A first-order fluid is another name for a power-law fluid with exponential dependence of viscosity on temperature.

${\displaystyle \mu _{\mathrm {eff} }({\dot {\gamma }},T)=\mu _{0}{\dot {\gamma }}^{n-1}\exp(-bT)}$

where γ̇ is the shear rate, T is temperature and μ₀, n and b are coefficients.

The model can be re-written as

${\displaystyle \mu _{\mathrm {eff} }({\dot {\gamma }},T)=\exp \left(A_{0}+A_{1}\ln {\dot {\gamma }}+A_{2}T\right)}$