Theoretical study on impingement heat transfer with single-phase free-surface slot jets
Introduction
Impinging jets have been widely used in industrial cooling or heating processes as a means of providing very high heat and mass transfer rates. In most cases air is employed as a working medium in jet impingement and a large amount of research on impinging air jets has been reported [1], [2]. Recently, more attention has been directed to the study of liquid jet impingement as the heat transfer rates can be increased several orders of magnitude in comparison with that of gas jets. Research on liquid jets was stimulated by their possible application to the cooling of heat engines [3], [4] or electronic devices [5], [6], [7], as well as in the thermal treatment of metals [8], [9].
Two principal jet configurations are relevant to the application of jet impingements: circular jets and slot jets, but for which flow and heat transfer mechanics are distinctly different. A significant amount of research has been published on the heat and mass transfer with circular impinging jets [1], [2], [10], [11]. Recently, however studies of heat and mass transfer with slot jet impingement have attracted more attention from scientists and engineers. Slot jet impingement becomes remarkable as it offers more beneficial features, such as higher cooling effectiveness, greater uniformity and more controllability. All these factors are suitable to countering the trend of continuously increasing heat flux and decreasing dimensions in compact electronics packages [12], [13], [14], [15], [16].
Schwarz [14] presented measurements and an analysis on the flow characteristics of two-dimensional jet impingement, but only for the turbulent wall-jet zone. Kendoush [15] studied the heat and mass transfer mechanics of an impinging slot jet by means of boundary-layer theory for laminar flow. The results were restricted just to the stagnation zone. Park [16] and Chiriac [17] reported the numerical solutions of stream and heat transfers in stagnation and wall jet zones for laminar flow, respectively, whereas the solutions to the confined slot jets were available only for a limited range of Reynolds numbers. The objective of the present study is to provide detailed theoretical solutions on laminar flow for free-surface slot jet impinging onto horizontal surfaces under arbitrary-heat-flux conditions. The influence of Prandtl numbers on heat and mass transfers is also considered.
Section snippets
Theoretical analyses
The stream of slot jet impingement is shown in Fig. 1, in which the flow field along a heated surface is divided into four regions including a stagnation zone and three wall-jet zones based on the characteristics of flow and heat transfer for Pr ⩾ 1, respectively. In this paper predicative formulas are provided for the entire range of lateral flow under arbitrary-heat-flux conditions.
According to boundary layer theory [18], the flow in a liquid film layer satisfies the following conservation
Comparison of analytical and experimental results
Theoretical expressions of heat transfer coefficients for free-surface slot jets were obtained by undertaking the mathematical analyses shown above. Comparisons of heat transfer coefficients in both the stagnation zone and the wall-jet zone were made between the present study and the analytical and experimental results in published literature.
Heat transfer coefficients at the stagnation line for slot jet impingement are shown in Fig. 2, in which both equations from this study and expressions
Conclusion
A theoretical analysis has been conducted to study heat transfer characteristics of free-surface liquid slot jet impingement. Equations for local heat transfer coefficients are obtained along heated surfaces with slot jets impingement based on the theory of laminar boundary layer. Also, the formula is compared with experimental results for both different working fluids and different nozzle sizes. Present theory shows good agreements with experimental results of for slot jet impingement. Further
Acknowledgements
The present research is supported by National Key Fundamental Research Plan (973) Project of China (no. 2000026304) and National Natural Science Foundation of China.
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