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A first-order fluid is another name for a power-law fluid with exponential dependence of viscosity on temperature.
![{\displaystyle \mu _{\mathrm {eff} }({\dot {\gamma }},T)=\mu _{0}{\dot {\gamma }}^{n-1}\exp(-bT)}](https://backend.710302.xyz/https/wikimedia.org/api/rest_v1/media/math/render/svg/017e115db562574c6992b4e4c68014835df40baf)
where γ̇ is the shear rate, T is temperature and μ0, n and b are coefficients.
The model can be re-written as
![{\displaystyle \mu _{\mathrm {eff} }({\dot {\gamma }},T)=\exp \left(A_{0}+A_{1}\ln {\dot {\gamma }}+A_{2}T\right)}](https://backend.710302.xyz/https/wikimedia.org/api/rest_v1/media/math/render/svg/fde64ca0d628c6ad66c9870923c10246490813dd)