### Abstract

Because of the importance of fundamental knowledge on turbulent heat transfer for further decreasing entropy production and improving efficiency in various thermofluid systems, we revisit a classical issue whether enhancing heat transfer is possible with skin friction reduced or at least not increased as much as heat transfer. The answer that numerous previous studies suggest is quite pessimistic because the analogy concept of momentum and heat transport holds well in a wide range of flows. Nevertheless, the recent progress in analyzing turbulence mechanics and designing turbulence control offers a chance to develop a scheme for dissimilar momentum and heat transport. By reexamining the governing equations and boundary conditions for convective heat transfer, the basic strategies for achieving dissimilar control in turbulent flow are generally classified into two groups, i.e., one for the averaged quantities and the other for the fluctuating turbulent components. As a result, two different approaches are discussed presently. First, under three typical heating conditions, the contribution of turbulent transport to wall friction and heat transfer is mathematically formulated, and it is shown that the difference in how the local turbulent transport of momentum and that of heat contribute to the friction and heat transfer coefficients is a key to answer whether the dissimilar control is feasible. Such control is likely to be achieved when the weight distributions for the stress and flux in the derived relationships are different. Second, we introduce a more general methodology, i.e., the optimal control theory. The Fréchet differentials obtained clearly show that the responses of velocity and scalar fields to a given control input are quite different due to the fact that the velocity is a divergence-free vector, while the temperature is a conservative scalar. By exploiting this inherent difference, the dissimilar control can be achieved even in flows where the averaged momentum and heat transport equations have the same form.

Original language | English |
---|---|

Article number | 031009 |

Journal | Journal of Heat Transfer |

Volume | 134 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2012 |

### Fingerprint

### Keywords

- analogy
- control
- skin friction
- turbulent convective heat transfer
- turbulent Prandtl number

### ASJC Scopus subject areas

- Mechanical Engineering
- Mechanics of Materials
- Materials Science(all)
- Condensed Matter Physics

### Cite this

*Journal of Heat Transfer*,

*134*(3), [031009]. https://doi.org/10.1115/1.4005151

**Control of turbulent transport : Less friction and more heat transfer.** / Kasagi, Nobuhide; Hasegawa, Yosuke; Fukagata, Koji; Iwamoto, Kaoru.

Research output: Contribution to journal › Article

*Journal of Heat Transfer*, vol. 134, no. 3, 031009. https://doi.org/10.1115/1.4005151

}

TY - JOUR

T1 - Control of turbulent transport

T2 - Less friction and more heat transfer

AU - Kasagi, Nobuhide

AU - Hasegawa, Yosuke

AU - Fukagata, Koji

AU - Iwamoto, Kaoru

PY - 2012

Y1 - 2012

N2 - Because of the importance of fundamental knowledge on turbulent heat transfer for further decreasing entropy production and improving efficiency in various thermofluid systems, we revisit a classical issue whether enhancing heat transfer is possible with skin friction reduced or at least not increased as much as heat transfer. The answer that numerous previous studies suggest is quite pessimistic because the analogy concept of momentum and heat transport holds well in a wide range of flows. Nevertheless, the recent progress in analyzing turbulence mechanics and designing turbulence control offers a chance to develop a scheme for dissimilar momentum and heat transport. By reexamining the governing equations and boundary conditions for convective heat transfer, the basic strategies for achieving dissimilar control in turbulent flow are generally classified into two groups, i.e., one for the averaged quantities and the other for the fluctuating turbulent components. As a result, two different approaches are discussed presently. First, under three typical heating conditions, the contribution of turbulent transport to wall friction and heat transfer is mathematically formulated, and it is shown that the difference in how the local turbulent transport of momentum and that of heat contribute to the friction and heat transfer coefficients is a key to answer whether the dissimilar control is feasible. Such control is likely to be achieved when the weight distributions for the stress and flux in the derived relationships are different. Second, we introduce a more general methodology, i.e., the optimal control theory. The Fréchet differentials obtained clearly show that the responses of velocity and scalar fields to a given control input are quite different due to the fact that the velocity is a divergence-free vector, while the temperature is a conservative scalar. By exploiting this inherent difference, the dissimilar control can be achieved even in flows where the averaged momentum and heat transport equations have the same form.

AB - Because of the importance of fundamental knowledge on turbulent heat transfer for further decreasing entropy production and improving efficiency in various thermofluid systems, we revisit a classical issue whether enhancing heat transfer is possible with skin friction reduced or at least not increased as much as heat transfer. The answer that numerous previous studies suggest is quite pessimistic because the analogy concept of momentum and heat transport holds well in a wide range of flows. Nevertheless, the recent progress in analyzing turbulence mechanics and designing turbulence control offers a chance to develop a scheme for dissimilar momentum and heat transport. By reexamining the governing equations and boundary conditions for convective heat transfer, the basic strategies for achieving dissimilar control in turbulent flow are generally classified into two groups, i.e., one for the averaged quantities and the other for the fluctuating turbulent components. As a result, two different approaches are discussed presently. First, under three typical heating conditions, the contribution of turbulent transport to wall friction and heat transfer is mathematically formulated, and it is shown that the difference in how the local turbulent transport of momentum and that of heat contribute to the friction and heat transfer coefficients is a key to answer whether the dissimilar control is feasible. Such control is likely to be achieved when the weight distributions for the stress and flux in the derived relationships are different. Second, we introduce a more general methodology, i.e., the optimal control theory. The Fréchet differentials obtained clearly show that the responses of velocity and scalar fields to a given control input are quite different due to the fact that the velocity is a divergence-free vector, while the temperature is a conservative scalar. By exploiting this inherent difference, the dissimilar control can be achieved even in flows where the averaged momentum and heat transport equations have the same form.

KW - analogy

KW - control

KW - skin friction

KW - turbulent convective heat transfer

KW - turbulent Prandtl number

UR - http://www.scopus.com/inward/record.url?scp=84856065359&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856065359&partnerID=8YFLogxK

U2 - 10.1115/1.4005151

DO - 10.1115/1.4005151

M3 - Article

VL - 134

JO - Journal of Heat Transfer

JF - Journal of Heat Transfer

SN - 0022-1481

IS - 3

M1 - 031009

ER -