Steady‐state temperature profiles in thermally thin substrates induced by arbitrarily shaped laser beams

1989 ◽  
Vol 66 (2) ◽  
pp. 488-491 ◽  
Author(s):  
K. Imen ◽  
J. Y. Lin ◽  
S. D. Allen
Keyword(s):  
Steady State ◽  
Laser Beams ◽  
Temperature Profiles ◽  
Steady State Temperature

scholarly journals On the crossing of intermediate unstable steady state solutions for thermal ignition in a sphere

2001 ◽  
Vol 43 (1) ◽  
pp. 77-85 ◽  
Author(s):  
R. O. Weber ◽  
G. C. Wake ◽  
H. S. Sidhu ◽  
G. N. Mercer ◽  
B. F. Gray ◽  
...  
Keyword(s):  
Steady State ◽  
Unit Sphere ◽  
Steady States ◽  
Temperature Profiles ◽  
Thermal Ignition ◽  
Unstable Steady State ◽  
Steady State Temperature ◽  
Parameter Values ◽  
Steady State Solutions ◽  
Unstable Intermediate

AbstractSteady state solutions for spontaneous thermal ignition in a unit sphere are considered. The multiplicity of unstable, intermediate, steady state, temperature profiles is calculated and shown for selected parameter values. The crossing of the temperature profiles corresponding to the unstable, intermediate, steady states is exhibited in a particular case and is proven in general using elementary ideas from analysis. Estimates of the location of crossing points are given.

scholarly journals Numerical studies on the Impact of the Last Glacial Cycle on recent borehole temperature profiles: implications for terrestrial energy balance

2014 ◽  
Vol 10 (5) ◽  
pp. 1693-1706 ◽  
Author(s):  
H. Beltrami ◽  
G. S. Matharoo ◽  
L. Tarasov ◽  
V. Rath ◽  
J. E. Smerdon
Keyword(s):  
Steady State ◽  
North America ◽  
Heat Content ◽  
Temperature Profiles ◽  
Glacial Cycle ◽  
Last Glacial ◽  
Steady State Temperature ◽  
Borehole Temperature ◽  
The Impact ◽  
The Last Glacial

Abstract. Reconstructions of past climatic changes from borehole temperature profiles are important independent estimates of temperature histories over the last millennium. There remain, however, multiple uncertainties in the interpretation of these data as climatic indicators and as estimates of the changes in the heat content of the continental subsurface due to long-term climatic change. One of these uncertainties is associated with the often ignored impact of the last glacial cycle (LGC) on the subsurface energy content, and on the estimate of the background quasi steady-state signal associated with the diffusion of accretionary energy from the Earth's interior. Here, we provide the first estimate of the impact of the development of the Laurentide ice sheet on the estimates of energy and temperature reconstructions from measurements of terrestrial borehole temperatures in North America. We use basal temperature values from the data-calibrated Memorial University of Newfoundland glacial systems model (MUN-GSM) to quantify the extent of the perturbation to estimated steady-state temperature profiles, and to derive spatial maps of the expected impacts on measured profiles over North America. Furthermore, we present quantitative estimates of the potential effects of temperature changes during the last glacial cycle on the borehole reconstructions over the last millennium for North America. The range of these possible impacts is estimated using synthetic basal temperatures for a period covering 120 ka to the present day that include the basal temperature history uncertainties from an ensemble of results from the calibrated numerical model. For all the locations, we find that within the depth ranges that are typical for available boreholes (≈600 m), the induced perturbations to the steady-state temperature profile are on the order of 10 mW m−2, decreasing with greater depths. Results indicate that site-specific heat content estimates over North America can differ by as much as 50%, if the energy contribution of the last glacial cycle in those areas of North America that experienced glaciation is not taken into account when estimating recent subsurface energy changes from borehole temperature data.

Transient Temperature Profiles in Tissues With Nonuniform Blood Flow Distributions

1982 ◽  
Vol 104 (3) ◽  
pp. 202-208 ◽  
Author(s):  
A. B. Elkowitz ◽  
A. Shitzer ◽  
R. C. Eberhart
Keyword(s):  
Heat Transfer ◽  
Blood Flow ◽  
Steady State ◽  
Flow Distribution ◽  
Tissue Blood Flow ◽  
Transient Temperature ◽  
Temperature Profiles ◽  
Heat Transfer Equation ◽  
Blood Flow Distribution ◽  
Steady State Temperature

Numerical methods and the bio-heat transfer equation are employed to calculate temperature profiles in tissues subjected to nonuniform blood flow distributions, for initial and boundary conditions which simulate experimental physiological situations. Results indicate that one can infer, from sudden changes in temperature distribution, the occurrence of sudden changes in tissue blood flow. However, prediction of blood flow distribution from near equilibrium or steady-state temperature profiles is of poor resolution, and does not appear useful as a practical technique. The methods and results are useful for predictions of temperature profiles in the absence of significant endogenous or exogenous heating; they can be extended to such applications by straightforward methods.

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