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Heat transfer on microstructured surfaces with pool boiling of various liquids

Recommendations for predicting heat transfer coefficients and critical heat fluxes are developed on the basis of available experimental data on heat transfer and critical heat fluxes for boiling of different liquids on microstructured surfaces realized by deformed cutting method. Microstructured surfaces allow intensifying heat transfer 1.1 to 6 times. Due to the variable wettability of microstructured surface elements, critical heat fluxes increase over 4 times. The proposed criteria equations allow predicting heat transfer coefficients with an error of 30%, and critical heat fluxes with an error of 30-35%. The equations are of interest for designing cooling systems for microelectronic devices, heat and mass transfer devices, boiling zones of heat pipes and thermosyphons, etc.


Introduction
Liquid cooling systems are currently used for cooling the heat loaded elements of power electrical equipment and microelectronics. In these systems, the liquid boils directly on the electronic components. For this purpose, they are placed directly in the liquid coolant. And to increase the reliability of cooling systems, critical heat fluxes have to be increased.
Methods of heat exchange enhancement during pool boiling are traditional [1]: influence on internal mechanisms of the process (increase of vaporization centers, wettability control, increase of liquid inflow into microlayer evaporation zone, etc.); and increase/development of the heat-exchange surface.
Nowadays the great majority of works are focused on searching and applying new technologies of surface structuring and boiling process control [1,2]. The main results of these works only demonstrate the effect without any detailed description of the investigated process for different coolants and conditions of experiments. Modern surface structuring technologies have been developed. They allow controlling the heat exchange during boiling, thus reducing the temperature head of the beginning of boiling, increasing the values of critical thermal head, and intensifying the heat transfer coefficient.
One of the methods for obtaining effective microstructured boiling surfaces is the deformation cutting technology [3,4]. This method is based on the process of partial cut allowance and targeted plastic deformation of the undercut surface layer. The resulting chips are not completely separated from the workpiece, maintaining a bond with it on its narrow side. The set of undercut surface layers, keeping their connection with the workpiece, form on the treated surface of a part of the developed macro relief. The technology has high productivity and a wide range of standard sizes of the resulting macro-relief and can be implemented both on specialized and unified metal-cutting equipment.
The selection of geometrical parameters of microstructured surfaces allows controlling the wettability of the surface and the inflow of liquid into the evaporation zone. The wetting angle affects the formation of the steam bubble [1]. The increase of the edge angle (wetting property deterioration) reduces the temperature head corresponding to the boiling beginning and intensifies the heat output. Improvement of wettability promotes the liquid inflow into the zone of intensive evaporation and increases critical heat fluxes. The combination of these factors allows for simultaneous heat transfer intensification and increases critical heat fluxes.

General correlations for heat transfer coefficient
Only surfaces obtained by deforming cutting were used to generalize data on pool boiling heat transfer of liquids heated to saturation temperature. All surfaces were divided into two groups ( Fig.1): surfaces with 2-D relief (microribs); and surfaces with 3-D relief (micro-pin structures).
The generalization was performed using the polynomial regression method: where α is the heat transfer coefficient on a microstructured surface, α0 is the heat transfer coefficient on a smooth surface, Kq is the dimensionless criterion -the scale of the average liquid velocity caused by the vaporization process K q =q•l 0 /(r•ρ"•'), l0 is the Laplace constant proportional to the tear-off diameter of the bubble. l 0 =√ /( ( ′ − ")), ρ' and ρ" are the liquid and vapour densities, v' is the fluid kinematic viscosity coefficient, r is the latent heat of vaporization, σ is the surface tension coefficient; and geometrical parameters , h, Δ,  are shown in Fig. 2. There are several approaches to normalizing geometric parameters in boiling dependences. For example, it is proposed to choose the initial diameter of the steam bubble as the defining size. However, analysis has shown that the most profitable is to use l0. This primarily depends on the boiling model -the calculation through the initial diameter of the steam bubble more describes the increase of the centers of vaporization and their exit from the microstructure elements, and l0 describes the control of wettability and increase of liquid inflow into the micro-layer evaporation zone. It is recommended to accept the equation of Borishansky -  Generalization of experimental data presented in Table 1 and Fig. 1 was carried out for geometric parameters of surfaces with 2-D relief (micro-rib) and regime parameters of pool boiling. The material of the surfaces was stainless steel, copper, titanium. Thickness of surfaces No. 1-23 is 0.2-0.3 mm. During generalization of more than 730 experimental points, dependence was obtained to calculate heat transfer coefficient at pool boiling water, ethanol, 60% of glycerine water solution, freons R113 and R123, Novec 649 refrigerant in big volume on boiling surfaces with 2-D relief (micro rib) (Fig.3):    Fig.2), Δ/l0=0.002-1.29 (relative distance between microrib element. Fig.2 ), /l0= 0.01-1 (relative thickness of the micro-rib profile. Fig.2), Pr=1.75-35.7, and F/F0=1.66-9.75 (increase in heat exchange area).

General correlations for critical heat fluxes
To generalize the data for critical heat fluxes, the surface data presented in Tables 1 and 2  where qcrit is the critical heat flux when liquid is pool boiling on a microstructured surface, and qcrit0 is the critical heat flux when liquid is boiling on a smooth surface. The values obtained experimentally are taken as the critical heat flux when liquid is boiling on a smooth surface qcrit0. They can be estimated using the dependence for Kutateladze critical heat flux: qcrit0=0.13r√ "√ ( ′ − ") 4 with recommendations on amendments to the thickness of thin-walled boiling surfaces of Gogonin [14]. It should be noted that the amount of experimental data is very limited.