Constructal multi scale cylinders with rotation cooled by natural convection

Abstract

In this paper we investigated the thermal behaviour of an assembly of multi scale cylinders in a staggered counterrotating configuration cooled by natural convection with the objective of maximizing the heat transfer density rate (heat transfer rate per unit volume). A numerical model was used to solve the governing equations that describe the temperature and flow fields and a mathematical optimisation algorithm was used to find the optimal structure for flow configurations with two degrees of freedom. The multi scale structure of the cylinder assembly was optimized for each flow regime (Rayleigh number) and cylinder rotation speed for two degrees of freedom. Smaller cylinders were placed at the entrance to the assembly, in the wedge-shaped flow regions occupied by fluid that had not yet been used for heat transfer, to create additional length scales to the flow configuration.It was found that there was almost no effect of cylinder rotation on the maximum heat transfer density rate, when compared to stationary cylinders, at each Rayleigh number; with the exception of high cylinder rotation speeds, which served to suppress the heat transfer density rate. It was, however, found that the optimized spacing decreased as the cylinder rotation speed was increased at each Rayleigh number. Results further show that the maximum heat transfer density rate for a multi scale configuration (without cylinder rotation) was higher than a single scale configuration (with rotating cylinders) with an exception at very low Rayleigh numbers.

Numerical investigation of the laminar natural convection heat transfer from two horizontally attached horizontal cylinders

“…Therefore, it is applied in present work and the detailed introduction will be presented in next section. Basing on the theory of the optimized heat transfer proposed by Bejan et al [42], BelloOchende et al performed the studies on optimizing the flow structures for single row of single-scale and multi-scale horizontal cylinders set in a horizontal array [43], and horizontal arrays of multi-scale cylinders in a staggered counter-rotating configuration [44]. They confirmed that when the thermal boundary layers of two consecutive cylinders just touch, the heat transfer density of single horizontal array of single-scale cylinders attains its maximum value.…”

Maximization of heat transfer density from a vertical array of flat tubes in cross flow under fixed pressure drop using constructal design

“…It was shown that the rate of heat transfer density can be maximized for all the studied Bejan numbers and all vertical axes of the tubes. Constructal designs from cyinders of different shapes cooled by natural convection can be found in refs . As a conclusion from the above references, the rate of heat transfer per unit volume from a vertical array in cross flow with different shapes of cylinder can be maximized under fixed pressure drop by using consturctal design.…”

Maximization of heat transfer density rate from a single row of rhombic tubes cooled by forced convection based on constructal design

“…They found that the optimal aspect ratio of the elliptic tubes decreases as Bejan number increases. Studies of constructal design for a row of cylinders immersed in non‐Newtonian fluids were carried out in Klein et al Constructal design from a row of single and multiscale circular cylinders cooled by natural convection can be found in Bello‐Ochende et al Constructal design for conduction heat transfer in solid wall with Y‐shaped cavities can be found in Lorenzini et al…”

“…They found that the optimal aspect ratio of the elliptic tubes decreases as Bejan number increases. Studies of constructal design for a row of cylinders immersed in non-Newtonian fluids were carried out in Klein et al [6][7][8] Constructal design from a row of single and multiscale circular cylinders cooled by natural convection can be found in Bello-Ochende et al [9][10][11] Constructal design for conduction heat transfer in solid wall with Y-shaped cavities can be found in Lorenzini et al 12 Away from the constructal design, there are many studies for convection heat transfer from a single row of cylinders. Yamamoto and Hattori 13 investigated the fluid and heat flow from a single row of circular cylinders in the Reynolds number range of 75 ≤ Re ≤ 500.…”