Unsteady Conduction in a Horizontal Solid Cylinder Cooled by Natural Convection: Alternate Lumped Criterion in Terms of the Solid Material

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Antonio Campo ◽  
Jaime Sieres
Keyword(s):  
Thermal Conductivity ◽  
Natural Convection ◽  
Heat Exchange ◽  
Solid Body ◽  
Biot Number ◽  
The Body ◽  
Convection Heat ◽  
Lumped Model ◽  
Convective Coefficient ◽  
The Mean

Within the framework of the potent lumped model, unsteady heat conduction takes place in a solid body whose space–mean temperature varies with time. Conceptually, the lumped model subscribes to the notion that the external convective resistance at the body surface dominates the internal conductive resistance inside the body. For forced convection heat exchange between a solid body and a neighboring fluid, the criterion entails to the lumped Biot number Bil=(h¯/ks)(V/A)<0.1, in which the mean convective coefficient h¯ depends on the impressed fluid velocity. However, for natural convection heat exchange between a solid body and a fluid, the mean convective coefficient h¯ depends on the solid-to-fluid temperature difference. As a consequence, the lumped Biot number must be modified to read Bil=(h¯max/ks)(V/A)<0.1, wherein h¯max occurs at the initial temperature Ti for cooling or at a future temperature Tfut for heating. In this paper, the equivalence of the lumped Biot number criterion is deduced from the standpoint of the solid thermal conductivity through the solid-to-fluid thermal conductivity ratio.

The Lumped Capacitance Model for Unsteady Heat Conduction in Regular Solid Bodies With Natural Convection to Nearby Fluids Engages the Nonlinear Bernoulli Equation

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Antonio Campo
Keyword(s):  
Heat Conduction ◽  
Natural Convection ◽  
Heat Equation ◽  
Biot Number ◽  
Bernoulli Equation ◽  
Convective Coefficient ◽  
Unsteady Heat Conduction ◽  
The Mean ◽  
Capacitance Model ◽  
Solid Bodies

For the analysis of unsteady heat conduction in solid bodies comprising heat exchange by forced convection to nearby fluids, the two feasible models are (1) the differential or distributed model and (2) the lumped capacitance model. In the latter model, the suited lumped heat equation is linear, separable, and solvable in exact, analytic form. The linear lumped heat equation is constrained by the lumped Biot number criterion Bil=h¯(V/S)/ks < 0.1, where the mean convective coefficient h¯ is affected by the imposed fluid velocity. Conversely, when the heat exchange happens by natural convection, the pertinent lumped heat equation turns nonlinear because the mean convective coefficient h¯ depends on the instantaneous mean temperature in the solid body. Undoubtedly, the nonlinear lumped heat equation must be solved with a numerical procedure, such as the classical Runge–Kutta method. Also, due to the variable mean convective coefficient h¯ (T), the lumped Biot number criterion Bil=h¯(V/S)/ks < 0.1 needs to be adjusted to Bil,max=h¯max(V/S)/ks < 0.1. Here, h¯max in natural convection cooling stands for the maximum mean convective coefficient at the initial temperature Tin and the initial time t = 0. Fortunately, by way of a temperature transformation, the nonlinear lumped heat equation can be homogenized and later channeled through a nonlinear Bernoulli equation, which admits an exact, analytic solution. This simple route paves the way to an exact, analytic mean temperature distribution T(t) applicable to a class of regular solid bodies: vertical plate, vertical cylinder, horizontal cylinder, and sphere; all solid bodies constricted by the modified lumped Biot number criterion Bil,max<0.1.

Experimental and Numerical Investigation on Natural Convection Heat Transfer of TiO2–Water Nanofluids in a Square Enclosure

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Yanwei Hu ◽  
Yurong He ◽  
Shufu Wang ◽  
Qizhi Wang ◽  
H. Inaki Schlaberg
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Natural Convection ◽  
Numerical Investigation ◽  
Convection Heat Transfer ◽  
Distribution Functions ◽  
Lattice Boltzmann Model ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Square Enclosure

An experimental and numerical investigation on natural convection heat transfer of TiO2–water nanofluids in a square enclosure was carried out for the present work. TiO2–water nanofluids with different nanoparticle mass fractions were prepared for the experiment and physical properties of the nanofluids including thermal conductivity and viscosity were measured. Results show that both thermal conductivity and viscosity increase when increasing the mass fraction of TiO2 nanoparticles. In addition, the thermal conductivity of nanofluids increases, while the viscosity of nanofluids decreases with increasing the temperature. Nusselt numbers under different Rayleigh numbers were obtained from experimental data. Experimental results show that natural convection heat transfer of nanofluids is no better than water and even worse when the Rayleigh number is low. Numerical studies are carried out by a Lattice Boltzmann model (LBM) coupling the density and the temperature distribution functions to simulate the convection heat transfer in the enclosure. The experimental and numerical results are compared with each other finding a good match in this investigation, and the results indicate that natural convection heat transfer of TiO2–water nanofluids is more sensitive to viscosity than to thermal conductivity.

Natural Convection in Rectangular Cavity With Nanoparticle Enhanced Ionic Liquids (NEILs)

2012 ◽  
Author(s):  
Titan C. Paul ◽  
A. K. M. M. Morshed ◽  
Elise B. Fox ◽  
Ann E. Visser ◽  
Nicholas J. Bridges ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Capacity ◽  
Ionic Liquid ◽  
Ionic Liquids ◽  
Natural Convection ◽  
Thermophysical Properties ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat

A systematic natural convection heat transfer experiment has been carried out of nanoparticle enhanced ionic liquids (NEILs) in rectangular enclosures (lengthxwidthxheight, 50×50×50mm and 50×50×75mm) heated from below condition. In the present experiment NEIL was made of N-butyl-N-methylpyrrolidinium bis{(trifluoromethyl)sulfonyl} imide, ([C4mpyrr][NTf2]) ionic liquid with 0.5% (weight%) Al2O3 nanoparticles. In addition to characterize the natural convection behavior of NEIL, thermophysical properties such as thermal conductivity, heat capacity, and viscosity were also measured. The result shows that the thermal conductivity of NEIL enhanced ∼3% from the base ionic liquid (IL), heat capacity enhanced ∼12% over the measured temperature range. The natural convection experimental result shows consistent for two different enclosures based on the degrading natural convection heat transfer rate over the measured Rayleigh number range. Possible reasons of the degradation of natural convection heat transfer may be the relative change of the thermophysical properties of NEIL compare to the base ionic liquid.

scholarly journals Enhancement of natural convection heat transfer in a U-shaped cavity filled with Al2O3-water nanofluid

2012 ◽  
Vol 16 (5) ◽  
pp. 1317-1323 ◽  
Author(s):  
Ching-Chang Cho ◽  
Her-Terng Yau ◽  
Cha’o-Kuang Chen
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Volume Fraction ◽  
Convection Heat Transfer ◽  
Heated Wall ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
The Mean

This paper investigates the natural convection heat transfer enhancement of Al2O3-water nanofluid in a U-shaped cavity. In performing the analysis, the governing equations are modeled using the Boussinesq approximation and are solved numerically using the finite-volume numerical method. The study examines the effects of the nanoparticle volume fraction, the Rayleigh number and the geometry parameters on the mean Nusselt number. The results show that for all values of the Rayleigh number, the mean Nusselt number increases as the volume fraction of nanoparticles increases. In addition, it is shown that for a given length of the heated wall, extending the length of the cooled wall can improve the heat transfer performance.

Effect on Natural Convection Heat Transfer of Nanofluid in an Enclosure Due to Uncertainties of Viscosity and Thermal Conductivity

2007 ◽  
Author(s):  
C. J. Ho ◽  
M. W. Chen ◽  
Z. W. Li
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Natural Convection ◽  
Dynamic Viscosity ◽  
Convection Heat Transfer ◽  
Alumina Nanoparticles ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Significant Difference ◽  
Effective Dynamic

In this study we aim to identify effects due to uncertainties in effective dynamic viscosity and thermal conductivity of nanofluid on laminar natural convection heat transfer in a square enclosure. Numerical simulations have been undertaken incorporating a homogeneous solid-liquid mixture formulation for the two-dimensional buoyancy-driven convection in the enclosure filled with alumina-water nanofluid. Two different formulas from the literature are each considered for the effective viscosity and thermal conductivity of the nanofluid. Simulations have been carried out for the pertinent parameters in the following ranges: the Rayleigh number, Raf = 103 ∼ 106 and the volumetric fraction of alumina nanoparticles, φ = 0 ∼ 4%. Significant difference in the effective dynamic viscosity enhancement of the nanofluid calculated from the two adopted formulas, other than that in the thermal conductivity enhancement, was found to play as a major factor, thereby leading to contradictory results concerning the heat transfer efficacy of using nanofluid in the enclosure.

Natural Convection Heat Transfer From Long Horizontal Isothermal Cylinders

1994 ◽  
Vol 116 (1) ◽  
pp. 96-104 ◽  
Author(s):  
S. B. Clemes ◽  
K. G. T. Hollands ◽  
A. P. Brunger
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Cross Section ◽  
Body Height ◽  
Convection Heat Transfer ◽  
Circular Cross Section ◽  
Correlation Equation ◽  
The Body ◽  
Natural Convection Heat Transfer ◽  
Convection Heat

A new set of measurements is reported on natural convection heat transfer in air from isothermal long horizontal cylinders of noncircular cross section at various orientations, covering the Rayleigh number (Ra) range from about 103 to about 109. The data are correlated reasonably well by a conduction layer model with a constant value (i.e., the same for all body shapes and orientations) of 5.42 for the Churchill-Usagi coefficient blending the laminar and turbulent asymptotes. The resulting correlation equation normally requires only the geometric specification of the body height and perimeter. This model is also tested against data in the literature on the subject problem, and found to be generally predictive, to within about ±10 percent. A new set of data covering the same Ra range is also reported for the circular cross-section case, i.e., the long horizontal isothermal circular cylinder. Comparison of this data with the several existing correlations for this well-known problems shows that the Kuehn and Goldstein equation predicts the data best, although the Raithby and Hollands equation also predicts the data very well, but only after a revision to the blending coefficient.

scholarly journals XVIII. On the direction assumed by plants

1848 ◽  
Vol 138 ◽  
pp. 253-275
Keyword(s):  
Solid Body ◽  
The Body ◽  
The Other ◽  
External Object ◽  
Metallic Wire ◽  
Slight Tendency ◽  
The Family ◽  
The Mean ◽  
Perennial Herbs

The plants with tendrils are very numerous. According to Mr. Palm there are about five hundred, divided into seventeen families. Of these, one hundred and sixty have a ligneous stem, eighty-three are perennial herbs, and one hundred and seventeen are annuals. My experiments on the mode of curling-up of these organs were made on the tendrils of the Tamus comunis , a plant of the family of the Asparageæ. The tendrils of this plant seem to be a thread-like degeneration of the footstalk of a leaf, whose place they occupy on the stem of the plant. They are at first straight, and are implanted perpendicularly on the stem, so as to form almost a right angle with it; the extreme end of the tendril only has a slight tendency to bend towards the stem. When the tendril of the Tamus is touched by any solid body whatever on a point of its surface not too far from the extremity, it contracts itself from the outside inwards, forming at first a hook and then a curl, so as to embrace the body closely if that body be circular; if angular, the knot is only tight on the angles, and bulges out on the surfaces. When a first knot is tied, the end of the tendril continues to roll itself up in a coil, though not in contact with the body in that part, and the coil slides over the external object, coming nearer and nearer to it so as to embrace it several times: in the mean while, the other end of the tendril continues also to contract itself. In this way as many as seven or eight knots are formed. I have frequently seen three tied before my eyes within the space of a quarter of an hour on a metallic wire, small branches of wood, a pencil, my finger, &c. The contact of any solid body whatever is sufficient to produce this effect; so much so, that although the tendril is evidently destined by nature to support the creeper to which it belongs, by means of the urrounding plants, yet if it chances to meet a part of the very same plant of Tamus of which it is itself a portion, the contact causes it immediately to roll itself up around that portion.

scholarly journals Numerical Investigation of the Effect of Baffle Inclination Angle on Nanofluid Natural Convection Heat Transfer in A Square Enclosure

2019 ◽  
Vol 12 (2) ◽  
pp. 61-71 ◽  
Author(s):  
Barik AL-Muhjaa ◽  
Khaled Al-Farhany
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Solid Wall ◽  
Convection Heat Transfer ◽  
Convection Heat

The characteristics of the conjugate natural convection of (Al2O3-water) nanofluid inside differentially heated enclosure is numerically analyzed using COMSOL Multiphysics (5.3a). The enclosure consists of two vertical walls, the left wall has a thickness and maintain at a uniform hot temperature, while the opposite wall at cold temperature and the horizontal walls are isolated. A high thermal conductivity thin baffle has been added on the insulated bottom wall at a different inclination angles. The effect of the volume fractions of nanoparticles (f), Rayleigh number (Ra), solid wall thermal conductivity ratio (Kr), baffle incline angles (Ø) and the thickness of solid wall (D) on the isothermal lines, fluid flow patterns and the average Nusselt number (Nu)  has been investigated. At low Rayleigh number (Ra=103 to 104) the Isothermal lines are parallel with the vertical wall which is characteristic of conduction heat transfer. on the other hand, when Rayleigh number increase to (Ra=106),  the isotherms lines distribution in the inner fluid become parallel curves with the adiabatic horizontal walls of the enclosure and smooth in this case convection heat transfer becomes dominant. As the Rayleigh number further increases, the average Nusselt number enhance because of buoyancy force become stronger. In addition, the fluid flow within the space is affected by the presence of a fin attached to the lower wall that causes blockage and obstruction of flow near the hot wall, hence the recirculation cores become weak and effect on the buoyant force. The maximum value of the stream function can be noticed in case of nanofluid at (Ø=60), whereas they decrease when (Ø > 60), where the baffle obstruction causing decreases in flow movement. So that the left region temperature increases which cause reduction of the convective heat transfer by the inner fluid temperatures. This is an indication of enhancing of insulation. When the inclination angle increases (Ø >90), the baffle obstruction on flow and fluid resistance becomes smaller and the buoyancy strength increase, as a result, the heat transfer is increasing in this case. As a result of increasing the thermal conductivity from 1 to 10, an increase in the amount of heat transferred through the solid wall to the internal fluid have been noticed. This change can be seen in the isothermal lines, also, there was growth and an increase in the temperature gradient. The increasing of wall thickness from (D=0.1 to 0.4) leads to reduce the intensive heating through the solid wall as well as small heat transferred to the inner fluid. Therefore, it can be noticed that when the wall thickness increases the stream function decrease.

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