Abstarct: The study of flow and heat transfer within ducts has a long history. Today, the development of industry and the need for channels with more compactness than circular sections, has led researchers to do research in this context for channels with a polygonal cross section. In the meantime, studies have been conducted in the field of channels with an equilateral triangle, isosceles and right angles, using different methods including laboratory, numerical and analytical methods. The present study investigates heat and flow transfer within triangular channels with arbitrary angles for the first time by the Ritz method. In addition, in this study, for the first time, heat transfer within triangular channels with desired angles, considering the viscous dissipation, is investigated. One of the advantages of using Ritz method in the present study is that for different states of the triangular section, the boundary conditions are always satisfied. In solving heat transfer considering the effect of the viscous dissipation, Brinkmann number (Br) is used and its effect on temperature distribution is investigated. Generally, heat transfer in the presence of the viscous dissipation is divided into two parts: cooling case (wall temperature less than fluid temperature) and heating case (wall temperature more than fluid temperature). Poiseuille number and Nusselt number obtained from flow and heat transfer solution are presented as problem solving results in this study and compared with the results of previous studies, which show the appropriate accuracy of the Ritz analytical method. The maximum difference between the obtained results and the results of previous studies is 0.76% for the Poiseuille number in isosceles triangles and 0.4% in right triangles. Also, the maximum difference related to the Nusselt number in this comparison for the case Br = 0, in isosceles triangles equal to 0.8% and in right triangles is equal to 0.4 percent. Among all triangular sections, the equilateral triangle has the highest value of Poiseuille number, the highest value of Nusselt number in Br = 0 and heating mode and the lowest value of Nusselt number in cooling mode. For the case Br≠0, by increasing the value of Brinkmann number, the Nusselt number decreases, also as Brinkman number increases/ decreases to ±∞, the Nusselt number tends to zero.