Analysis of Laminar Slip-Flow Thermal Transport in Microchannels With Transverse Rib and Cavity Structured Superhydrophobic Walls at Constant Heat Flux

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
D. Maynes ◽  
B. W. Webb ◽  
J. Crockett ◽  
V. Solovjov
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Thermal Transport ◽  
Peclet Number ◽  
Average Nusselt Number ◽  
Slip Flow ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Péclet Number

This paper presents an analytical investigation of the thermal transport in a parallel-plate channel comprised of superhydrophobic walls. An analytical solution is obtained for the thermally developing state, however, it is the condition far downstream from the entrance where the temperature field exhibits repeating periodic streamwise variation that is of primary interest here. The superhydrophobic walls considered in this paper exhibit alternating microribs and cavities positioned perpendicular to the flow direction and the transport scenario analyzed is that of constant wall heat flux through the rib surfaces with negligible thermal transport through the vapor cavity interface. Axial conduction is neglected in the analysis and the problem is one of Graetz flow with apparent slip-flow and periodicity of constant heating. Closed form solutions for the local Nusselt number and wall temperature are presented and are in the form of infinite series expansions. Previously, it has been shown that significant reductions in the overall frictional pressure drop can be expected relative to the classical smooth channel laminar flow. The present results reveal that the overall thermal transport is markedly influenced by the relative cavity region (cavity fraction), the relative rib/cavity module width, and the flow Peclet number. The following conclusions can be made regarding thermal transport for a constant heat flux channel exhibiting the superhydrophobic surfaces considered: (1) Increases in the cavity fraction lead to decreases in the average Nusselt number; (2) Increasing the relative rib/cavity module length yields a decrease in the average Nusselt number; and (3) as the Peclet number increases the average Nusselt number increases. For all parameters explored, the limiting upper bound on the fully developed average Nusselt number corresponds to the limiting case scenario of classical laminar flow through a smooth-walled channel with constant heat flux.

Analysis of Laminar Slip-Flow Thermal Transport in Microchannels With Transverse Rib and Cavity Structured Superhydrophobic Walls at Constant Heat Flux

2011 ◽  
Author(s):  
D. Maynes ◽  
B. W. Webb ◽  
V. Soloviev
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Thermal Transport ◽  
Peclet Number ◽  
Average Nusselt Number ◽  
Slip Flow ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Péclet Number

This paper presents an analytical investigation of the thermally developing and periodically fully-developed flow in a parallel-plate channel comprised of superhydrophobic walls. The superhydrophobic walls considered in this paper exhibit alternating micro-ribs and cavities positioned perpendicular to the flow direction and the transport scenario analyzed is that of constant wall heat flux through the rib surfaces with negligible thermal transport through the vapor cavity interface. Axial conduction is neglected in the analysis and the problem is one of Graetz flow with apparent slip-flow and periodicity of constant heating. Closed form solutions for the local Nusselt number and wall temperature are presented and are in the form of infinite series expansions. Previously it has been shown that significant reductions in the overall frictional pressure drop can be expected relative to the classical smooth channel laminar flow. The present results reveal that the overall thermal transport is markedly influenced by the relative cavity region (cavity fraction), the relative rib/cavity module width, and the flow Peclet number. The following conclusions can be made regarding thermal transport for a constant heat flux channel exhibiting the superhydrophobic surfaces considered: 1) Increases in the cavity fraction lead to decreases in the average Nusselt number; 2) Increasing the relative rib/cavity module length yields a decrease in the average Nusselt number; and 3) as the Peclet number increases the average Nusselt number increases. For all parameters explored, the limiting upper bound on the fully-developed average Nusselt number corresponds to the limiting case scenario of classical laminar flow through a smooth-walled channel with constant heat flux.

Fully-Developed Thermal Transport in Microchannels With Streamwise Grooved Superhydrophobic Walls at Constant Heat Flux

2012 ◽  
Author(s):  
D. Maynes ◽  
J. Vanderhoff ◽  
G. Rosengarten
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Thermal Transport ◽  
Average Nusselt Number ◽  
Temperature Jump ◽  
Slip Length ◽  
Relative Size ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Hydrodynamic Slip

This paper presents an analytical investigation of constant property, steady, fully-developed, laminar thermal transport in a parallel-plate channel comprised of metal superhydrophobic walls. The superhydrophobic walls considered here exhibit micro-ribs and cavities aligned in the streamwise direction. The cavities are assumed to be non-wetting and contain air, such that the Cassie-Baxter state is the interfacial state considered. The scenario considered is that of constant heat flux through the rib surfaces with negligible thermal transport through the air cavity interface. Closed form solutions for the local Nusselt number and local wall temperature are presented and are in the form of infinite series expansions. The analysis show the relative size of the cavity regions compared to the total rib and cavity width (cavity fraction) exercises significant influence on the aggregate thermal transport behavior. Further, the relative size of the rib and cavity module width compared to the channel hydraulic diameter (relative module width) also influences the Nusselt number. The spatially varying Nusselt number and wall temperature are presented as a function of the cavity fraction and the relative module width over the ranges 0–0.99 and 0.01–1.0, respectively. From these results the rib/cavity module averaged Nusselt number was determined as a function of the governing parameters. The results reveal that increases in either the cavity fraction or relative module width lead to decreases in the average Nusselt number and results are presented over a wide range of conditions from which the average Nusselt number can be determined for heat transfer analysis. Further, analogous to the hydrodynamic slip length, a temperature jump length describing the apparent temperature jump at the wall is determined in terms of the cavity fraction. Remarkably, it is nearly identical to the hydrodynamic slip length for the scenario considered here and allows straightforward determination of the average Nusselt number for any cavity fraction and relative rib/cavity module width.

Apparent Temperature Jump and Thermal Transport in Channels With Streamwise Rib and Cavity Featured Superhydrophobic Walls at Constant Heat Flux

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
D. Maynes ◽  
J. Crockett
Keyword(s):  
Nusselt Number ◽  
Thermal Transport ◽  
Average Nusselt Number ◽  
Temperature Jump ◽  
Slip Length ◽  
Relative Size ◽  
Constant Heat Flux ◽  
Apparent Temperature ◽  
Constant Heat ◽  
Hydrodynamic Slip

This paper presents an analytical investigation of constant property, steady, fully developed, laminar thermal transport in a parallel-plate channel comprised of metal superhydrophobic (SH) walls. The superhydrophobic walls considered here exhibit microribs and cavities aligned in the streamwise direction. The cavities are assumed to be nonwetting and contain air, such that the Cassie–Baxter state is the interfacial state considered. The scenario considered is that of constant heat flux through the rib surfaces with negligible thermal transport through the air cavity interface. Closed form solutions for the local Nusselt number and local wall temperature are presented and are in the form of infinite series expansions. The analysis show the relative size of the cavity regions compared to the total rib and cavity width (cavity fraction) exercises significant influence on the aggregate thermal transport behavior. Further, the relative size of the rib and cavity module width compared to the channel hydraulic diameter (relative module width) also influences the Nusselt number. The spatially varying Nusselt number and wall temperature are presented as a function of the cavity fraction and the relative module width over the ranges 0–0.99 and 0.01–1.0, respectively. From these results, the rib/cavity module averaged Nusselt number was determined as a function of the governing parameters. The results reveal that increases in either the cavity fraction or relative module width lead to decreases in the average Nusselt number and results are presented over a wide range of conditions from which the average Nusselt number can be determined for heat transfer analysis. Further, analogous to the hydrodynamic slip length, a temperature jump length describing the apparent temperature jump at the wall is determined in terms of the cavity fraction. Remarkably, it is nearly identical to the hydrodynamic slip length for the scenario considered here and allows straightforward determination of the average Nusselt number for any cavity fraction and relative rib/cavity module width.

Entropy Generation Minimization of Fully Developed Internal Convective Flows With Constant Heat Flux

2003 ◽  
Author(s):  
Eric B. Ratts ◽  
Atul G. Raut
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Entropy Generation ◽  
Cross Sections ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Entropy Generation Minimization

This paper addresses the thermodynamic optimum of single-phase convective heat transfer in fully developed flow for uniform and constant heat flux. The optimal Reynolds number is obtained using the entropy generation minimization (EGM) method. Entropy generation due to viscous dissipation and heat transfer dissipation in the flow passage are summed, and then minimized with respect to Reynolds number based on hydraulic diameter. For fixed mass flow rate and fixed total heat transfer rate, and the assumption of uniform heat flux, an optimal Reynolds number for laminar as well as turbulent flow is obtained. In addition, the method quantifies the flow irreversibilities. It was shown that the ratio of heat transfer dissipation to viscous dissipation at minimum entropy generation was 5:1 for laminar flow and 29:9 for turbulent flow. For laminar flow, the study compared non-circular cross-sections to the circular cross-section. The optimal Reynolds number was determined for the following cross-sections: square, equilateral triangle, and rectangle with aspect ratios of two and eight. It was shown that the rectangle with the higher aspect ratio had the smallest optimal Reynolds number, the smallest entropy generation number, and the smallest flow length.

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