Constructal design of longitudinally finned tubes cooled by forced convection

AbstractThe constructal design method is used in the present study to find the configuration of longitudinally finned tubes cooled by forced convection. The finned tubes are arranged in parallel inside a fixed two‐dimensional domain. Two degrees of freedom inside the domain are considered for the design. The first degree of freedom is the tube‐to‐tube spacing, and the second is the length of the longitudinal fin. For both these degrees of freedom, a three‐fin position inside the domain is considered. The fin is placed in the front, back, and front and back of the tube in the first, second, and third positions, respectively. Maximization of the heat flow density (heat transfer/volume) from the finned tubes to the cold cross flow is the objective function of the present study. For the three fin positions, the constant pressure difference between the upstream and the downstream drives the cross flow. The dimensionless continuity, momentum, and energy equations for two dimensional, steady, and incompressible flows are solved by discretizing it according to the finite volume method. The thermal condition of the fins and the tubes is constant surface temperature. The dimensionless pressure drop known as Bejan number is varied in the range of 103 ≤ Be ≤ 105. The fin length is changed from Lf = 0 (unfinned tube) to Lf = 0.2, 0.4, and 0.4. The tubes are cooled by air (Prandtl number = 0.71). The results illustrated that for the considered Bejan numbers and fin positions, the spacing between the unfinned and the finned tubes can be adjusted to optimal spacing such that the heat flow from the tubes to the coolant is maximum.