Heat transfer enhancement based on single phase natural circulation loops
Introduction
Heat transfer enhancement has been remained one of the major topics in academic researches and industrial applications of heat transfer. It is well known that an enhancement technique in heat transfer may bring directly or indirectly benefits of smaller in size of equipment, less material consumption, lower cost, higher efficiency of energy systems, etc. In general, the enhancement techniques can be classified into active methods and passive methods for single phase convective heat transfer [1, 2]. The active methods need some external power supply to enhance the convective heat transfer rate, such as the mechanical aid, the pulsating jet flow, the interactions of dielectric fluid medium in electric field [3], Ferrofluid in magnetic field [4], etc. The usage of active methods is limited due to limitation of practical application and difficulty of external power supply in many cases [5]. The passive methods do not require any external power to enhance heat transfer but utilizes modified or extended surfaces for creating the turbulence or breaking the thermal boundary layer. Comparing with the active methods, the passive methods are routinely used in many industrial applications. However, the passive methods may generally increase the pumping power due to the increase of pressure drop of fluid flow after replacing smooth or flat surfaces with extended surfaces (finned, twisted, corrugated, etc.). Together with the emergence of new technique in enhancement of heat transfer, the studies on the mechanism and evaluation about those techniques have never been absent [6]. One of the representative theories is the constructal theory proposed by Bejan in about two decades ago [7]. The constructal theory as firstly applied to the conductive cooling of electronics, but now to problems in not only engineering but other branches of science [8,9]. The other theory of field synergy principle has been controversial since it was put forward [10,11]. In the following, we will not discuss these theories in detail in the present paper. However, it should be pointed out that the gap between the outputs from those theories and experiments still remains, even for the problems of single-phase conduction and convection.
It is well known that the heat transfer process for a single-phase fluid flow through a heated plate is dominated by heat conduction followed by Fourier's law and heat convection followed by Newton's cooling law if the radiant heat is ignored. In addition, the convective thermal resistance can be approximated by according to the boundary layer theory, where δt and λf are the thickness of thermal boundary layer and the thermal conductivity of fluid. Therefore, a dozen of heat transfer enhancement techniques are based on the principle of reducing the thickness of δt or disturbing its growth. The empirical Newton's cooling law says the heat flux nominated to the solid surface can be written as , where Tf is the bulk (or cross section averaged in a confined duct) fluid temperature out of the thermal boundary layer, Tw is the local solid surface temperature. The heat flux route for a surface type heat exchanger is that heat from bulk hot fluid side transfers through the thermal boundary layer of hot fluid, followed by the solid wall, then the thermal boundary layer of cold fluid, and finally the bulk cold fluid. One question may be raised is that if there is a short cut that can directly transfer heat from the bulk hot fluid side to the bulk cold fluid. In order to do that a simple rectangular natural circulation loop (NCL) was designed with one half in the hot fluid side and the remained half in the cold fluid side. The third fluid inside the loop can absorb heat from the side in the hot fluid and release it in the cold fluid through natural circulation. The natural circulation is started and maintained in the gravity field without extra power supply but driven by the hot and cold fluids themselves.
In the present paper, the influencing factors on the heat transfer performance of such a NCL were analyzed by numerical simulation, and a comparable model of the same shaped and sized copper fin was established. The equivalent heat transfer condition of the NCL with that of the copper fin, and its trend in minimization was discussed as well.
Section snippets
The model of NCL in heat transfer enhancement
The surface type heat exchangers for heat transfer between two streams of hot and cold fluids are routinely applied in various industries. Fig. 1 shows a simple counter current heat exchanger model with hot fluid flowing under a flat plate from right to left, and cold fluid above the plate flowing from left to right. If ignore the present of the NCL, the overall heat transfer coefficient U without taking into account the thermal resistance due to fouling can be given by,
Numerical model of NCL for heat transfer enhancement
In order to evaluate the heat transfer performance of a single phase NCL across a plate, a simplified model was assumed, which contains only one NCL in a horizontal plate, as shown in Fig. 2. The geometry structure consists of a horizontal plate, an upper half rectangular duct, a lower half rectangular duct and one natural circulation loop (NCL), of which one half U-bend in the upper duct and the other half in the lower duct. The hot fluid flows from the right to the left in the lower
Results and discussion
The circulating mass flow rate in the NCL is an important parameter for evaluating its performance of heat transfer, which depends mainly on the driving temperature difference between heating and cooling fluids, the geometric configuration of the NCL, the thermophysical properties of circulating fluid inside NCL, and flowing conditions outside NCL. In the following the influences of temperatures and flowrates of both heating and cooling fluids on the circulating mass flow rate were discussed.
Conclusion
A numerical heat transfer analysis was performed for a square single phase NCL embedded in a horizontal adiabatic plate with hot and cold air flowing in counter current at the bottom and top, respectively. An emphasis was given on the mechanism of heat transfer enhancement by using such a configuration. To this end, a same shaped and sized square loop copper fin was also numerically studied as the comparative counterpart. The results show that the heat transfer rate is lower for the NCL than
Declaration of Competing Interest
None.
Acknowledgements
This work is financially supported by the National Science Foundation of China (Grant no. 41672234 and 41574176)
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