Fin design for conjugate heat transfer optimization in double pipe

Abstract

Optimal design of longitudinal fins augmented to the outer surface of the inner pipe in a double pipe, is investigated for maximizing conjugate heat transfer coefficient. Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) has been used for fin-surface representation at each step of the optimization process with control points as the design variables. Genetic algorithm has been employed as the optimizer together with the Discontinuous Galarkin Finite Element Method (DG-FEM) as the solver of the governing equations. The results show that the optimal fin design is greatly influenced by the characteristic length, the number of fins, the conductivity of the material of heated surface and the number of control points. Optimal designs based on the equivalent diameter give upto 289% improvement in the heat transfer coefficient and those based on the hydraulic diameter render such improvement upto 70%. Optimal fin shape has also out-performed the conventional fin shapes present in the literature and shown upto 203%, 263% and 227% increase in the heat transfer coefficient relative to the equivalent diameter for trapezoidal, triangular and parabolic fins respectively. For the case of hydraulic diameter, these figures are respectively 482%, 70% and 117%. The optimal designs based on the equivalent diameter corresponding to Ω = 500 have proven to be the best in view of cost, frictional loss and heat transfer coefficient. These give upto 39% higher heat transfer coefficient than the corresponding increase in frictional loss due to augmentation of the fins to the double pipe. The validity and accuracy of the present results has been shown by comparison with the available literature results.