Field synergy principle for enhancing convective heat transfer––its extension and numerical verifications

doi:10.1016/S0017-9310(02)00097-2

International Journal of Heat and Mass Transfer

Volume 45, Issue 18, August 2002, Pages 3849-3856

https://doi.org/10.1016/S0017-9310(02)00097-2 Get rights and content

Abstract

The concept of enhancing parabolic convective heat transfer by reducing the intersection angle between velocity and temperature gradient is reviewed and extended to elliptic fluid flow and heat transfer situation. Five examples of elliptic flow are provided to show the validity of the new concept (field synergy principle). Two further examples are supplemented to demonstrate the importance of the concept in the design of the enhanced surfaces.

Introduction

The enhancement of convective heat transfer is an everlasting subject for both the researchers of heat transfer community of academia and the technicians in industry. Numerous investigations, both experimental and numerical have been conducted and great achievements have been obtained [1], [2], [3], [4], [5]. However, there is no unified theory which can reveal the essence of heat transfer enhancement common to all enhancement methods. In 1998, Guo and his co-workers proposed a novel concept for enhancing convective heat transfer of parabolic flow [6], [7], the reduction of the intersection angle between velocity and temperature gradient can effectively enhance convective heat transfer. The purpose of this paper are threefold: the major idea of this novel concept will be extended to the general elliptic fluid flow and heat transfer; the numerical example will be provided to show the correctness of this new idea; and some examples of application will be provided to show the importance of this new concept.

Guos' proposal [6], [7] will be briefly reviewed here. For two-dimensional (2-D) boundary layer flow and heat transfer along a plate with a temperature different from the oncoming flow, the energy equation takes following form: $ρc_{p} u ∂ T ∂ x +v ∂ T ∂ y = ∂ ∂ y k ∂ T ∂ y$ Integrating above equation along the thermal boundary layer and notice that at the outer edge of the thermal boundary layer (∂T/∂y)_{y=δ_t}=0, we have $ρc_{p} ∫^{δ_{t}}_{0} (U → · grad T) d y=− k ∂ T ∂ y_{y=0} =q_{w}$ The convective term has been transformed to the dot product form of the velocity vector and the temperature gradient, and the right-hand side is the heat flux between the solid wall and the fluid, i.e., the convective heat transfer rate. The dot product $(U → · grad T)=| U → || grad T| cos θ$ , where θ is the intersection angle between velocity and temperature gradient. It is obvious that for a fixed flow rate and temperature difference, the smaller the intersection angle between the velocity and the temperature gradient, the larger the heat transfer rate. That is, the reduction of the intersection angle will increase the convective heat transfer. According to the Webster Dictionary [8], when several actions or forces are cooperative or combined, such situation can be called “synergy”. Thus, this idea introduced for enhancing convective heat transfer focuses on the synergy between velocity and temperature gradient and will be hereafter called “field synergy principle”.

Section snippets

Extension of the field synergy principle to elliptic flow cases

Most convective heat transfer problems encountered in engineering are of elliptic type, and hence, extending the “field synergy principle” to elliptic cases will be of great importance.

Consider a typical elliptic convective heat transfer case—fluid flow and heat transfer over a backward step, as shown in Fig. 1. The solid walls are of constant temperature T_w, and fluid with temperature T_f flows into the domain. The 2-D energy equation for this case can be written as $ρc_{p} u ∂ T ∂ x +v ∂ T ∂ y = ∂ ∂ x k ∂ T ∂ x + ∂ ∂ y k ∂ T$

Primary verifications

For more than 10 heat transfer surfaces, numerical computations were carried out to obtain the integral of $∫∫_{Ω} ρc_{p} (U → · grad T) d A$ over the whole computation domain and the average Nusselt number for the configuration studied. For the simplicity of presentation, the integral will be represented by “Int” and the numerical results of five cases are provided. All computations were conducted by finite volume method, with SIMPLE algorithm to deal with the linkage between velocity and pressure. The

Applying field synergy principle to develop new heat transfer surfaces

Probably the most challenging task of developing the field synergy principle is to design enhanced heat transfer surfaces at the guidance of the principle. Such work is now underway in the authors' group. Some computational results are presented for illustration.

Conclusions

In this paper, the new concept “field synergy principle” proposed firstly in [6], [7] is extended from parabolic flow to elliptic flow. According to this principle, the convective heat transfer can be enhanced by reducing the intersection angle between the velocity and the temperature gradient. Several numerical examples are provided to show the validity of the principle.

Acknowledgements

This work was supported by the National Fundamental R&D Project of China (Grant number 2000026303). The authors are grateful to Mr. Z.G. Qu, X. Liu, F.Q. Song, Ms. X. Wang, and M.X. Li, for carrying out some numerical computations.

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View full text

Field synergy principle for enhancing convective heat transfer––its extension and numerical verifications

Abstract

Introduction

Section snippets

Extension of the field synergy principle to elliptic flow cases

Primary verifications

Applying field synergy principle to develop new heat transfer surfaces

Conclusions

Acknowledgements

Int. J. Heat Mass Transfer

Heat transfer enhancement—the maturing of the second-generation heat transfer technology

Heat Transfer Engineering

Heat transfer enhancement—the encouragement and accommodation of high heat fluxes

ASME J. Heat Transfer

Techniques to enhance heat transfer

Enhanced heat transfer: endless frontier, or mature and routine?

Enhanced Heat Transfer