Steady‐state temperature profiles in narrow thin‐film conductors

1985 ◽  
Vol 57 (3) ◽  
pp. 777-784 ◽  
Author(s):  
C. G. Shirley
Keyword(s):  
Thin Film ◽  
Steady State ◽  
Temperature Profiles ◽  
Steady State Temperature

Steady‐state temperature profile for a thin‐film resistor under bias

1992 ◽  
Vol 72 (9) ◽  
pp. 3862-3866 ◽  
Author(s):  
Roya Sabeti ◽  
E. M. Charlson ◽  
E. J. Charlson
Keyword(s):  
Thin Film ◽  
Steady State ◽  
Temperature Profile ◽  
Film Resistor ◽  
Thin Film Resistor ◽  
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.

scholarly journals On the Steady-State Temperature Rise During Laser Heating of Multilayer Thin Films in Optical Pump–Probe Techniques

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Jeffrey L. Braun ◽  
Chester J. Szwejkowski ◽  
Ashutosh Giri ◽  
Patrick E. Hopkins
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Thermal Conductivity ◽  
Steady State ◽  
Temperature Rise ◽  
Laser Heating ◽  
Thermal Parameters ◽  
Heat Diffusion ◽  
Multilayer Thin Films ◽  
Steady State Temperature

In this study, we calculate the steady-state temperature rise that results from laser heating of multilayer thin films using the heat diffusion equation. For time- and frequency-domain thermoreflectance (TDTR and FDTR) that rely on modulated laser sources, we decouple the modulated and steady-state temperature profiles to understand the conditions needed to achieve a single temperature approximation throughout the experimental volume, allowing for the estimation of spatially invariant thermal parameters within this volume. We consider low thermal conductivity materials, including amorphous silicon dioxide (a-SiO2), polymers, and disordered C60, to demonstrate that often-used analytical expressions fail to capture this temperature rise under realistic experimental conditions, such as when a thin-film metal transducer is used or when pump and probe spot sizes are significantly different. To validate these findings and demonstrate a practical approach to simultaneously calculate the steady-state temperature and extract thermal parameters in TDTR, we present an iterative algorithm for obtaining the steady-state temperature rise and measure the thermal conductivity and thermal boundary conductance of a-SiO2 with a 65-nm gold thin film transducer. Furthermore, we discuss methods of heat dissipation to include the use of conductive substrates as well as the use of bidirectional heat flow geometries. Finally, we quantify the influence of the optical penetration depth (OPD) on the steady-state temperature rise to reveal that only when the OPD approaches the characteristic length of the temperature decay does it alter the temperature profile relative to the surface heating condition.

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