Transient Heat Conduction in an Infinite Plate With a Transverse Circular Cylindrical Hole

1973 ◽  
Vol 95 (3) ◽  
pp. 414-416 ◽  
Author(s):  
C. D. Michalopoulos ◽  
J. J. Seco
Keyword(s):  
Heat Conduction ◽  
Temperature Distribution ◽  
Infinite Plate ◽  
Transient Heat Conduction ◽  
Cylindrical Hole ◽  
The Other ◽  
Graphical Form ◽  
Zero Temperature ◽  
Temperature Distributions ◽  
Axisymmetric Temperature

The flow of heat in an infinite plate with a transverse circular cylindrical hole is considered. The boundary conditions are zero temperature on the cylindrical surface and arbitrary but axisymmetric temperature distributions on the plane surfaces. The solution is obtained by means of Laplace and an unconventional Hankel transforms. Numerical results are given in graphical form for a plate with a step temperature distribution on one face and zero temperature on the other.

The Transient Temperature Distribution in a Slab Subject to Thermal Radiation

1965 ◽  
Vol 87 (1) ◽  
pp. 117-130 ◽  
Author(s):  
R. D. Zerkle ◽  
J. Edward Sunderland
Keyword(s):  
Temperature Distribution ◽  
Thermal Radiation ◽  
Radiant Heat ◽  
Analog Computer ◽  
Graphical Form ◽  
Transient Temperature ◽  
Transient Temperature Distribution ◽  
Temperature Distributions ◽  
Approximate Analytical Solutions ◽  
Wide Range

The transient, one-dimensional temperature distribution is determined for a slab, insulated on one face, and subjected to thermal radiation at the other face. The slab is initially at a uniform temperature and is assumed to be homogeneous, isotropic, and opaque; the physical properties are assumed to be independent of temperature. Transient temperature distributions for both heating and cooling situations are obtained by means of a thermal-electrical analog computer. A diode limiter circuit is used to simulate the nonlinear radiant heat flux. The transient temperature distributions are presented in a dimensionless, graphical form for a wide range of variables. Approximate analytical solutions are also given which complement and extend the solution charts over ranges of parameters not covered in the charts.

Analytic solutions of the temperature distribution in Blasius viscous flow problems

2002 ◽  
Vol 453 ◽  
pp. 411-425 ◽  
Author(s):  
SHIJUN LIAO ◽  
ANTONIO CAMPO
Keyword(s):  
Temperature Distribution ◽  
Viscous Flow ◽  
Infinite Plate ◽  
Analytic Solutions ◽  
Analytic Approximation ◽  
Plate Temperature ◽  
Flow Problems ◽  
Temperature Distributions ◽  
Homotopy Analysis ◽  
Constant Coefficients

We apply a new analytic technique, namely the homotopy analysis method, to give an analytic approximation of temperature distributions for a laminar viscous flow over a semi-infinite plate. An explicit analytic solution of the temperature distributions is obtained in general cases and recurrence formulae of the corresponding constant coefficients are given. In the cases of constant plate temperature distribution and constant plate heat flux, the first-order derivative of the temperature on the plate at the 30th order of approximation is given. The convergence regions of these two formulae are greatly enlarged by the Padé technique. They agree well with numerical results in a very large region of Prandtl number 1[les ]Pr[les ]50 and therefore can be applied without interpolations.

Transient Heat Transfer Analysis of Alloy Solidification

1973 ◽  
Vol 95 (3) ◽  
pp. 324-331 ◽  
Author(s):  
J. C. Muehlbauer ◽  
J. D. Hatcher ◽  
D. W. Lyons ◽  
J. E. Sunderland
Keyword(s):  
Temperature Distribution ◽  
Eutectic Composition ◽  
Approximate Solutions ◽  
The Other ◽  
Heat Transfer Analysis ◽  
Uniform Temperature ◽  
One Dimensional ◽  
Temperature Distributions ◽  
Finite Slab ◽  
Good Agreement

Approximate solutions are obtained for the temperature distribution and rate of phase change for the transient one-dimensional solidification of a finite slab of a binary alloy. The alloy is selected to avoid the eutectic composition so that solidification takes place over a range of temperatures. The slab is initially superheated and has a uniform temperature distribution. Solidification occurs after one surface is cooled by convection while the other surface is insulated. Temperature distributions are determined analytically and experimentally and are in reasonably good agreement.

scholarly journals Analysis of temperature distribution in a pipe with inner mineral deposit

2014 ◽  
Vol 35 (2) ◽  
pp. 37-49
Author(s):  
Magda Joachimiak ◽  
Michał Ciałkowski ◽  
Jarosław Bartoszewicz
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Heat Conduction ◽  
Temperature Distribution ◽  
Mineral Deposit ◽  
Mineral Deposits ◽  
Heat Conduction Coefficient ◽  
Temperature Distributions

Abstract The paper presents the results of calculations related to determination of temperature distributions in a steel pipe of a heat exchanger taking into account inner mineral deposits. Calculations have been carried out for silicate-based scale being characterized by a low heat transfer coefficient. Deposits of the lowest values of heat conduction coefficient are particularly impactful on the strength of thermally loaded elements. In the analysis the location of the thermocouple and the imperfection of its installation were taken into account. The paper presents the influence of determination accuracy of the heat flux on the pipe external wall on temperature distribution. The influence of the heat flux disturbance value on the thickness of deposit has also been analyzed.

Solutions of Heat-Conduction Problems With Nonseparable Domains

1963 ◽  
Vol 30 (4) ◽  
pp. 493-499 ◽  
Author(s):  
Daniel Dicker ◽  
M. B. Friedman
Keyword(s):  
Heat Conduction ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Transient Heat Conduction ◽  
Steady State Solution ◽  
Zero Temperature ◽  
Rapid Convergence ◽  
Curved Boundaries ◽  
Convex Quadrilateral ◽  
The One

A method is presented for obtaining eigenfunctions of and solutions to the transient heat-conduction equation for a wide class of three-dimensional convex hexahedral domains and two-dimensional convex quadrilateral domains having straight or curved boundaries for which separation of variables cannot be applied. The method is employed to solve for the temperature distribution in a trapezoidal domain, initially at zero temperature, the boundaries of which are subjected to suddenly applied values at the initial instant. The solution is obtained in the form of a series and an examination of successive terms indicates fairly rapid convergence; it is found that the one-term solution yields almost as good values as a four-term solution, which is significant since the former is obtained with little effort. An independent method is utilized for obtaining the steady-state solution, i.e., t → ∞, and it is found that all approximations by the former method are substantially equal to the correct value for this case.

Unsteady Surface Element Method

1981 ◽  
Vol 103 (4) ◽  
pp. 759-764 ◽  
Author(s):  
N. R. Keltner ◽  
J. V. Beck
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Finite Difference ◽  
Transient Heat Conduction ◽  
The Other ◽  
Surface Element ◽  
Contact Conductance ◽  
The Given ◽  
Duhamel’S Integral ◽  
Element Method

A method for the solution of transient heat conduction problems, called the unsteady surface element (USE) method, is developed and applied to several problems. The method is intended for thermally contacting bodies of similar or dissimilar geometries such as occur in contact conductance and intrinsic thermocouple problems. The method utilizes Duhamel’s integral in several ways. Two different procedures are presented, one utilizing temperature-based kernels and the other uses heat flux-based kernels. One of the given applications is to the intrinsic thermocouple problem. Several solutions are given and the results agree very well with two finite difference solutions.

Radial–Axial Transient Heat Conduction in a Region Bounded Internally by a Circular Cylinder of Finite Length and Appreciable Heat Capacity

1973 ◽  
Vol 51 (11) ◽  
pp. 1182-1186 ◽  
Author(s):  
W. T. Kierkus ◽  
N. Mani ◽  
J. E. S. Venart
Keyword(s):  
Heat Capacity ◽  
Heat Conduction ◽  
Circular Cylinder ◽  
Finite Length ◽  
Transient Heat Conduction ◽  
Zero Temperature ◽  
Transient Hot Wire ◽  
Hot Wire ◽  
Wire Method ◽  
Long Cylinder

The problem of two-dimensional transient heat conduction from a circular cylinder of finite length and appreciable heat capacity has been solved using a Laplace transformation with respect to time and a finite Fourier sine transformation with respect to the axial variable. A case of constant surface heat flux with the ends of the cylinder maintained at zero temperature is considered. The solution, valid for all values of time, is compared with that of Jaeger for the infinitely long cylinder. The results are of use in the evaluation of heat losses for the transient hot-wire method of determining the thermal conductivity of fluids.

scholarly journals Discontinuities in an axisymmetric generalized thermoelastic problem

2005 ◽  
Vol 2005 (7) ◽  
pp. 1015-1029 ◽  
Author(s):  
Moncef Aouadi
Keyword(s):  
Temperature Distribution ◽  
Shear Wave ◽  
Inversion Formula ◽  
Fourier Expansion ◽  
Thick Plate ◽  
Hankel Transform ◽  
The Other ◽  
Stress Fields ◽  
Generalized Thermoelastic ◽  
Axisymmetric Temperature

This paper deals with discontinuities analysis in the temperature, displacement, and stress fields of a thick plate whose lower and upper surfaces are traction-free and subjected to a given axisymmetric temperature distribution. The analysis is carried out under three thermoelastic theories. Potential functions together with Laplace and Hankel transform techniques are used to derive the solution in the transformed domain. Exact expressions for the magnitude of discontinuities are computed by using an exact method developed by Boley (1962). It is found that there exist two coupled waves, one of which is elastic and the other is thermal, both propagating with finite speeds with exponential attenuation, and a third which is called shear wave, propagating with constant speed but with no exponential attenuation. The Hankel transforms are inverted analytically. The inversion of the Laplace transforms is carried out using the inversion formula of the transform together with Fourier expansion techniques. Numerical results are presented graphically along with a comparison of the three theories of thermoelasticity.

TRANSIENT HEAT CONDUCTION IN ANISOTROPIC SOLIDS

1974 ◽  
Author(s):  
Kozo Katayama ◽  
Akio Saito ◽  
Nariyoshi Kobayashi
Keyword(s):  
Heat Conduction ◽  
Transient Heat Conduction
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