Steady-State Component of Three-Dimensional Slab-on-Grade Foundation Heat Transfer

2000 ◽  
Vol 123 (1) ◽  
pp. 18-29 ◽  
Author(s):  
Pirawas Chuangchid ◽  
Moncef Krarti
Keyword(s):  
Steady State ◽  
Heat Loss ◽  
Parametric Analysis ◽  
Three Dimensional ◽  
Thermal Characteristics ◽  
U Value ◽  
Rectangular Slab ◽  
Steady State Heat ◽  
Profile Estimation ◽  
State Component

General semi-analytical solutions for the steady-state heat conduction problems for circular and three-dimensional rectangular slab-on-grade floors with uniform insulation are presented. The soil temperature field, and the total slab heat loss are presented and analyzed using the Interzone Temperature Profile Estimation (ITPE) technique. A parametric analysis is conducted to determine the effect of thermal insulation U-value, slab size, and water table depth on the total slab heat loss. In particular, it was found that the total slab heat loss is independent of its shape but is strongly affected by the slab size and thermal characteristics.

Steady-Periodic Three-Dimensional Foundation Heat Transfer From Refrigerated Structures

2000 ◽  
Vol 122 (2) ◽  
pp. 69-83 ◽  
Author(s):  
Pirawas Chuangchid ◽  
Moncef Krarti
Keyword(s):  
Heat Transfer ◽  
Parametric Analysis ◽  
Three Dimensional ◽  
Thermal Characteristics ◽  
Mean Amplitude ◽  
Phase Lag ◽  
Heat Gain ◽  
U Value ◽  
The Mean ◽  
Rectangular Slab

Analytical solutions for steady-periodic ground-coupled heat conduction problems for cylindrical and three-dimensional rectangular slab-on-grade floors beneath refrigerated structures with uniform and partial insulation are presented in this paper. The solutions provide the soil temperature field, and the total slab heat gain. A parametric analysis is conducted to determine the effect of thermal insulation U-value and insulation width on the mean, amplitude, and phase lag of total slab heat gain. In particular, it was found that the mean and the amplitude of the total slab heat gain are effectively independent of its shape but are strongly affected by the slab size and thermal characteristics. [S0199-6231(00)00502-5]

ITPE Technique Applications to Time-Varying Three-Dimensional Ground-Coupling Problems

1990 ◽  
Vol 112 (4) ◽  
pp. 849-856 ◽  
Author(s):  
M. Krarti ◽  
D. E. Claridge ◽  
J. F. Kreider
Keyword(s):  
Heat Loss ◽  
Parametric Analysis ◽  
Three Dimensional ◽  
Time Dependent ◽  
Time Varying ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Dimensional Model ◽  
Approximate Analytical Solutions ◽  
Profile Estimation

Approximate analytical solutions for the three-dimensional heat transfer between slab-on-grade floors and rectangular basements under steady-periodic conditions are developed using the Interzone Temperature Profile Estimation (ITPE) method. The slab-on-grade solution is the first analytical slab-on-grade solution that treats the presence of insulation on/under the floor, while the basement solution is the first analytical solution of the time-dependent three-dimensional problem for basements. Solutions are given for the temperature field and expressions are derived for the annual heat loss. Parametric analysis is used to emphasize the effect of geometric dimensions on the magnitude and phase of heat loss relative to ambient temperature. The results obtained are compared with those from the two-dimensional model, and the three-dimensional characteristics of heat flow from slabs and basements are examined.

Three-Dimensional, Steady-State Heat Conduction in Cylinders of General Anisotropic-Media

1979 ◽  
Vol 101 (3) ◽  
pp. 548-553 ◽  
Author(s):  
Y. P. Chang ◽  
K. C. Poon
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Fourier Transforms ◽  
Coupling Effect ◽  
Three Dimensional ◽  
Anisotropic Media ◽  
State Heat ◽  
Change Of Variables ◽  
Steady State Heat ◽  
Kummer's Equation

This paper provides the analytical solution of three-dimensional steady-state heat conduction in solid and hollow cylinders of general anisotropic-media. By the use of Fourier transforms and a change of variables the partial differential equation is reduced to Kummer’s equation. Some calculated results for a solid cylinder are shown and discussed. A parameter γ is found to represent the coupling effect of three-dimensional anisotropy. For small values of γ, an approximate solution is recommended. The inequality σ > 0 which was found in an earlier paper is further discussed.

Some Implications of Dundurs' Theorem for Thermoelastic Contact and Crack Problems

1980 ◽  
Vol 22 (5) ◽  
pp. 229-232 ◽  
Author(s):  
J. R. Barber
Keyword(s):  
Steady State ◽  
Thick Plate ◽  
Line Element ◽  
Three Dimensional ◽  
Contact Problems ◽  
Free Boundaries ◽  
Principal Curvatures ◽  
State Heat ◽  
Crack Problems ◽  
Steady State Heat

It is well known that a simply-connected isotropic elastic body in a state of plane strain and with traction-free boundaries remains free of stress if it is subject to steady-state heat conduction. A recent theorem due to Dundurs shows that in this state the curvature of any initially straight line element is proportional to the heat flux across the line element. A closely related three dimensional result is proved for the sum of the principal curvatures of planes parallel to the faces of an infinite thick plate. These results have certain implications for thermoelastic crack and contact problems. For example: (i) thermal distortion has no effect on the contact pressure distribution at an insulated interface or at an interface between two similar materials, (ii) the thermal stress in a cracked solid depends on the temperature field only through the value of a certain constant related to the average temperature difference across the crack, (iii) steady-state heat flow induces no stresses in an axisymmetric thick plate containing an external crack.

Experimental Measurements of Temperature Distribution in Three Dimensional Stacked Package

2007 ◽  
Author(s):  
Anand Desai ◽  
James Geer ◽  
Bahgat Sammakia
Keyword(s):  
Experimental Study ◽  
Heat Conduction ◽  
Steady State ◽  
Temperature Distribution ◽  
Numerical Model ◽  
Analytical Solution ◽  
Three Dimensional ◽  
Power Input ◽  
Experimental Measurements ◽  
Steady State Heat

This paper presents the results of an experimental study of steady state heat conduction in a three dimensional stack package. The temperatures are measured at different interfaces within the stacked package. Delphi devices are used in the experiment which enables controlled power input and surface temperature of the devices. The experiment is carried out for three different boundary conditions on the package. The power input in varied to study its effects. A numerical model is created to compare to the experimental results. The results are also compared with the analytical solution presented in Desai et al [5] and Geer et al [6]. The results indicate that the experimental, numerical and analytical solutions follow the same trend. The agreement between the experimental and numerical results improves when the lateral losses are taken into account.

Calculation of three-dimensional nearly singular boundary element integrals for steady-state heat conduction

2015 ◽  
Vol 60 ◽  
pp. 137-143 ◽  
Author(s):  
Guizhong Xie ◽  
Liangwen Wang ◽  
Jianming Zhang ◽  
Dehai Zhang ◽  
Hao Li ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Boundary Element ◽  
Three Dimensional ◽  
Singular Boundary ◽  
State Heat ◽  
Steady State Heat
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