channel was found to be greater than that in the highly eccentric channel, while the mass flow rate was higher in the eccentric channel. A novel finding for the eccentric channel was that the location of maximum velocity was intermediate between the narrow and wide gaps. Another novel observation, which was attributed to radiation effects, was that the fluid temperature in the wide gap region was lower than that of an adiabatic wall. The paper contains additional observations that would be of interest to designers of systems containing annular channels.

This paper addresses nonlinear mixed convection flow due to Riga plate with double stratification. Heat transfer analysis is reported for heat generation/absorption and nonlinear thermal radiation. Physical problem is mathematically modeled and nonlinear system of partial differential equations is achieved. Transformations are then utilized to obtain nonlinear system of ordinary differential equations. Homotopic technique is utilized for the solution procedure. Graphical descriptions for velocity, temperature, and concentration distributions are captured and argued for several set of physical variables. Features of skin friction and Nusselt and Sherwood numbers are also illustrated. Our computed results indicate that the attributes of radiation and temperature ratio variables enhance the temperature distribution. Moreover, the influence of buoyancy ratio and modified Hartmann number has revers effects on rate of heat transfer.

A computational study of natural convection from biheaters of finite thickness and finite conductivity placed on a finite thickness and a finite conductive bottom plate of a cavity is performed under constant heat input condition. Cavity is cooled by the sidewalls, while the top and backside of the bottom plate are insulated. Streamline, isotherms, and local heat flux distribution of the sidewalls are discussed. Base Grashof number is chosen as 2.5 × 10 6 . Biheater maintains a nondimensional distance of 0.4 between them. The left heater is placed at a nondimensional distance of 0.2 from the left wall. Heater length ratio is varied from 0.4 to 1.7, while heater strength ratio is varied from 0.25 to 7.0. Optimum operating temperature condition is found from the analysis.

Natural circulation loop (NCL) based secondary fluid systems are simple, reliable, and inexpensive due to the absence of any moving components such as pumps. Water-based NCLs are widely used in applications such as solar collectors and nuclear reactors. Also, most of the studies on NCLs do not consider the three-dimensional (3D) variation of the field variables. In the subject work, 3D steady flow simulation of water based, single-phase rectangular NCL with isothermal source and sink has been carried out to study the effects of different design and operating parameters such as loop height, temperature lift, in plane and out of plane tilt angles on the rate of heat transfer, and the rate of entropy generation due to both fluid flow and heat transfer. The rate of entropy generation due to both heat transfer and fluid flow for turbulent flow regimes in a NCL is calculated for a wide range of design and operating parameters. In turbulent flow regimes, the rate of entropy generation due to fluid flow is significant although the rate of entropy generation due to heat transfer is dominant. All the above-mentioned design and operating parameters have significant effect on the rate of entropy generation and the rate of heat transfer as well. With increases in loop height and temperature lift, the rate of entropy generation increases. As the tilt angle increases in the XY plane, the rate of the entropy generation initially increases but after certain tilt angle it starts decreasing.

This paper reports the changes made in the flow and heat transfer characteristics of a closed enclosure in the presence of sidewalls with symmetrical linear heating. The flow inside the enclosure is primarily driven by a centrally placed discrete heater with thermal radiation included at all surfaces involved. Finite volume method-based computational results corresponding to the resulting steady-state were obtained. The factors causing augmentation and suppression of heat transfer are discussed for two types of sidewall heating. Moreover, it is found that the role of radiation is well stronger than convection in determining the total heat transfer rate when the sidewall heating is decreasing with height.

The present study considers the coupled natural convection and surface radiation process through an open fracture of a solid wall facing a reservoir containing isothermal quiescent fluid (air). The fracture is modeled as a regular, C-shape path through the wall, with the vertical surface being heated and the horizontal ones adiabatic. The solid center section of the fracture is thermally participant inasmuch it can be heated or cooled by the natural convection process and by the radiation effect from the other surfaces of the fracture. The convection-radiation phenomenon is mathematically modeled and numerically simulated in a systematic parametric study of the thermal process as affected by changes in the fracture channel size, via changes in the size of the solid center section 0 < D < 1.0, surface emissivity 0 ≤ ε ≤ 1.0, Rayleigh number 10 5 ≤ Ra ≤ 10 8 , and Pr = 0.71. Attention is given to the radiation shadowing effect caused by the center section of the fracture and of the interference effect, as the fracture channel changes in size, affecting the natural convection process through the fracture. An analytical prediction of the interference effect and an empirical correlation for predicting the total Nusselt number, both validated against the numerical results, are presented.

Numerical investigation of natural convective heat transfer and fluid flow in a differentially heated square cavity filled with a CuO-water nanofluid having variable properties is performed. Governing partial differential equations formulated in nondimensional stream function, vorticity, temperature, and nanoparticles volume fraction are solved by the second-order accurate finite difference method and taking into account the Brownian diffusion and thermophoresis. The effects of Rayleigh number (Ra = 10 4 –10 6 ), initial nanoparticles volume fraction (C 0 = 0–0.09), location of the heater (Δ = 0.0–0.9), and dimensionless time ( τ = 0–300) on flow patterns, isotherms, and concentration fields as well as the local and average Nusselt numbers at the heater surface are studied. The isoconcentrations reveal that for most of the cavity domain the nanoparticle concentration is around the initial average concentration of nanoparticles except for a very limited variation in a region close to the cavity walls that experiences minor deviation from the initial concentration. It was found that the flow strength within the cavity (i.e., ψ max Ra ⋅ Pr ) is inversely proportional to the heater location Δ and is directly proportional to the Rayleigh number. Also, it was found that the best location of the heater, from a heat transfer perspective, is placing it entirely at the left wall of the cavity where a maximum average Nusselt number is registered. This study revealed that for all heater locations there is always an adverse impact of nanoparticles on the heat transfer and the worst case is registered for the Δ = 0 and the least deterioration is noticed for Δ = 0.9.

In the present study, turbulent forced and mixed convection heat transfer to a liquid metal flowing upwards in a concentric annulus is numerically investigated by means of large eddy simulation (LES). The inner-to-outer radius ratio is 0.5. The Reynolds number based on bulk velocity and hydraulic diameter is 8900, while the Prandtl number is set to a value of 0.026. A uniform and equal heat flux is applied on both walls. LES has been chosen to provide sufficiently accurate results for validating Reynolds-averaged turbulence models. Moreover, with the thermal sublayer thickness of liquid metals being much larger than the viscous hydrodynamic one, liquid metals present a separation between the turbulent thermal and hydrodynamic scales. Thus, with the same grid resolution, it is possible to perform a LES for the flow field and a “thermal” direct numerical simulation (DNS) for the temperature field. Comparison of the forced convection results with available DNS simulations shows satisfying agreement. Results for mixed convection are analyzed and the differences with respect to forced convection at the same Reynolds number are thoroughly discussed. Moreover, where possible, a comparison with air is made.

This paper presents an analytical solution for the Joule heating problem of a segmented wire made of two materials with different properties and suspended as a bridge across two fixed ends. The paper first establishes the one-dimensional (1D) governing equations of the steady-state temperature distribution along the wire with the consideration of heat conduction and free-heat convection phenomena. The temperature coefficient of resistance of the constructing materials and the dimension of the each segmented wires were also taken into account to obtain analytical solution of the temperature. COMSOL numerical solutions were also obtained for initial validation. Experimental studies were carried out using copper and nichrome wires, where the temperature distribution was monitored using an IR thermal camera. The data showed a good agreement between experimental data and the analytical data, validating our model for the design and development of thermal sensors based on multisegmented structures.

This study investigates the convective heat transfer of a hybrid nanofluid filled in a triangular cavity subjected to a constant magnetic field and heated by a constant heat flux element from below. The inclined side of the cavity is cooled isothermally while the remaining sides are thermally insulated. The finite difference method with the stream function-vorticity formulation of the governing equations has been utilized in the numerical solution. The problem is governed by several pertinent parameters namely, the size and position of the heater element, B = 0.2–0.8 and D = 0.3–0.7, respectively, the Rayleigh number, Ra = 10 2 –10 6 , the Hartmann number, Ha = 0–100, the volume fraction of the suspended nanoparticles, ϕ = 0–0.2, and the heat generation parameter Q = 0–6. The results show significant effect of increasing the volume fraction of the hybrid nanofluid when the natural convection is very small. Moreover, the hybrid nanofluid composed of equal quantities of Cu and Al 2 O 3 nanoparticles dispersed in water base fluid has no significant enhancement on the mean Nusselt number compared with the regular nanofluid.

Mixed convection heat transfer of Al 2 O 3 nanofluid in a lid-driven square cavity with differentially heated vertical walls is studied numerically with lattice Boltzmann method (LBM). In order to understand the reasons for the conflicting results on heat transfer enhancement in cavity problems, formulation of nondimensional properties and modeling thermophysical properties, in accordance with the relative effects of natural and forced convection flows, are examined. In addition to gain more insight into the physics, one of the goals of the study is to identify the reasons of existing contradictory findings; therefore, a single-phase formulation is adopted as has been the case in the majority of related literature to date. To isolate the effects of thermophysical properties on the results and to maintain the same natural and forced convection effects, all nondimensional parameters are defined using the corresponding thermophysical properties of the fluid under examination. Two different effective thermal conductivity and viscosity models are tested for a range of Reynolds and Rayleigh numbers to investigate their effects on the nanofluid behavior. Depending on the effective viscosity model, an increase or decrease is obtained in the average Nusselt number. It is also illustrated that the relative magnitudes of effective thermal conductivity values for different models do not translate into the heat transfer enhancement due to convective effects. Moreover, it is shown that thermal behavior of nanofluid approaches to the one of base fluid's as the buoyancy driven flow gets stronger, which is independent of the employed effective property models.

A high-temperature natural circulation loop (NCL) using supercritical carbon dioxide as loop fluid is modeled to study the effects of operating variables and relevant design parameters on loop performance. The steady-state system model duly considers the axial conduction through loop fluid as well as loop wall and heat transfer with surroundings. The heat source is considered to be a heater with controlled heat flux and the heat sink is modeled as an end heat exchanger with water as the external cold fluid. The governing conservation equations for mass, momentum, and energy are nondimensionalized and are solved numerically discretizing in finite volume method. The numerical results are validated against experimental results reported in the literature in terms of modified Grashof number (Grm) and Reynolds number (Re). Results show that heat loss to the ambient affects the loop performance significantly for the high-temperature loop. It is also observed that the heat input at which the circulation becomes maximum can be increased by increasing either the diameter and/or the loop height. However, better performance is obtained with larger diameter tubes instead of longer loop heights. Axial conduction is seen to have a negligible effect on the overall loop performance. Boussinesq approximation appears to be reasonable as the operating conditions of the supercritical loop are away from the critical point.

The problem of unsteady conjugate natural convection and entropy generation within a semicircular porous cavity bounded by solid wall of finite thickness and conductivity has been investigated numerically. The governing partial differential equations with the corresponding initial and boundary conditions have been solved by the finite difference method using the dimensionless stream function, vorticity, and temperature formulation. Numerical results for the isolines of the stream function, temperature, and the local entropy generation due to heat transfer and fluid friction as well as the average Nusselt and Bejan numbers, and the average total entropy generation and fluid flow rate have been analyzed for different values of the Rayleigh number, Darcy number, thermal conductivity ratio, and the dimensionless time. It has been found that low values of the temperature difference reflect the entropy generation, mainly in the upper corners of the cavity, while for high Rayleigh numbers, the entropy generation occurs also along the internal solid–porous interface. A growth of the thermal conductivity ratio leads to an increase in the average Bejan number and the average entropy generation due to a reduction of the heat loss inside the heat-conducting solid wall.

The present study is devoted to the problem of oscillatory convective flow in the presence of viscous dissipation around different positions of a sphere. The system of differential equations governing the flow phenomenon is transformed into dimensionless form by using suitable group of variables and then transformed into convenient form for integration by using primitive variable formulation. Numerical simulation based on finite difference method is carried out to analyze the mixed convection flow mechanism. Special focus is given on the transient shear stress and the rate of heat transfer characteristics and their dependency on various dimensionless parameters that is mixed convection parameter λ, Prandtl number Pr, dissipation parameter N , and angular frequency parameter ω . The angles X = 30 deg , 90 deg , and 360 deg are the favorable positions around the sphere for different parameters, where the transient rate of shear stress and heat transfer is noted maximum. Later, the obtained results are presented graphically by using Tech Plot-360 and compared with the previous work given in the literature.

This discussion concerns some doubtful results included in this paper.

Natural convection heat transfer from a vertical hollow cylinder suspended in air has been analyzed numerically by varying the Rayleigh number (Ra) in the laminar (10 4 ≤ Ra ≤ 10 8 ) regime. The simulations have been carried out by changing the ratio of length to pipe diameter (L/D) in the range of 0.05 ≤ L/D ≤ 20 . Full conservation equations have been solved numerically for a vertical hollow cylinder suspended in air using algebraic multigrid solver of fluent 13.0 . The flow and the temperature field around the vertical hollow cylinder have been observed through velocity vectors and temperature contours for small and large L/D. It has been found that the average Nusselt number (Nu) for vertical hollow cylinder suspended in air increases with the increase in Rayleigh number (Ra) and the Nu for both the inner and the outer surface also increases with Ra. However, with the increase in L/D, average Nu for the outer surface increases almost linearly, whereas the average Nu for the inner surface decreases and attains asymptotic value at higher L/D for low Ra. In this study, the effect of parameters like L/D and Ra on Nu is analyzed, and a correlation for average Nusselt number has been developed for the laminar regime. These correlations are accurate to the level of ± 6 % .

The heat function concept introduced by Kimura and Bejan (1983, “The Heatline Visualization of Convective Heat Transfer,” ASME J. Heat Transfer, 105 (4), pp. 916–919) for two-dimensional (2D) heat transfer is being extended in this note to three dimensions. It is shown that a heat flux vector potential exists and can be used in three-dimensional (3D) heat convection problems. It is further shown that this heat flux vector potential degenerates to the heat function introduced by Kimura and Bejan (1983, “The Heatline Visualization of Convective Heat Transfer,” ASME J. Heat Transfer, 105 (4), pp. 916–919) when the heat convection is two-dimensional.

Natural convection during solidification of liquids is known to impact the freezing characteristics and also lead to defect formation. In this study, we report the findings of real-time interferometric observation of bottom-cooled solidification of pure water in a cubical cavity. The results show first quantitative evidence of full-field thermal history during solidification, clearly depicting the anomalous expansion of water below 4 °C. Furthermore, based on the strength of natural convection, characterized by the Rayleigh number, we identify and report four distinct regimes of solidification, namely—conduction dominated, early convection, front instability, and sustained convection. A critical Rayleigh number that initiates instability in the solidifying front has been proposed, which is significantly different from conventional calculations of Rayleigh number relating to the initiation of flow. The study shows full-field quantitative evidence of a well-known phenomenon and provides a further understanding of flow driven nonhomogeneities in the solidifying interfaces.