The heat transfer through exponential fins in movement and under the influence of heat generation (absorption) is the fundamental subject of the present paper. Obtaining exact formulas for the thermal features like the distribution of temperature as well as the efficiency of exponential fins is the main target. As a consequence of the current research, combined effects of the Peclet number due to the fin movement, and of the heat generation parameter due to the presence of a heat source on the efficiency of exponential fins versus rectangular fins can be analyzed and compared. Better fin efficiency anticipated for growing type of exponential fins provides practical advantages for the designing engineers. Moreover, simulation of more complex phenomena using modern numerical schemes can be tested by the presented closed-form formulae. (C) 2017 Elsevier Ltd. All rights reserved.