1. Peculiarities of Heat Transfer on Micro-Structured Surfaces
第50回日本伝熱シンポジウム講演論文集
Peculiarities of Heat Transfer on Micro-Structured Surfaces
Boris Kosoy (オデッサ州立冷凍大) 伝正Yoshio Utaka (横国大)

2. Outlines Introduction Effective Thermal Conductivity
Nucleate Boiling Enhancement
Universal Model of Evaporation on Micro-Structured Surfaces
Conclusions

3. Introduction
Focus of interest →electronic cooling convection and nucleate boiling processes
active techniques (require an external power supply) and passive techniques (micro-structuring of the surface)
Methods to create micro-structured surfaces: inscribing open grooves in the surface with a sharp pointed scribe, forming three-dimensional cavities by cold pressing conical cavities into the surface, electroplating, wet chemical etching, sintering metal particles or metal fibers onto the surface, spraying molten metal onto the surface, coating the surface with a particle-containing paint, laser etching, and plasma etching.
Heat transfer modes on micro-structured surfaces:
Heat conduction from/to opposite external surfaces of micro-structure at low flow rates accounting the effective thermal conductivity mechanism;
Forced convection between the surface and single-phase flow inside the micro-structure;
Condensation on the external surface of the micro-structure;
Nucleate boiling on the external surface of micro-structure.
Objective: to investigate the particulars of heat transfer on micro-structured surfaces

4. Effective Thermal Conductivity
Heat conduction from/to opposite micro-structure external surfaces depends dramatically on the accurate picking out of elementary representative cell within the present micro-structure, and demands on understanding of physical and chemical specifics of micro-structure creation, its spatial geometry, etc. Also this step is crucially important for numerical simulations adequacy
Assumptions for definition of effective thermal conductivity:
The porous medium is uniform, or the porosity variation can be accurately calculated.
Natural convection and radiation effects inside the porous medium can be neglected.
The physical properties of the solid and fluid phases remain constant throughout the temperature range.
The solid and fluid phases are in local thermal equilibrium.
Main factors effect the skeleton thermal conductivity :
micro-structure elements contact type (mechanical pressing, soldering, welding, gluing, etc.),
contact spot size, and number of contacts within the representative cell;
deformation of the heat flux patterns in the contact zones and related supplementary thermal resistance;
roughness of porous structure elements.

5. Effective Thermal Conductivity
Forced Convection Mechanism = effect of convection inside the micro-structure + heat conduction through the solid skeleton
Presence of the solid structure elements in the vicinity of the wall dumps significantly convection and affects the turbulence mixing mechanism.
Local porosity increases essentially, and number of contacts lowers:
→ formation of a specific film thermal resistance close to the wall (the overall heat transfer coefficient in the vicinity of the wall can be attained by assembling a chain of local thermal resistances)
Condensation on the external surface of the micro-structure:
the coupled effect of heat conduction through the condensate thin film and through the wetted micro-structure.
For number of cases it is reasonable to neglect with thermal resistance of condensate thin film and to account effective heat conduction only.

6. Nucleate Boiling Enhancement
Mechanisms of vapor bubbles formation and transportation:
thin film evaporation of the superheated liquid surrounding the growing bubble (heat transfer via latent energy),
stripping of the thermal boundary layer at the wall by departing bubbles (heat transfer via sensible energy),
generation of turbulence in the liquid pool by escaping bubbles which produces a forced convection process (heat transfer via sensible energy).
Variables affecting boiling heat flux:
wall superheat, spatial distribution of nucleation site density, spatial distribution of bubble departure diameter, contact angle, heater orientation, gravity, etc.
Critical coating thickness: The heat transfer will be enhanced when the coating thickness is less than critical value. In thick micro-structures, bubble can easily form vapor film because of large resistance.
Usually, external surfaces of micro-structure are drained out through evaporation, i.e. evaporation occurs from the liquid meniscus inside micro-structure elements; however, heat is transferred by the solid skeleton.
The skeleton thermal conductivity exceeds considerably a thermal conductivity of a fluid. Consequently, heat flow patterns are deforming significantly that is similar to appearance of the surplus thermal resistance.

7. Universal Model of Evaporation on Micro-Structured Surfaces
The common drawback of all known micro-structured surfaces evaporation models is associated with a lack of universal approach to justification of extensive experimental regularities obtained.
General principles for universal calculation procedure at evaporation on micro-structured surfaces:
It was assumed that the maximum heat flux could be achieved, when the liquid supply to a certain zone or to the entire heating wall appears impossible.
The irreversibility minimum principle was used for calculating ratio of liquid and vapor phases’ concentrations inside the micro-structure, activated representative cells density and their characteristic sizes.
One should vary the following conditions requesting a specific mathematical model, i.e. set of equations, boundary conditions and constrains with respect to the particular hydrodynamic and heat transfer regularities:
1) evaporation on the heat transfer surface covered with micro- structure and submerged into a liquid (evaporation occurs in the boiling regime);
2) evaporation on heat transfer surface covered with micro- structure in the capillary feeding conditions at horizontal location (excess liquid is absent on the external surface of micro-structure);

8. Universal Model of Evaporation on Micro-Structured Surfaces
3) evaporation on heat transfer surface covered with micro- structure in the capillary feeding conditions at small inclinations (<10o), when liquid layer is in the foot zone of the external part of capillary structure;
4) evaporation on heat transfer surface covered with micro- structure in the capillary feeding conditions at vertical or inclined position (< 0o);
5) evaporation on heat transfer surface covered with micro- structure in the capillary feeding conditions at vertical or inclined position (> 0o);
In cases 2...5, as boiling both evaporative heat removal regimes are feasible.
Evaporation inside the micro-structure is visible only in the case when the wall superheat is sufficient for activation at least of some fraction of representative cells.
The condition of cells stable activation (the minimum superheat)
Δ Tmin = Tw –Ts >2σ Ts /(rρ” Di )
Di - micro-structure representative cell characteristic size.
For picking the low limit of boiling thermal regime in flooding case, it is requested to identify such micro-structure cells, those activation is more probable at a given wall superheat ΔT.
In any steady boiling regime, those cells will be activated, which action sustains the irreversibility minimum principle inside the two-phase boundary layer, minimum wall superheat ΔTmin at given heat flux or maximum heat flux at given wall superheat.

9. Conclusions
Peculiarities of micro-structures heat transfer enhancement were analyzed due to their high potential for increasing thermal processes capability.
By help of thermodynamic simulations it could be demonstrated that the two-phase heat transfer can be improved by use of micro-structured surfaces.
Primarily, the surface enlargement has the determining influence on the heat transfer efficiency. However, the design of the geometries and the arrangement of the structures also effect the heat transfer. Especially for nucleate boiling processes the influence of these parameters has to be examined in further investigations.
The available literatures imply that we need distinguish between boiling within micro-structure and boiling on micro-structured surfaces, in other words, different models are required to describe the two cases.
An incentive for future work is that, though rich in experimental investigations, available studies are limited in theoretical analyses and generalizations.

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