Steady and transient thermal convection in a fluid layer with uniform volumetric energy sources

1977 ◽  
Vol 83 (2) ◽  
pp. 375-395 ◽  
Author(s):  
F. A. Kulacki ◽  
A. A. Emara
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Steady State ◽  
Rayleigh Number ◽  
Time Scales ◽  
Temperature Difference ◽  
Number Range ◽  
Volumetric Heating ◽  
Steady State Temperature

Measurements of the overall heat flux in steady convection have been made in a horizontal layer of dilute aqueous electrolyte. The layer is bounded below by a rigid zero-heat-flux surface and above by a rigid isothermal surface. Joule heating by an alternating current passing horizontally through the layer provides a uniformly distributed volumetric energy source. The Nusselt number at the upper surface is found to be proportional to Ra0[sdot ]227 in the range 1[sdot ]4 ≤ Ra/Rac ≤ 1[sdot ]6 × 109, which covers the laminar, transitional and turbulent flow regimes. Eight discrete transitions in the heat flux are found in this Rayleigh number range. Extrapolation of the heat-transfer correlation to the conduction value of the Nusselt number yields a critical Rayleigh number which is within -6[sdot ]7% of the value given by linearized stability theory. Measurements have been made of the time scales of developing convection after a sudden start of volumetric heating and of decaying convection when volumetric heating is suddenly stopped. In both cases, the steady-state temperature difference across the layer appears to be the controlling physical parameter, with both processes exhibiting the same time scale for a given steady-state temperature difference, or [mid ]ΔRa[mid ]. For step changes in Ra such that [mid ]ΔRa[mid ] > 100Rac, the time scales for both processes can be represented by Fo [vprop ] [mid ]ΔRa[mid ]m, where Fo is the Fourier number of the layer. Temperature profiles of developing convection exhibit a temperature excess in the upper 15–20 % of the layer in the early stages of flow development for Rayleigh numbers corresponding to turbulent convection. This excess disappears when the average core temperature becomes large enough to permit eddy transport and mixing processes near the upper surface. The steady-state limits in the transient experiments yield heat-transfer data in agreement with the results of the steady-state experiments.

Heat transfer characteristics of nanofluids from a sinusoidal corrugated cylinder placed in a square cavity

2021 ◽  
pp. 095440622110272
Author(s):  
Salaika Parvin ◽  
Nepal Chandra Roy ◽  
Litan Kumar Saha ◽  
Sadia Siddiqa
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Heat Transfer Characteristics ◽  
Number Range ◽  
Transfer Characteristics ◽  
Wide Range

A numerical study is performed to investigate nanofluids' flow field and heat transfer characteristics between the domain bounded by a square and a wavy cylinder. The left and right walls of the cavity are at constant low temperature while its other adjacent walls are insulated. The convective phenomena take place due to the higher temperature of the inner corrugated surface. Super elliptic functions are used to transform the governing equations of the classical rectangular enclosure into a system of equations valid for concentric cylinders. The resulting equations are solved iteratively with the implicit finite difference method. Parametric results are presented in terms of streamlines, isotherms, local and average Nusselt numbers for a wide range of scaled parameters such as nanoparticles concentration, Rayleigh number, and aspect ratio. Several correlations have been deduced at the inner and outer surface of the cylinders for the average Nusselt number, which gives a good agreement when compared against the numerical results. The strength of the streamlines increases significantly due to an increase in the aspect ratio of the inner cylinder and the Rayleigh number. As the concentration of nanoparticles increases, the average Nusselt number at the internal and external cylinders becomes stronger. In addition, the average Nusselt number for the entire Rayleigh number range gets enhanced when plotted against the volume fraction of the nanofluid.

Application of a Complex Nusselt Number to Heat Transfer During Compression and Expansion

1994 ◽  
Vol 116 (3) ◽  
pp. 536-542 ◽  
Author(s):  
A. A. Kornhauser ◽  
J. L. Smith
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Temperature Difference ◽  
Rate Of Change ◽  
Transfer Model ◽  
Volume Data ◽  
Piston Cylinder ◽  
Compression And Expansion ◽  
Experimental Pressure

Heat transfer during compression and expansion can be out of phase with bulk gas-wall temperature difference. An ordinary convective heat transfer model is incapable of predicting this phenomenon. Expressions for compression/expansion heat transfer developed from simple conduction models use a complex heat transfer coefficient. Thus, heat flux consists of one part proportional to temperature difference plus a second part proportional to rate of change of temperature. Surface-averaged heat flux was calculated from experimental pressure-volume data for piston-cylinder gas springs over a range of speeds, pressures, gases, and geometries. The complex Nusselt number model proved capable of correlating both magnitude and phase of the measured heat transfer as functions of an oscillation Peclet number.

scholarly journals Numerical study of combined convection heat transfer for thermally developing upward flow in a vertical cylinder

2008 ◽  
Vol 12 (2) ◽  
pp. 89-102 ◽  
Author(s):  
Hussein Mohammed ◽  
Yasin Salman
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Temperature Profile ◽  
Local Nusselt Number ◽  
Convection Heat Transfer ◽  
Convection Heat ◽  
Flux Boundary Condition ◽  
Number Range ◽  
Dimensionless Velocity

The problem of the laminar upward mixed convection heat transfer for thermally developing air flow in the entrance region of a vertical circular cylinder under buoyancy effect and wall heat flux boundary condition has been numerically investigated. An implicit finite difference method and the Gauss elimination technique have been used to solve the governing partial differential equations of motion (Navier Stocks equations) for two-dimensional model. This investigation covers Reynolds number range from 400 to 1600, heat flux is varied from 70 W/m2 to 400 W/m2. The results present the dimensionless temperature profile, dimensionless velocity profile, dimensionless surface temperature along the cylinder, and the local Nusselt number variation with the dimensionless axial distance Z+. The dimensionless velocity and temperature profile results have revealed that the secondary flow created by natural convection have a significant effect on the heat transfer process. The results have also shown an increase in the Nusselt number values as the heat flux increases. The results have been compared with the available experimental study and with the available analytical solution for pure forced convection in terms of the local Nusselt number. The comparison has shown satisfactory agreement. .

Alternative and Relevant Representation to Heat Transfer Coefficient for Modeling the Heat Transfer Between a Fluid and a Non-Isothermal Wall in Transient Regime

2010 ◽  
Author(s):  
Benjamin Remy ◽  
Alain Degiovanni
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Steady State ◽  
Boundary Conditions ◽  
Transfer Coefficient ◽  
Flat Plate ◽  
Temperature Difference ◽  
Interfacial Heat Transfer ◽  
Thermal Boundary Conditions

This paper deals with the relevant model that can be proposed for modeling the interfacial heat transfer between a fluid and a wall in the case of space and time varying thermal boundary conditions. Usually, for a constant and uniform heat transfer (unidirectional steady-state regime), the problem can be solved introducing a heat transfer coefficient h, uniform in space and constant in time that linearly links the surface heat flux and the temperature difference between the wall temperature Tw and an equivalent fluid temperature Tf. The problem we consider in this work concerns the heat transfer between a steady-state fluid flow and a wall submitted to a transient and non uniform thermal solicitations, as for instance a steady-state flow on a flat plate submitted to a transient and space reduced heat flux. We will show that the more interesting representation for describing the interfacial heat transfer is not to define as usually done a non-uniform and variable heat transfer coefficient h(x,t) because as it depends on the thermal boundary conditions, it is not really intrinsic. We propose an alternative approach, which consists in introducing a generalized impedance Z(ω,p) that links in space and time domain the heat flux and the temperature difference through a double convolution product instead of a scalar product. After the presentation of the general problem, the simple case of a stationary piston flow that can be solved analytically will be considered for validation both in thermal steady-state and transient regimes. To conclude and show the interest of our approach, a comparison between a global approach and a numerical simulation in a more complex and realistic case taking into account the thermal coupling with a flat plate will be presented.

Natural Convection Heat Transfer of Concentric/Eccentric Annulus Subjected to Inner Tube of Constant Heat Flux

2011 ◽  
Author(s):  
R. Hosseini ◽  
M. Alipour ◽  
A. Gholaminejad
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Surface Temperature ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Eccentric Annulus

This paper describes the experimental results of natural convection heat transfer from vertical, electrically heated cylinder in a concentric/eccentric annulus and develops correlations for the dependence of the average annulus Nusselt number upon the Rayleigh number. Wall surface temperature have been recorded for diameter ratio of d/D = 0.4, with the apparatus immersed in stagnant air with uniform temperature. Measurements have been carried out for eccentric ratios of E = 0, 0.19, 0.34, 0.62 and 0.89 in the range of heat flux of 45 to 430 W/m2. The surface temperature of the heater was found to increase upwards and reach a maximum at some position, beyond which it decreases again. It is observed, that this maximum temperature occurs near h/l = 0.8 for 0 ≤ E ≤ 0.62 at almost all power levels, but shifts downwards for E = 0.89. Moreover, empirical correlations between the average Nusselt number and the Rayleigh number are derived for concentric and eccentric annuli.

The Effect of Temperature Modulation on Natural Convection in a Horizontal Layer Heated From Below: High-Rayleigh-Number Experiments

1994 ◽  
Vol 116 (3) ◽  
pp. 614-620 ◽  
Author(s):  
J. Mantle ◽  
M. Kazmierczak ◽  
B. Hiawy
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Rayleigh Number ◽  
Temperature Difference ◽  
Wall Temperature ◽  
Bottom Wall ◽  
Large Temperature ◽  
Temperature Modulation ◽  
Mean Temperature ◽  
The Mean

An experimental investigation was conducted to study the effects of wall temperature modulation in a horizontal fluid layer heated from below. A series of 45 transient experiments was performed in which the bottom wall temperature changed periodically with time in a “sawtoothlike” fashion. The amplitude of the bottom wall temperature oscillation varied from 3 to 70 percent of the enclosure’s mean temperature difference, and the period of the temperature swings ranged from 43 seconds to 93 minutes. With water as the fluid in the test cell, the flow was fully turbulent at all times. The Rayleigh number of the experiments (based on the enclosure’s height and on the mean temperature difference) was 0.4 × 108 < Ra < 1.2 × 109. It was found that for small changes in the bottom wall temperature, the cycle-averaged heat transfer through the layer was unchanged, independent of the period, and was equal in magnitude to the well-established steady-state value when the hot wall is evaluated at the mean temperature. However, this study shows that the cycle-averaged heat transfer increases notably, up to 12 percent as compared to the steady-state value, for the experiments with large temperature modulations. Futhermore, it was observed that the enchancement was a function of the amplitude and period of the oscillation.

Experimental Investigation of Natural Convective Heat Transfer From Horizontal, Inclined and Vertical Cylinder With Constant Heat Flux

2010 ◽  
Author(s):  
A. Gharehghani ◽  
R. Hoseini ◽  
M. M. Salahi
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Constant Heat Flux ◽  
Experimental Results ◽  
Constant Heat ◽  
Constant Length

In this study, natural convective heat transfer from cylindrical slender rods with different length and diameters and different angles of inclination (from horizontal to vertical) at constant heat flux condition was measured. For each inclination angle, average natural heat transfer coefficient was obtained. The effects of the angle of inclination and that of the diameter and length of cylinders on heat transfer rates were examined. The angles of 0°, 15°, 30°, 45°, 60°, 75° and 90° were studied. Experimental results show that increasing the diameter of the cylinder, with constant length and the Rayleigh number based on length causes the decrease of the Nusselt number. Increasing the length of the cylinders, with constant diameter and Rayleigh number based on diameter causes the decrease of the Nusselt number. Increasing either the angle of inclination or length decreases the effect of diameter on the heat transfer rate. Experimental results in terms of Nusselt number were correlated as a function of modified Rayleigh number and dimensionless parameters containing diameter, length and orientation angle.

Natural Convection and Entropy Generation in a Cavity Filled With Two Horizontal Layers of Nanofluid and Porous Medium in Presence of a Magnetic Field

2015 ◽  
Author(s):  
Ali Al-Zamily ◽  
M. Ruhul Amin
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Rayleigh Number ◽  
Entropy Generation ◽  
Darcy Number ◽  
Bejan Number ◽  
Flow Heat

A numerical analysis is performed to study the fluid flow, heat transfer and entropy generation inside a square cavity embedded with heat flux and subject to the horizontal magnetic field. The cavity is consist of two same width layers: first layer filled with nanofluid (Al2O3+water) and second one is saturated porous media filled with a same nanofluid. The uniform constant heat flux is applied partly at the base wall, and the other parts of the base wall are assumed adiabatic. The upper horizontal wall kept adiabatic, while the vertical walls are maintained at constant cold temperature. Finite element method based on the variational formulation is employed to solve the main equations. The results of the present study are based on visualization of heat flow via isotherms and heatfunctions (heatlines), fluid flow via streamfunctions, and irreversibility via Bejan number. Comparisons with previously numerical and experimental published works are performed and the results are found to be in a good agreement. In this study, the effect of the main pertinent parameters, such as: nanoparticles volume fraction (0≤Φ≤0.15), Rayleigh number (104≤Ra≤107), Darcy number (10−1≤Da≤10−5), Hartmann number (0≤Ha≤60) on the fluid flow, heat transfer and entropy generation are investigated. The results show that the effect of the Hartmann on Nusselt number increases as Darcy number increases especially at high Rayleigh number. Also, at Ra=107 and Φ=0.15, the percentage decreasing in Nusselt number due to present magnetic field (Ha=40) are 85.89% at Da=10−1, 87.12% at Da=10−3 and 98.69% at Da=10−5.

scholarly journals Free Convection Heat Transfer from Horizontal Cylinders

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 559
Author(s):  
Janusz T. Cieśliński ◽  
Slawomir Smolen ◽  
Dorota Sawicka
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Free Convection ◽  
Convection Heat Transfer ◽  
Horizontal Tube ◽  
Correlation Equations ◽  
Convection Heat ◽  
Number Range ◽  
Heated Cylinder ◽  
Free Convection Heat

The results of experimental investigation of free convection heat transfer in a rectangular container are presented. The ability of the commonly accepted correlation equations to reproduce present experimental data was tested as well. It was assumed that the examined geometry fulfils the requirement of no-interaction between heated cylinder and bounded surfaces. In order to check this assumption recently published correlation equations that jointly describe the dependence of the average Nusselt number on Rayleigh number and confinement ratios were examined. As a heat source served electrically heated horizontal tube immersed in an ambient fluid. Experiments were performed with pure ethylene glycol (EG), distilled water (W), and a mixture of EG and water at 50%/50% by volume. A set of empirical correlation equations for the prediction of Nu numbers for Rayleigh number range 3.6 × 104 < Ra < 9.2 × 105 or 3.6 × 105 < Raq < 14.8 × 106 and Pr number range 4.5 ≤ Pr ≤ 160 has been developed. The proposed correlation equations are based on two characteristic lengths, i.e., cylinder diameter and boundary layer length.

A New Nusselt Number for Complicated Configurations

2013 ◽  
Author(s):  
Tom I-Ping Shih ◽  
Srisudarshan Krishna Sathyanarayanan
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Local Heat ◽  
Negative Slope ◽  
Test Problems ◽  
Rectangular Duct ◽  
Circular Duct ◽  
Flow And Heat Transfer ◽  
Local Heat Flux

Convective heat transfer over surfaces is generally presented in the form of the heat-transfer coefficient (h) or its nondimensional form, the Nusselt number (Nu). Both require the specification of the free-stream temperature (Too) or the bulk (Tb) temperature, which are clearly defined only for simple configurations. For complicated configurations with flow separation and multiple temperature streams, the physical significance of Too and Tb becomes unclear. In addition, their use could cause the local h to approach positive or negative infinity if Too or Tb is nearly the same as the local wall temperature (Twall). In this paper, a new Nusselt number, referred to as the SCS number, is proposed, that provides information on the local heat flux but does not use h and hence by-passes the need to define Too or Tb. CFD analysis based on steady RANS with the shear-stress transport model is used to compare and contrast the SCS number with Nu for two test problems: (1) compressible flow and heat transfer in a straight duct with a circular cross section and (2) compressible flow and heat transfer in a high-aspect ratio rectangular duct with a staggered array of pin fins. Parameters examined include: Reynolds number at the duct inlet (3,000 to 15,000 for the circular duct and 15,000 and 150,000 for the rectangular duct), wall temperature (Twall = 373 K to 1473 K for the circular duct and 313 K and 1,173 K for the rectangular duct), and distance from of the inlet of the duct (up to 100D for the circular duct and up to 156D for the rectangular duct). For the circular duct, Nu was found to decrease rapidly from the duct inlet until reaching a minimum and then to rise until reaching a nearly constant value in the “fully” developed region if the wall is heating the gas. If the wall is cooling the gas, then Nu has a constant positive slope in the “fully” developed region. The location of the minimum in Nu and where Nu becomes nearly constant in value or in slope are strong functions of Twall. For the SCS number, the decrease from the duct inlet is monotonic with a negative slope, whether the wall is heating or cooling the gas. Also, different SCS curves for different Twall approach each other as the distance from the inlet increases. For the rectangular duct, Nu tends to oscillate about a constant value in the pin-fin region, whereas SCS tends to oscillate about a line with a negative slope. For both test problems, the variation of SCS is not more complicated than Nu, but SCS yields the local heat flux without need for Tb, a parameter that is hard to define and measure for complicated problems.

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