The relationship between maximum temperature and heating rate is determined for an internally heated flat plate, which is cooled on both sides by either forced or natural convection. Convection heat transfer is calculated using the energy integral boundary layer equations instead of solving governing partial differential equations numerically. The results are presented in simple analytical correlations. Solutions to a heated plate were used in the study of a plate fin with a uniform heat flux at the base in cases of forced and natural convection. New simple analytical equations for the maximum fin temperature were derived using the result on the heated plate. Solutions to a fin with uniform base heat flux include also those to a uniform fin base temperature as limiting cases. The validity of the simple new solutions to an internally heated plate and a fin with a uniform heat flux at the base were verified by comparing results to numerically obtained conjugated heat transfer solutions, analytical solutions, and to some experimental data for a heated plate. (C) 2016 Elsevier Ltd. All rights reserved.