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ABSTRACT
A model was developed to simulate the performance of a microgrooved surface undergoing organized, steady-state, thin-film evaporation subject to a superheat at its base. The model is intended to serve as a comprehensive design tool that can be used to optimize the design of a microgrooved surface for a given application. A parametric study was conducted to evaluate the effects of base superheat, channel width, fin-channel width ratio, and channel aspect ratio on the base heat transfer coefficient. Multidimensional optimization was then performed, and it revealed a geometry capable of dissipating 320 W/cm2 with 10 K base superheat using octane.
Nomenclature
| A | = | disjoining pressure coefficient, J |
| AR | = | aspect ratio (Lf/wch), - |
| hbase | = | average base heat transfer coefficient, W/m2-K |
| hfg | = | latent heat of vaporization, kJ/kg |
| kl | = | thermal conductivity of liquid, W/m-K |
| ks | = | thermal conductivity of solid, W/m-K |
| Lb | = | length of substrate base, µm |
| Lf | = | length of fin, µm |
| m″ | = | interfacial evaporative mass flux, kg/m2-s |
| = | molecular mass of fluid, kg/mol | |
| Nu | = | Nusselt number, - |
| Pc, Pd, Pl, Pv | = | capillary, disjoining, liquid, and vapor pressures, respectively, Pa |
| Psat | = | equivalent saturation pressure at T = Tlv, Pa |
| Pv, eq | = | equivalent vapor pressure at T = Tlv, Pa |
| q″ | = | heat flux in thin film, W/m2 |
| = | average Base Heat Flux, W/m2 | |
| Q | = | total cumulative heat, W/m |
| R | = | radius of curvature, m |
| = | universal gas constant, J/mol-K | |
| R* | = | radius of curvature of intrinsic meniscus, m |
| Tb, Tlv, Tv, Tw | = | base, liquid–vapor, vapor, and wall temperatures, respectively, K |
| wch | = | width of channel, µm |
| wf | = | thickness of fin, µm |
| WR | = | width ratio (wf/wch), - |
| z | = | length along thin-film coordinate direction, µm |
| Γ | = | liquid mass flow rate, kg/s |
| δ | = | liquid film thickness; coordinate direction, m |
| ΔT | = | base superheat (Tbase − Tv), K |
| ϵ | = | initial adsorbed thin-film offset, - |
| υl | = | kinematic viscosity of liquid, m2/s |
| ρl | = | liquid density, kg/m3 |
| σ | = | liquid surface tension, N/m |
| = | evaporation coefficient, - | |
| φ | = | apparent contact angle, rad |
| ω | = | angle at end of intrinsic meniscus, rad |
Nomenclature
| A | = | disjoining pressure coefficient, J |
| AR | = | aspect ratio (Lf/wch), - |
| hbase | = | average base heat transfer coefficient, W/m2-K |
| hfg | = | latent heat of vaporization, kJ/kg |
| kl | = | thermal conductivity of liquid, W/m-K |
| ks | = | thermal conductivity of solid, W/m-K |
| Lb | = | length of substrate base, µm |
| Lf | = | length of fin, µm |
| m″ | = | interfacial evaporative mass flux, kg/m2-s |
| = | molecular mass of fluid, kg/mol | |
| Nu | = | Nusselt number, - |
| Pc, Pd, Pl, Pv | = | capillary, disjoining, liquid, and vapor pressures, respectively, Pa |
| Psat | = | equivalent saturation pressure at T = Tlv, Pa |
| Pv, eq | = | equivalent vapor pressure at T = Tlv, Pa |
| q″ | = | heat flux in thin film, W/m2 |
| = | average Base Heat Flux, W/m2 | |
| Q | = | total cumulative heat, W/m |
| R | = | radius of curvature, m |
| = | universal gas constant, J/mol-K | |
| R* | = | radius of curvature of intrinsic meniscus, m |
| Tb, Tlv, Tv, Tw | = | base, liquid–vapor, vapor, and wall temperatures, respectively, K |
| wch | = | width of channel, µm |
| wf | = | thickness of fin, µm |
| WR | = | width ratio (wf/wch), - |
| z | = | length along thin-film coordinate direction, µm |
| Γ | = | liquid mass flow rate, kg/s |
| δ | = | liquid film thickness; coordinate direction, m |
| ΔT | = | base superheat (Tbase − Tv), K |
| ϵ | = | initial adsorbed thin-film offset, - |
| υl | = | kinematic viscosity of liquid, m2/s |
| ρl | = | liquid density, kg/m3 |
| σ | = | liquid surface tension, N/m |
| = | evaporation coefficient, - | |
| φ | = | apparent contact angle, rad |
| ω | = | angle at end of intrinsic meniscus, rad |