Non-uniform distribution of heat flux as a wall boundary condition is used for laminar developing pipe flow to find the optimum case in which minimum entropy is generated. Several cases are solved for the same amount of heat rate but with different heat flux distribution and entropy generation is determined for each one. It is shown that entropy generation in the cases with decreasing heat flux distribution is always more than the cases with the same amount of heat flux at sections but with increasing distribution. In addition, it is found that the generated entropy for the cases with decreasing heat flux distribution is always more than the case of uniform heat flux. It is also seen that the optimum case is not the case with uniform heat flux distribution and the least generated entropy is due to a case with increasing heat flux distribution. (C) 2010 Published by Elsevier Ltd.