The quasi-steady assumption is commonly adopted in existing transient fluid–solid-coupled convection–conduction (conjugate) heat transfer simulations, which may cause non-negligible errors in certain casesof practical interest. In the present work, we adopt a new multi-scale framework for the fluid domainformulated in a triple-timing form. The slow-varying temporal gradient corresponding to the time scalesin the solid domain has been effectively included in the fluid equations as a source term, ...