Conjugate forced convection heat transfer in a plane channel: longitudinally periodic regime

The present paper studies the conjugate heat transfer problem in a parallel-plane channel. Laminar and stationary forced convection is studied, with a boundary condition given by a temperature distribution on the external side of the channel wall, which undergoes a sinusoidal longitudinal change. The local energy balance equation is written with reference to the fully developed region, where the temperature distribution can be expressed as a periodic function of the longitudinal coordinate. The temperature field in the solid wall and in the fluid, as well as the local and average Nusselt number, are determined analytically and numerically. A comparison between the values obtained analytically, by employing a complex temperature method, and those evaluated numerically, by employing a Bubnov–Galerkin finite element method, reveals an excellent agreement.