The One-Dimensional Analysis of Oscillatory Heat Transfer in a Fin Assembly

1992 ◽  
Vol 114 (3) ◽  
pp. 548-552 ◽  
Author(s):  
J. M. Houghton ◽  
D. B. Ingham ◽  
P. J. Heggs
Keyword(s):  
Heat Transfer ◽  
Thermal Effects ◽  
Transient Heat Transfer ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Extended Surface ◽  
Extended Surfaces ◽  
The One ◽  
Physical Boundary ◽  
Surface Heat Exchanger

Studies of the transient heat transfer within extended surfaces have so far considered the fins in isolation. The isolated fin model is not representative of the physical boundary conditions within an extended surface heat exchanger since it does not account for the thermal effects of the supporting interface. The aim of this study is to extend the work on transient heat transfer within finned surfaces by incorporating the supporting wall in the problem. A mathematical one-dimensional solution for harmonic oscillatory heat transfer in a fin assembly is derived. It is concluded that, unlike steady-state situations, the transient heat transfer in a fin assembly can only be found by considering both the wall and the fins simultaneously.

Two-Dimensional Analysis of Conduction-Controlled Rewetting With Precursory Cooling

1976 ◽  
Vol 98 (3) ◽  
pp. 407-413 ◽  
Author(s):  
S. S. Dua ◽  
C. L. Tien
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Dimensional Analysis ◽  
Vertical Surface ◽  
Dimensionless Temperature ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
One Dimensional ◽  
The One

This paper presents a two-dimensional analysis of the effect of precursory cooling on conduction-controlled rewetting of a vertical surface, whose initial temperature is higher than the sputtering temperature. Precursory cooling refers to the cooling caused by the droplet-vapor mixture in the region immediately ahead of the wet front, and is described mathematically by two dimensionless constants which characterize its magnitude and the region of influence. The physical model developed to account for precursory cooling consists of an infinitely extended vertical surface with the dry region ahead of the wet front characterized by an exponentially decaying heat flux and the wet region behind the moving film-front associated with a constant heat transfer coefficient. Apart from the two dimensionless constants describing the extent of precursory cooling, the physical problem is characterized by three dimensionless groups: the Peclet number or the dimensionless wetting velocity, the Biot number and a dimensionless temperature. Limiting solutions for large and small Peclet numbers have been obtained utilizing the Wiener-Hopf technique coupled with appropriate kernel substitutions. A semiempirical matching relation is then devised for the entire range of Peclet numbers. Existing experimental data with variable flow rates at atmospheric pressure are very closely correlated by the present model. Finally a comparison is drawn between the one-dimensional limit of the present analysis and the corresponding one-dimensional solution obtained by treating the dry region ahead of the wet front characterized by an exponentially decaying heat transfer coefficient.

scholarly journals Some numerical experiments on firn ventilation with heat transfer

1993 ◽  
Vol 18 ◽  
pp. 161-165 ◽  
Author(s):  
M.R. Albert
Keyword(s):  
Heat Transfer ◽  
Surface Pressure ◽  
Thermal Effects ◽  
Numerical Experiments ◽  
Temperature Gradients ◽  
Pressure Amplitude ◽  
Two Dimensional ◽  
One Dimensional ◽  
Thermal Signature ◽  
Spatially Varying

Preliminary estimates of the thermal signature of ventilation in polar firn are obtained from two-dimensional numerical calculations. The simulations show that spatially varying surface pressure can induce airflow velocities of 10−5m s−1at 1.5 m depth in uniform firn, and higher velocities closer to the surface. The two-dimensional heat-transfer results generally agree with our earlier one-dimensional conclusions that the thermal effects of ventilation tend to decrease the temperature gradient in the top portions of the pack. Field observations of ventilation through temperature measurements are most likely to be observed when the firn temperature at depths on the order of 10 m is close to the air temperature, since steep temperature gradients can mask the thermal effects of ventilation. Preliminary indications are that, as long as surface-pressure amplitude is sufficient to move the air about in the top tens of centimeters in the snow, the resulting temperature profile during ventilation is fairly insensitive to the frequency of the surface-pressure forcing for pressure frequencies in the range 0.1–10.0 Hz.

scholarly journals One-Phase Problems for Discontinuous Heat Transfer in Fractal Media

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Ming-Sheng Hu ◽  
Dumitru Baleanu ◽  
Xiao-Jun Yang
Keyword(s):  
Heat Transfer ◽  
Differential Operator ◽  
Transient Heat Transfer ◽  
Fractal Models ◽  
Fractal Media ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
The One

We first propose the fractal models for the one-phase problems of discontinuous transient heat transfer. The models are taken in sense of local fractional differential operator and used to describe the (dimensionless) melting of fractal solid semi-infinite materials initially at their melt temperatures.

First Paper: A General Approach to Hydraulic Lock

1967 ◽  
Vol 182 (1) ◽  
pp. 595-602 ◽  
Author(s):  
P. Dransfield ◽  
D. M. Bruce ◽  
M. Wadsworth
Keyword(s):  
Reynolds Equation ◽  
Lateral Force ◽  
Hydraulic Control ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Particular Solutions ◽  
Piston Cylinder ◽  
The One ◽  
Hydraulic Control System ◽  
General Method

The present state of knowledge on the hydraulic lock phenomena of oil hydraulic control system components is reviewed briefly. A general one-dimensional solution of the Reynolds equation which governs hydraulic lock is presented. The solution embraces the particular solutions of past workers, and allows ready solution for piston-cylinder configurations for which a one-dimensional solution is adequate. A general method for making full solutions of the Reynolds equation is presented, requiring the use of a digital computer for particular solutions. Pressure distribution, the lateral force on the piston which produces hydraulic lock, and the location of the lateral force can be obtained. The commonly occurring case of a single-land piston lying tilted in its bore is examined in detail. The limit of accuracy of a one-dimensional solution is clearly shown by illustrating the discrepancies between the one-dimensional and two-dimensional solutions for several configurations.

On the Transiant Response of Convective Extended Surface Heat Transfer: A New Approach

2006 ◽  
Author(s):  
P. Razelos ◽  
G. Michalakeas
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Transient Response ◽  
Surface Heat ◽  
Constant Thickness ◽  
Conduction Model ◽  
Steady State Condition ◽  
Surface Heat Transfer ◽  
Extended Surface ◽  
Extended Surfaces

This work is devoted to the study of the extended surfaces transient response. Although, the steady-state fin analysis has attracted considerable attention for a very long time, the interest in the transient response started in the last quarter of the past century. Several publications have appeared since, either analytical using the 1-D, conduction model, or experimental. Perusing the pertinent literature, however, we have observed that, in all previous published papers the authors treat the transient response of extended surfaces, or fins, like regular solids. However, fin endeavors rest on certain fundamental concepts, leading to some simplified assumptions, that we shall briefly discuss in the next section, which allows using the 1-D conduction model, and affect their steady-state operation. Therefore, the need for re-examining and revising the previously used methods becomes apparent. However, the authors are indebted to the pioneer workers on this topic that opened new avenues in the field of extended surface heat transfer. The aim of this work is to offer a different point of view to this problem, by introducing a new spatial coordinate system, and a new time scale. The solutions presented here, rest on the previously mentioned certain fundamental concepts developed recently. In the following we show step by step, how the existing pertinent equations and formulas of fins' transient response, are transformed to new simpler forms, expressed in terms of more appropriate dimensionless parameters, in accord with those appearing in recent publications. In the following, we confine to the analysis of constant thickness longitudinal and pin fins subject to specific1 boundary conditions. Each case is accompanied with an example that, for reasons of comparison are taken from the literature. We also discuss what is meant by "the time required for transient response to attain the steady-state condition."

Fundamental Concepts and an Innovating Approach for Extended Surface Heat Transfer

2005 ◽  
Author(s):  
Panagiotis Razelos
Keyword(s):  
Heat Transfer ◽  
Heat Dissipation ◽  
Vital Role ◽  
Surface Heat ◽  
Surface Heat Transfer ◽  
Novel Approach ◽  
Mathematical Expressions ◽  
Extended Surface ◽  
Simplifying Assumptions ◽  
The One

In this work we re-examine the main fin equation qf = ηfAfΔT, proposed by Gardner [1] that has been used for the last sixty years to determine the performance of fins. The fundamental concepts of extended surface heat transfer are introduced, and their mathematical expressions are derived. The vital role of fin effectiveness, a term also introduced by Gardner [1] is established. It is shown that the effectiveness is inextricably linked in proving the validity of the simplifying assumptions that most of the fins’ endeavors are based on. It is also shown that the common practice of using the efficiency to predict the fin’s performance leads to serious errors. A novel approach to fin analysis, based on a proposed transformation of coordinates, is presented, which can be employed to considerably simplify the pertinent differential equations and obtain more friendly expressions describing the fin’s performance. The heat dissipation is expressed in a non-dimensional form and for several practical cases polynomial expressions have developed, that will help students to engage in rudimentary fin designs. It is also shown that, the one-dimensional approach can be used to obtain solutions involving extended surfaces made from anisotropic material. Three examples serve to illustrate the usefulness of our method.

Applicability of One-Dimensional Transient Solutions for Ground-Coupled Heat Transfer in Buildings

2013 ◽  
Vol 361-363 ◽  
pp. 386-390 ◽  
Author(s):  
J Daniel Mena Baladés ◽  
Ismael Rodríguez Maestre ◽  
Pascual Álvarez Gómez ◽  
J. Luis Foncubierta Blázquez
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Finite Element Software ◽  
Coupled Heat Transfer ◽  
Transient Solutions ◽  
Detailed Simulation ◽  
Different Dimensions ◽  
Multidimensional Effects

The ground-coupled heat transfer in buildings is a complex, transient and multidimensional problem. There have been many studies focused to obtain the heat flux in slab and basement foundations. Most of them include the multidimensional effects occur at the perimeter however there are situations in which the heat transfer is mainly one-dimensional. This paper presents a study that aims to establish the accurate of an analytical one-dimensional solution to estimate the ground-coupled heat transfer. Detailed simulation by using finite element software is used to obtain the total heat flux at indoor surface of the building for a whole year. Typical slabs and basements foundations for different dimensions have been analyzed. A correlation to estimate the relative error is proposed.

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