Constructal design of longitudinally finned tubes cooled by forced convection

Abstract

The 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 10 3 ≤ Be ≤ 10 5 . The fin length is changed from L f = 0 (unfinned tube) to L f = 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. K E Y W O R D SBejan number, constructal design, forced convection, longitudinally finned tubes

Constructal design of crossflow heat exchanger with concentric and eccentric circular fins

“…The finite volume method with SIMPLE algorithm is used to solve the three-dimensional governing Equations ( 7)- (11). These equations are firstly transformed from the physical domain of coordinates (X, Y, Z) to the computational domain of body-fitted coordinates (ζ, η, Z).…”

“…Other constructal designs for single and multiscale tubes and fins are found in Mustafa and colleagues. [7][8][9][10][11][12][13] On the other side, there were many numerical and experimental studies of heat exchangers with circular fins. Mon and Gross 14 investigated numerically the forced convection from a four-row heat exchanger with circular fins.…”

“…The presence of the smaller fins had a significant enhancement of the heat density. Other constructal designs for single and multiscale tubes and fins are found in Mustafa and colleagues 7–13 …”

Constructal design of vertical multiscale triangular fins in natural convection

“…It was shown that the optimal fins number occurred at ( N = 6) with angle between the fins (10°). Constructal design from single‐scale tubes with different shapes in forced and natural convections can be found in Mustafa and colleagues 10–14 . Constructal design of cavities can be seen in Lorenzini and colleagues 15,16 …”

“…Constructal design from singlescale tubes with different shapes in forced and natural convections can be found in Mustafa and colleagues. [10][11][12][13][14] Constructal design of cavities can be seen in Lorenzini and colleagues. 15,16 Several multiscale constructal designs for fins are exist in the literature.…”