Thermal free convection from a solid sphere

Summary Thermal free convection from a sphere has been studied by melting solid benzene spheres in excess liquid benzene (Pr=8,3; 10⁸<Gr<10⁹). Overall heat transfer as well as local heat transfer were investigated. For the effect of cold liquid produced by the melting a correction has been applied. Results are compared with those obtained by other workers who used alternative experimental methods.Nomenclature coefficient of heat transfer - d characteristic length, here diameter of sphere - thermal conductivity - g acceleration of free fall - cubic expansion coefficient - T temperature difference between wall and fluid at infinity - kinematic viscosity - density - c specific heat capacity - a thermal diffusivity (=/c) - D diffusion coefficient - Nu dimensionless Nusselt number (=d/) - Nu* the analogous number for mass transfer (=kd/D) - mean value of Nusselt number - Gr dimensionless Grashof number (=gd ³T/ ²) - Gr* the analogous number for mass transfer (=gd ³x/ ²) - Pr dimensionless Prandtl number (=/a) - Sc dimensionless Schmidt number (=/D)     

Study of thermal flows from two-dimensional,upward-facing isothermal surfaces using a laser speckle photography technique

A laser specklegram or speckle photography technique allows a direct measurement of surface temperature gradients and provides a full field interrogation with an extremely high resolution from a single data taking. The specklegram technique has been successfully applied to investigate the natural convection heat transfer from an upward-facing isothermal plate. For a plate with a large aspect ratio of 15, both local and global Nusselt numbers have been determined from the direct measurement of local temperature gradients. The Rayleigh number, based on the length scale equivalent to the ratio of the surface area to the perimeter, has been varied from 9.0 × 10³ to 4.0 × 10⁴. The present result for the global heat transfer has shown that a 1/5-power law, i.e., Nu = C₁ Ra ^1/5, correlates the data more properly whilst previously published results showed a large scatter in the exponent, ranging from 1/8-power to 1/4-power. The proportional constant, C₁ has been determined to be 0.56 which shows a fairly good agreement with previously published theoretical results. The laser specklegram technique has shown a strong potential as a powerful and convenient method for an experimental assessment of natural convection heat transfer problems. The specklegram technique at the same time has eliminated the deficiencies of both the mass transfer analogy technique and the classical heat transfer measurement technique.List of symbols a characteristic length scale defined as a = A/P where A is the surface area and P is the perimeter of the plate edge [mm] - AR aspect ratio [L/H] - c defocusing distance [mm] - d image distance of Young's fringes from speckle negative - h thermal convection coefficient [W/m² · K] - average thermal convection coefficient [W/m² · °C] - H width of the test section measured perpendicular to the optic axis [mm] - k thermal conductivity [W/m · K] - L length of the test section measured parallel to the optical axis [mm] - n index of refraction - Nu local Nusselt number [ha/k] - global Nusselt number - Pr Prandtl number [v/] - q heat flux per unit area [W/m² · s] - Ra Rayleigh number - s fringe spacing [mm] - Sc Schmidt number [v/D] - T temperature [K] Greek symbols thermal diffusivity [m²/s] - volumetric coefficient of expansion (1/T) - v kinematic viscosity of air [m²/s] - wavelength of helium-neon laser [632.8 nm] - amount of speckle dislocation     

Natural convection heat transfer in enclosures with microemulsion phase change material slurry

This paper has dealt with the natural convection heat transfer characteristics of microemulsion slurry composed of water, fine particles of phase change material (PCM) in rectangular enclosures. The microemulsion slurry exhibited non-Newtonian pseudoplastic fluid behavior, and the phase changing process can show dramatically variations in both thermophysical and rheological properties with temperature. The experiments have been carried out separately in three subdivided regions in which the state of PCM in microemulsion is in only solid phase, two phases (coexistence of solid and liquid phases) or only liquid phase. The complicated heat transfer characteristics of natural convection have appeared in the phase changing region. The phase change phenomenon of the PCM enhanced the heat transfer in natural convection, and the Nusselt number was generalized by introducing a modified Stefan number. However, the Nusselt number did not show a linear output with the height of the enclosure, since a top conduction lid or stagnant layer was induced over a certain height of the enclosure. The Nusselt number increased with a decrease in aspect ratio (width/height of the rectangular enclosure) even including the side-wall effect. However, the microemulsion was more viscous while the PCM was in the solid phase, the side-wall effect on heat transfer was greater for the PCM in the solid region than that for the PCM in the liquid region. The correlation generalized for the PCM in a single phase is $ Nu = 1/3(1 - C_1 )Ra^{{1 \over {3.5n + 1}}} , $ where C ₁ = e ^–0.09AR for the PCM in solid phase and C ₁ = e ^–0.33AR for the PCM in liquid phase. For the PCM in the phase changing region, the correlation can be expressed as $ Nu = CRa^{{1 \over {7n + 2}}} Ste^{ - (1.9 - 1.65n)} , $ where C = 1.22 – 0.035AR for AR > 10 and C = 0.55 – 16.4e ^–1.1AR for AR < 10. The enclosure height used in the present experiments was varied from H = 5.5 [mm] to 30.4 [mm] at the fixed width W = 120 [mm] and depth D = 120 [mm]. The experiments were done in the range of modified Rayleigh number 7.0 × 10² ≤ Ra ≤ 3.0 × 10⁶, while the enclosure aspect ratio AR varied from 3.9 to 21.8.     

Forced convection heat transfer and friction characteristics in multi-exit -rectangular package with inclined tube bundles

An experiment was carried out to investigate the characteristics of the heat transfer and pressure drop for forced convection airflow over tube bundles that are inclined relative to the on-coming flow in a rectangular package with one outlet and two inlets. The experiments included a wide range of angles of attack and were extended over a Reynolds number range from about 250 to 12,500. Correlations for the Nusselt number and pressure drop factor are reported and discussed. As a result, it was found that at a fixed Re, for the tube bundles with attack angle of 45 ° has the best heat transfer coefficient, followed by 60, 75 and 90 °, respectively. This investigation also introduces the factors which can be used for finding the heat transfer and the pressure drop factor on the tube bundles positioned at different angles to the flow direction. Moreover, no perceptible dependence of Cand C on Re was detected. In addition, flow visualizations were explored to broaden our fundamental understanding of the heat transfer for the present study.     

The Mixed Convection Boundary Layer on a Vertical Melting Front in a Non-Darcian Porous Medium

The effect of surface melting on the dual solutions that can arise in the problem of the mixed convection boundary-layer flow past a vertical surface embedded in a non-Darcian porous medium is considered. The problem is described by M, melting parameter, \(\lambda \), mixed convection parameter, and \(\gamma \), the flow inertia coefficient, numerical results being obtained in terms of these three parameters. It is seen that the melting phenomenon reduces the heat transfer rate and enhances the boundary-layer separation at the solid–liquid interface. Asymptotic solutions for the forced convection, \(\lambda =0\), and free convection, large \(\lambda \), limits are derived.     

Heat transfer from a slowly rotating sphere

The problem of steady state forced convection heat transfer in a viscous incompressible fluid occupying the annular region between two concentric spheres is considered. The inner sphere is maintained at a constant temperatureT ₀ and rotates slowly around an axis through the centre. The outer sphere is at rest and the temperature of its surface is prescribed as a function of the spherical coordinates and. It is shown that, when viscous dissipation is small, the overall rate of heat transfer from the rotating sphere into the fluid is unaffected by convection from the sphere surface, in case of a slow rotation, where the Stokes solution holds.     

Theoretical analysis of convective heat transfer enhancement of microencapsulated phase change material slurries

This paper analyzes the convective heat transfer enhancement mechanism of microencapsulated phase change material slurries based on the analogy between convective heat transfer and thermal conduction with thermal sources. The influence of each factor affecting the heat transfer enhancement for laminar flow in a circular tube with constant wall temperature is analyzed using an effective specific heat capacity model. The model is validated with results available in the literature. The analysis and the results clarify the heat transfer enhancement mechanism and the main factors influencing the heat transfer. In addition, the conventional Nusselt number definition of phase change slurries for internal flow is modified to describe the degree of heat transfer enhancement of microencapsulated phase change material slurries. The modification is also consistent evaluation of the convective heat transfer of internal and external flows.c volumetric concentration of microcapsules - c_m mass concentration of microcapsules - c_p specific heat, kJ kg^–1 K^–1 - h_fs phase change material heat of fusion, kJ kg^–1 - h_m* modified convective heat transfer coefficient, W m^–2 K^–1 - k thermal conductivity, W m^–1 K^–1 - k_e effective thermal conductivity of slurry, W m^–1 K^–1 - k_b slurry bulk thermal conductivity, W m^–1 K^–1 - ML dimensionless initial subcooling - Mr dimensionless phase change temperature range - Nu conventional Nusselt number - Nu* improved Nusselt number - q_wⁿ wall heat flux, Wm^–2 - Pe Peclet number - Pr Prandtl number - Re Reynolds number - r radial coordinate, m - r₀ duct radius, m - r₁ dimensionless radial coordinate - Ste Stefan number - T temperature, K - T₁ lower phase change temperature limit, K - T₂ upper phase change temperature limit, K - T_i slurry inlet temperature, K - u axial velocity, m/s - v radial velocity, m/s - x axial coordinate, m - x₁ dimensionless axial coordinate - thermal diffusivity, m²/s - dimensionless temperature - dynamic viscosity, N·s/m² - kinematic viscosity, m²/s - _t width of thermal boundary, m - degree of heat transfer enhancement, = h_m*/(h_m*)_single - b bulk fluid (slurry) - b0 slurry without phase change - l liquid - m mean - s solid - f suspending fluid - p microcapsule particles - w wall - single single-phase fluid     

Experimental investigations of fluid flow and heat transfer characteristics of a slot jet impinging on a rectangular cylinder

Experimental investigations on flow characteristics and average heat transfer due to slot jet impinging on a rectangular cylinder have been carried out for different non-dimensional parameters. The minimum value of the pressure coefficient is found on the lower face of the rectangular cylinder at an angle of inclination of 15°. Drag coefficient calculated from the measured pressure distribution is found to be maximum within a range of breadth/width ratio of 0.67 to 1.5 of rectangular cylinders. The maximum value of heat transfer rate is obtained at the angle of inclination of 15° of the cylinder to the jet axis. An increasing trend of heat transfer rate is observed with higher Reynolds numbers. A correlation of average Nusselt number is presented for rectangular cylinders.

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Experimentelle Untersuchung der Strömungs- und Wärmeübergangs-charakteristik eines auf einen rechteckigen Zylinder auftreffenden Strahls aus einer Schlitzdüse

Zusammenfassung Es wurden experimentelle Untersuchungen des Strömungs- und Wärmeübergangsverhaltens an einem rechteckigen, durch einen Strahl aus einer Schlitzdüse beaufschlagten Zylinders für verschiedene dimensionslose Parameter durchgeführt. Der Kleinstwert des Druckbeiwertes tritt an der Unterfläche des rechteckigen Zylinders bei einem Neigungswinkel von 15° auf. Der ausder gemessenen Druckverteilung berechnete Widerstandsbeiwert erreicht bei einem Breiten-Dicken-Verhältnis des Zylinders zwischen 0,67 und 1,5 Maximalwerte. Den maximalen Wärmestrom erhält man bei einem Neigungswinkel zwischen Zylinder und Strahlachse von 15°. Mit steigenden Reynoldszahlen erhöht sich der abgeführte Wärmestrom. Eine Korrelation für die mittlere Nusseltzahl an rechteckigen Zylindern wird mitgeteilt.

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Nomenclature A surface area of the rectangular cylinder - a width of the rectangular cylinder - b breadth of the rectangular cylinder - C _D drag coefficient =D/ - C _p pressure coefficient = (p – p _a )/ - C _pb base pressure coefficient = (p _b –p _a )/ - D drag force - h _f free convection heat transfer coefficient - average heat transfer coefficient - k thermal conductivity of air - L distance of the axis of the square cylinder from the nozzle exit - l length of the rectangular cylinder - Pr Prandtl number - p static pressure - P _a atmospheric pressure - P _b base pressure on the rear face - Nu _f free convection Nusselt number - average Nusselt number - q heat loss - q _f heat loss due to free convection - Re Reynolds number =u _j W/ _a - T _a ambient air temperature - average surface temperature - u _j average jet velocity at the nozzle exit - W nozzle width - angle of inclination of the rectangular cylinder to the jet axis in degrees - _a kinematic viscosity of air - _a density of air     

The buoyancy effects on the boundary layers induced by continuous surfaces stretched with rapidly decreasing velocities

Heat and mass transfer characteristics of the self-similar boundary layer flows induced by continuous surfaces stretched with rapidly decreasing power law velocities U_w x^m, m < –1 are considered for mixed convection flow. The effect of various governing parameters, such as Prandtl number Pr, temperature exponent n, dimensionless injection/suction velocity f_w, and the mixed convection parameter = s Gr/Re² are studied. These parameters have great effects on velocity and temperature profiles, heat transfer coefficient, and skin friction coefficient at the moving surface. Results show that similarity solutions exist only when the condition n = 2m – 1 is satisfied. Critical values of , Nu/Re^0.5 and C_f Re^0.5 are obtained for predominate natural convection for different Prandtl numbers at m = –2, –6 and n = –5, and –13 respectively. Results also show that the effect of buoyancy is more significant for weak than for strong suction. Furthermore, critical Prandtl numbers where f_w profiles have minimums are obtained for m = –2 and –6. Finally, critical values of , C_f Re^0.5 are also obtained for predominate natural convection for both m = –2 and –6.     

Variable permeability effect on convection in binary mixtures saturating a porous layer

The Darcy Model with the Boussinesq approximation is used to study natural convection in a shallow porous layer, with variable permeability, filled with a binary fluid. The permeability of the medium is assumed to vary exponentially with the depth of the layer. The two horizontal walls of the cavity are subject to constant fluxes of heat and solute while the two vertical ones are impermeable and adiabatic. The governing parameters for the problem are the thermal Rayleigh number, R _T, the Lewis number, Le, the buoyancy ratio, φ, the aspect ratio of the cavity, A, the normalized porosity, ε, the variable permeability constant, c, and parameter a defining double-diffusive convection (a = 0) or Soret induced convection (a = 1). For convection in an infinite layer, an analytical solution of the steady form of the governing equations is obtained on the basis of the parallel flow approximation. The onset of supercritical convection, or subcritical, convection are predicted by the present theory. A linear stability analysis of the parallel flow model is conducted and the critical Rayleigh number for the onset of Hopf’s bifurcation is predicted numerically. Numerical solutions of the full governing equations are found to be in excellent agreement with the analytical predictions.     

Mixed convection film condensation from downward flowing vapors onto a sphere with variable wall temperature

A model is developed for the study of mixed- convection film condensation from downward flowing vapors onto a sphere with variable wall temperature. The model combined natural convection dominated and forced convection dominated film condensation, concerning effects of pressure gradient (P), interfacial vapor shear drag and non-uniform wall temperature variation (A), has been investigated and solved numerically. The effect of pressure gradient on the dimensionless mean heat transfer, NuˉRe^−1/2 will remain almost uniform with increasing P until for various corresponding available values of F. Meanwhile, the dimensionless mean heat transfer, NuˉRe^−1/2 is increasing significantly with F for its corresponding available values of P. Although the non-uniform wall temperature variation has an appreciable influence on the local film flow and heat transfer; however, the dependence of mean heat transfer on A can be almost negligible. Received on 10 October 1996     

An Example of Finite-time Singularities in the 3d Euler Equations

Let be the exterior of the closed unit ball. Consider the self-similar Euler system

Optimum rib size to enhance forced convection in a horizontal triangular duct with ribbed internal surfaces

The optimum rib size to enhance heat transfer had been proposed through an experimental investigation on the forced convection of a fully developed turbulent flow in an air-cooled horizontal equilateral triangular duct fabricated on its internal surfaces with uniformly spaced square ribs. Five different rib sizes (B) of 5 mm, 6 mm, 7 mm, 7.9 mm and 9 mm, respectively, were used in the present investigation, while the separation (S) between the center lines of two adjacent ribs was kept at a constant of 57 mm. The experimental triangular ducts were of the same axial length (L) of 1050 mm and the same hydraulic diameter (D) of 44 mm. Both the ducts and the ribs were fabricated with duralumin. For every experimental set-up, the entire inner wall of the duct was heated uniformly while the outer wall was thermally insulated. From the experimental results, a maximum average Nusselt number of the triangular duct was observed at the rib size of 7.9 mm (i.e. relative rib size ). Considering the pressure drop along the triangular duct, it was found to increase almost linearly with the rib size. Non-dimensional expressions had been developed for the determination of the average Nusselt number and the average friction factor of the equilateral triangular ducts with ribbed internal surfaces. The developed equations were valid for a wide range of Reynolds numbers of 4,000 < Re _D < 23,000 and relative rib sizes of under steady-state condition. A Inner surface area of the triangular duct [m²] - A _C Cross-sectional area of the triangular duct [m²] - B Side length of the square rib [mm] - C _P Specific heat at constant pressure [kJ·kg^–1·K^–1] - C ₁, C ₂, C ₃ Constant coefficients in Equations (10), (12) and (13), respectively - D Hydraulic diameter of the triangular duct [mm] - Electric power supplied to heat the triangular duct [W] - f Average friction factor - F View factor for thermal radiation from the duct ends to its surroundings - h Average convection heat transfer coefficient at the air/duct interface [W·m^–2 ·K^–1] - k Thermal conductivity of the air [W·m^–1 ·K^–1] - L Axial length of the triangular duct [mm] - Mass flow rate [kg·s^–1] - n ₁, n ₂, n ₃ Power indices in Equations (10), (12) and (13), respectively - Nu _D Average Nusselt number based on hydraulic diameter - P Fluid pressure [Pa] - Pr Prandtl number of the airflow - _c Steady-state forced convection from the triangular duct to the airflow [W] - _l Heat loss from external surfaces of the triangular duct assembly to the surroundings [W] - _r Radiation heat loss from both ends of the triangular duct to the surroundings [W] - Re _D Reynolds number of the airflow based on hydraulic diameter - S Uniform separation between the centre lines of two consecutive ribs [mm] - T Fluid temperature [K] - T _a Mean temperature of the airflow [K] - T _ai Inlet mean temperature of the airflow [K] - T _ao Outlet mean temperature of the airflow [K] - T _s Mean surface temperature of the triangular duct [K] - T Ambient temperature [K] - U Mean air velocity in the triangular duct [m·s^–1] - _r Mean surface-emissivity with respect to thermal radiation - Dynamic viscosity of the fluid [kg·m^–1·s^–1] - Kinematic viscosity of the airflow [m²·s^–1] - Density of the airflow [kg·m^–3] - Stefan-Boltzmann constant [W·m^–2·K^–4]     

Friction and forced convective heat transfer in a sintered porous channel with obstacle blocks

This work experimentally studies the flow characteristics and forced convective heat transfer in a sintered porous channel that filled with sintered copper beads of three average diameters ( 0.830, and 1.163 mm). The pressure drop and the local temperature measurements can be applied to figure out the distributions of the friction coefficient and the heat transfer coefficient. Three sintered porous channels differ in the arrangement of obstacle blocks. Model A has no obstacle. Models B and C have five obstacle blocks facing down and up, respectively, in a sintered porous channel. The range of experimental parameters, porosity, heat flux, and effect of forced convection are 0.370 ≤ ɛ ≤ 0.385, q=0.228, 0.872, 1.862 W/cm², and 200 ≤ Re _d ≤ 800. The permeability and inertia coefficient of each of the three sintered porous channels are analyzed. The results for Model A agree with those obtained by previous investigations in C _f distribution. The heat transfer of Model C exceeds that of Model A by approximately 20%. Finally, a series of empirical correlation equations were obtained for practical applications and engineering problems.     

Effect of Conduction in Bottom Wall on B��nard Convection in a Porous Enclosure with Localized Heating and Lateral Cooling

Darcy-Bénard convection in a square porous enclosure with a localized heating from below and lateral cooling is studied numerically in the present paper. A finite-thickness bottom wall is locally heated, the top wall is kept at a lower temperature than the bottom wall temperature, and the lateral walls are cooled. The finite difference method has been used to solve the dimensionless governing equations. The analysis in the undergoing numerical investigation is performed in the following ranges of the associated dimensionless groups: the heat source length?? ${0.2\leq H \leq 0.9}$ , the wall thickness?? ${0.05\leq D \leq 0.4}$ , the thermal conductivity ratio?? ${0.8\leq K_{\rm r} \leq 9.8}$ , and the Biot number?? ${0.1\leq Bi \leq 1.1}$ . It is observed that the heat transfer rate could increase with increasing heat source lengths, thermal conductivity ratio, and cooling intensity. There exists a critical wall thickness for a high wall conductivity below which the increasing wall thickness increases the heat transfer rate and above which the increasing wall thickness decreases the heat transfer rate.     

Experimental investigation of mixed convection from an array of discrete heat sources at the bottom of a horizontal channel

Mixed convection heat transfer from an array of discrete heat sources inside a rectangular channel has been investigated experimentally under various operating conditions for air. The lower surface of the channel was equipped with 8 × 4 flush-mounted heat sources subjected to uniform heat flux, sidewalls and the upper wall are insulated and adiabatic. The experimental parametric study was made for an aspect ratio of AR = 10, Reynolds numbers 241 Re_Dh 980, and modified Grashof numbers Gr^* = 9.53 × 10⁵ to 1.53 × 10⁷ . From the experimental measurements, surface temperature distributions of the discrete heat sources were obtained and effects of Reynolds and Grashof numbers on these temperatures were investigated. Furthermore, Nusselt number distributions were calculated for different Reynolds and Grashof numbers, with emphasis on changes obtained for different discrete heat source locations. From these results, the buoyancy affected secondary flow and the onset of instability have been discussed. Results show that surface temperatures increase with increasing Grashof number and decrease with increasing Reynolds number. However, with the increase in the buoyancy affected secondary flow and the onset of instability, temperatures level off and even drop as a result of heat transfer enhancement. This outcome can also be observed from the variation of the row-averaged Nusselt number showing an increase towards the exit, especially for low Reynolds numbers.     

Prediction of roll temperature with a non-uniform heat flux at tool and workpiece interface

In a metal forming process, plastic deformation of the workpiece takes place at tool and workpiece interface region. Tool has been identified as one of the key parameters in controlling the productivity of any manufacturing industry. The deformation of metals and friction at the contact region produce large amount of heat, a part of that heat is conducted towards the tool where it is removed by forced convection. These cooling and heating cycles finally result in a substantial change in the temperature distribution in the roll. In this paper, an attempt is made to study the temperature and heat flux distribution in the roll by considering a non-uniform heat flux at the roll-workpiece interface for a cold rolling process. Adopting an elemental approach, a methodology has been proposed to model non-uniform heat flux at the interface. For this purpose both tool and workpiece has been considered together, thus a coupled approach is used to model both deformation and heat transfer phenomenon. It is demonstrated that the present approach of modeling is more general than that available in the literature. For example, a constant value of heat flux at the interface that is considered by several investigators is shown to be a special case of the present investigation, particularly when the deformation and relative velocity is very small. It is shown that the error in maximum temperature associated with constant heat flux assumption could be more than 5% in situations when reduction and relative velocity is high. The results are presented for temperature and heat flux distributions in the roll for different operating conditions.a thermal diffusivity, (m²/sec) - B pre-strain coefficient - C yield stress at unit strain, (N/m²) - e rate of deformation heat generation per unit volume, (W/m³) - f friction factor - h heat transfer coefficient, (W/m² °C) - k thermal conductivity, (W/m °C) - K yield stress at unit strain, (N/m²) - L bite length, (m) - n strain hardening exponent - P pressure between tool and workpiece, (N/m²) - q heat flux, (W/m²) - q_f friction heat flux, (W/m²) - heat flux entering towards the roll for any arbitrary element j (W/m²) - R roll radius, (m) - S_o yield stress in plane strain, (N/m²) - T temperature difference (T = T_r – T_o), (°C) - T surrounding temperature, (°C) - y strip thickness, (m) - V_rel relative slipping velocity, (m/sec) - V velocity, (m/sec) - Pe Peclet number - Bi Biot number - _T Total bite angle - mean effective strain - mean true stress, (N/m²) - mean strain rate - friction stress, (N/m²) - coefficient of friction - angle between heating and cooling regions - angle of cooling spray region - r, polar coordinates - x, y Cartesian coordinates - o initial value - f final value - r related to roll - s related to strip - a average value - j elemental region     

Thermal Non-equilibrium Heat Transfer and Entropy Generation due to Natural Convection in a Cylindrical Enclosure with a Truncated Conical,Heat-Generating Porous Bed

Natural convection in enclosures driven by heat-generating porous media has diverse applications in fields like geothermal, chemical, thermal and nuclear energy. The present article focuses on heat transfer and entropy generation characteristics of a heat-generating porous bed, placed centrally within a fluid-filled cylindrical enclosure. Pressure drop and heat transfer in the porous bed are modelled using the Darcy–Brinkmann–Forchheimer approximation and the local thermal non-equilibrium model, respectively. Energy flux vectors have been utilised for visualising convective energy transfer within the enclosure. The study of a wide range of Rayleigh number (\(10^{7}\)–\(10^{11}\)) and Darcy number (\(10^{-6}\)–\(10^{-10}\)) reveals that heat transfer in the porous region can be classified into conduction-dominated and convection-dominated regimes. This is supplemented with an entropy generation analysis in order to identify and characterise the irreversibilities associated with the phenomenon. It is observed that entropy generation characteristics of the enclosure closely follow the above-mentioned regime demarcation. Numerical computations for the present study have been conducted using ANSYS FLUENT 14.5. The solid energy equation is solved as a user-defined scalar equation, while data related to energy flux vectors and entropy generation are obtained using user-defined functions.     

Thermal free convection from an ice sphere in water

Summary Thermal free convection in water is studied by melting ice spheres in water, the uniform temperature of which is varied between 0 and 10°C. Flow patterns as well as local heat transfer are examined. In particular, the effect of anomalous thermal expansion is investigated. From our observations a more accurate picture of the flow phenomena can be obtained that agrees not only with our experimental heat transfer data but also with theoretical results from existing literature.Nomenclature a thermal diffusivity, /(c) - c specific heat capacity - d characteristic length, here diameter of sphere - g gravitational acceleration - coefficient of heat transfer - thermal expansion coefficient - as above, at ambient temperature - temperature difference between fluid and melting ice - as above, for fluid at infinity - thermal conductivity - kinematic viscosity - density - angular distance from upper stagnation point (see Figs. 1, 2, and 3) - Nu Nusselt number, d/ - mean value of Nusselt number - Gr Grashof number, - Pr Prandtl number, /a