# Unsteady laminar flow with convective heat transfer through a rotating curved square duct with small curvature

## Abstract

Unsteady laminar flow with convective heat transfer through a curved square duct rotating at a constant angular velocity about the center of curvature is investigated numerically by using a spectral method, and covering a wide range of the Taylor number −300≤Tr≤1000 for the Dean number Dn = 1000. A temperature difference is applied across the vertical sidewalls for the Grashof number Gr = 100, where the outer wall is heated and the inner wall cooled, the top and bottom walls being adiabatic. Flow characteristics are investigated with the effects of rotational parameter, Tr, and the pressure-driven parameter, Dn, for the constant curvature 0.001. Time evolution calculations as well as their phase spaces show that the unsteady flow undergoes through various flow instabilities in the scenario ‘multi-periodic → chaotic → steady-state → periodic → multi-periodic → chaotic’, if Tr is increased in the positive direction. For negative rotation, however, time evolution calculations show that the flow undergoes in the scenario ‘multi-periodic → periodic → steady-state’, if Tr is increased in the negative direction. Typical contours of secondary flow patterns and temperature profiles are obtained at several values of Tr, and it is found that the unsteady flow consists of two- tomore »

- Authors:

- Department of Mathematics, Jagannath University, Dhaka-1100 (Bangladesh)
- Department of Mathematics, Vikarunnesa Nun School and College, Boshundhara, Dhaka (Bangladesh)
- Department of Mechanical and Systems Engineering, Okayama University, Okayama 700-8530 (Japan)

- Publication Date:

- OSTI Identifier:
- 22608546

- Resource Type:
- Journal Article

- Journal Name:
- AIP Conference Proceedings

- Additional Journal Information:
- Journal Volume: 1754; Journal Issue: 1; Conference: ICME 2015: 11. international conference on mechanical engineering, Dhaka (Bangladesh), 18-20 Dec 2015; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANGULAR VELOCITY; DUCTS; FLUIDS; GRASHOF NUMBER; HEAT; HEAT TRANSFER; HEATING; INSTABILITY; LAMINAR FLOW; MIXING; PERIODICITY; PHASE SPACE; ROTATION; STEADY-STATE CONDITIONS; STRONG INTERACTIONS; TEMPERATURE GRADIENTS; UNSTEADY FLOW; VORTICES; FUNDAMENTAL INTERACTIONS

### Citation Formats

```
Mondal, Rabindra Nath, E-mail: rnmondal71@yahoo.com, Shaha, Poly Rani, Roy, Titob, and Yanase, Shinichiro, E-mail: yanase@okayama-u.ac.jp.
```*Unsteady laminar flow with convective heat transfer through a rotating curved square duct with small curvature*. United States: N. p., 2016.
Web. doi:10.1063/1.4958362.

```
Mondal, Rabindra Nath, E-mail: rnmondal71@yahoo.com, Shaha, Poly Rani, Roy, Titob, & Yanase, Shinichiro, E-mail: yanase@okayama-u.ac.jp.
```*Unsteady laminar flow with convective heat transfer through a rotating curved square duct with small curvature*. United States. doi:10.1063/1.4958362.

```
Mondal, Rabindra Nath, E-mail: rnmondal71@yahoo.com, Shaha, Poly Rani, Roy, Titob, and Yanase, Shinichiro, E-mail: yanase@okayama-u.ac.jp. Tue .
"Unsteady laminar flow with convective heat transfer through a rotating curved square duct with small curvature". United States. doi:10.1063/1.4958362.
```

```
@article{osti_22608546,
```

title = {Unsteady laminar flow with convective heat transfer through a rotating curved square duct with small curvature},

author = {Mondal, Rabindra Nath, E-mail: rnmondal71@yahoo.com and Shaha, Poly Rani and Roy, Titob and Yanase, Shinichiro, E-mail: yanase@okayama-u.ac.jp},

abstractNote = {Unsteady laminar flow with convective heat transfer through a curved square duct rotating at a constant angular velocity about the center of curvature is investigated numerically by using a spectral method, and covering a wide range of the Taylor number −300≤Tr≤1000 for the Dean number Dn = 1000. A temperature difference is applied across the vertical sidewalls for the Grashof number Gr = 100, where the outer wall is heated and the inner wall cooled, the top and bottom walls being adiabatic. Flow characteristics are investigated with the effects of rotational parameter, Tr, and the pressure-driven parameter, Dn, for the constant curvature 0.001. Time evolution calculations as well as their phase spaces show that the unsteady flow undergoes through various flow instabilities in the scenario ‘multi-periodic → chaotic → steady-state → periodic → multi-periodic → chaotic’, if Tr is increased in the positive direction. For negative rotation, however, time evolution calculations show that the flow undergoes in the scenario ‘multi-periodic → periodic → steady-state’, if Tr is increased in the negative direction. Typical contours of secondary flow patterns and temperature profiles are obtained at several values of Tr, and it is found that the unsteady flow consists of two- to six-vortex solutions if the duct rotation is involved. External heating is shown to generate a significant temperature gradient at the outer wall of the duct. This study also shows that there is a strong interaction between the heating-induced buoyancy force and the centrifugal-Coriolis instability in the curved channel that stimulates fluid mixing and consequently enhances heat transfer in the fluid.},

doi = {10.1063/1.4958362},

journal = {AIP Conference Proceedings},

issn = {0094-243X},

number = 1,

volume = 1754,

place = {United States},

year = {2016},

month = {7}

}