This paper considers transient conjugate heat transfer in the matrix of a thermal regenerator. Analysis is presented for the two-dimensional temperature fields in the fluid and solid for both laminar and turbulent flows. The independent governing parameters were identified and the equations were solved using finite-difference techniques. Results were obtained for a selected range of parameters. The range of parameters was identified wherein conjugate heat transfer and two-dimensional effects are significant. The results showed that the role of conjugate heat transfer is insignificant for flow through wide channels (γ≥2). © 1988 Taylor 8 Francis Group, LLC.