The DOI matches its Crossref record.
A Unified Field Approach for Heat Conduction From Macro- to Micro-Scales
Abstract
A universal constitutive equation between the heat flux vector and the temperature gradient is proposed to cover the fundamental behaviors of diffusion (macroscopic in both space and time), wave (macroscopic in space but microscopic in time), phonon–electron interactions (microscopic in both space and time), and pure phonon scattering. The model is generalized from the dual-phase-lag concept accounting for the lagging behavior in the high-rate response. While the phase lag of the heat flux captures the small-scale response in time, the phase lag of the temperature gradient captures the small-scale response in space. The universal form of the energy equation facilitates identifications of the physical parameters governing the transition from one mechanism (such as diffusion or wave) to another (the phonon–electron interaction).
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Bonding mechanism in cold gas spraying
Assadi, H., Gärtner, F., Stoltenhoff, T., & Kreye, H. (2003) · Acta Materialia · doi:10.1016/s1359-6454(03)00274-x · Cited by 1,811
Development of a generalized parameter window for cold spray deposition
Schmidt, T., Gärtner, F., Assadi, H., & Kreye, H. (2006) · Acta Materialia · doi:10.1016/j.actamat.2005.10.005 · Cited by 1,183
Non-Fourier analysis of skin biothermomechanics
Xu, F., Seffen, K. A., & Lu, T. J. (2008) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2007.10.024 · Cited by 373
Metadata
- Authors
- Tzou, D. Y.
- Venue
- Journal of Heat Transfer
- Publisher
- ASME International
- Published
- 1995-02-01
- Volume
- 117
- Issue
- 1
- Pages
- 8-16
- ISSN
- 0022-1481 (ISSN-L)
- 1528-8943
- OpenAlex
- W2038940027
- Cited by
- 2,140
- References
- 0
- FWCI
- 10.09
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: A Unified Field Approach for Heat Conduction From Macro- to Micro-Scales. https://app.cochat.ai/papers/10.1115/1.2822329
- The paper
- Tzou, D. Y. (1995). A Unified Field Approach for Heat Conduction From Macro- to Micro-Scales. Journal of Heat Transfer. https://doi.org/10.1115/1.2822329
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
