Use of the method of manufactured solutions for the verification of conjugate heat transfer solvers

Abstract

This paper demonstrates the use of the method of manufactured solutions to verify the implementation of tightly coupled conjugate heat transfer for fluid-solid solvers. The interface conditions in the prescribed manufactured solutions were implemented to mimic real effects such as no-slip, and temperature/heat flux match between the solid and fluid domains. The newly developed solid heat transfer solver was verified in standalone mode using this prescribed manufactured solution and was found to have no apparent coding errors. Our pre-existing in-house compressible fluid solver (Eilmer) was used to demonstrate the conjugate heat transfer implementation. Both the fluid and solid solvers showed an expected spatial order of convergence of 2.0 in the standalone mode. The coupled conjugate heat transfer mode also showed no coding errors and demonstrated that the spatial order of convergence was again 2.0. The one-sided spatial discretisation utilised to enforce the tight coupling for the interface conditions were effectively equivalent to a central difference. Hence, the overall spatial order of the error convergence for the entire domain, including the interface, was 2.0. The method prescribed in this work can be extended for verification of other conjugate heat transfer solvers, in particular for compressible flow scenarios where analytical solutions may not be readily available.