The rate of heat flow through a flat vertical wall due to conjugate heat transfer

Free convection along both sides of a vertical flat plate is studied within the framework of the laminar boundary-layer theory and for the case where only the temperature of the fluid far away from the wall is prescribed. Corrections to the Pohlhausen solution for the temperature at the plate surface are calculated. It is found that for good thermal conductors, the corrections are small (within a few percent), while for poor thermal conductors the corrections may be substantial (∼30% for a wall with conductivity similar to brick). In addition, expressions for the heat transfer coefficient h as well as for the Nusselt number are derived and the corresponding convective heat transfer rate is determined.