Conjugate heat transfer in a plate - One surface at constant temperature and the other cooled by forced or natural convection

Simple analytical solutions for the steady-state total heat transfer rate are presented for a flat plate cooled on one surface by forced or natural convection while the other side remains at uniform temperature. These solutions are also used to determine the unknown interface temperature of the surface. The solutions are based on one-dimensional conduction in the plate and on the heat transfer coefficients of an isothermal surface. The results are compared with those in the literature combined with a brief discussion of the most relevant studies in the field. In addition, presented are also numerically calculated results that take into account two-dimensional conduction in the plate and the effect of non-uniform surface temperature on convection. The calculations show that the results are valid also for thick plates. The solution procedure proved very accurate and produced new simple results for engineering applications.