# Heat Transfer Improvement in a Double Backward-Facing Expanding Channel Using Different Working Fluids

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

^{2}) are examined. The top wall of the passage and the bottom wall of the upstream section are adiabatic, while the walls of both the first and second steps downstream are heated. The results show that the local Nusselt number rises with the augmentation of the Reynolds number, and the critical effects are seen in the entrance area of the first and second steps. The maximum average Nusselt number, which represents the thermal performance, can be seen clearly in case 1 for EG in comparison to water and ammonia. Due to the expanding of the passage, separation flow is generated, which causes a rapid increment in the local skin friction coefficient, especially at the first and second steps of the downstream section for water, ammonia liquid and EG. The maximum skin friction coefficient is detected in case 1 for water with Re = 512. Trends of velocities for positions (X/H1 = 2.01, X/H2 = 2.51) at the first and second steps for all the studied cases with different types of convectional fluids are indicated in this paper. The presented findings also include the contour of velocity, which shows the recirculation zones at the first and second steps to demonstrate the improvement in the thermal performance.

## 1. Introduction

_{2}-based nanofluid flow in an annular pipe with a sudden reduction. A rise in the surface heat transfer coefficient was found with growing nanoparticle volume fractions and Reynolds numbers. Laminar fluid flow over a BFS and FFS with three obstacles was studied by Shujit Kumar Bala et al. by implementing the lattice Boltzmann method (LBM) [33]. It was noticed that heat transfer could rise up to 80% with a Reynolds number increase of 100. Additionally, Yuan et al. [34] conducted a study on heat transfer for MWCNT (Multi-Walled Carbon Nanotube)-Fe

_{3}O

_{4}/water hybrid nanofluid flow over forward- and backward-facing step channels with a baffle fixed on its top wall. The results showed an increase in the average Nusselt number as the length of the baffle increased or as the baffle moved towards the backward-facing step. Fetta et al. [35] performed a numerical investigation into the influence of Bingham fluid flow over a backward-facing step to enhance the thermal performance. They found that increases in the Bingham number led to the reduction of recirculation zones, and increases in the Richardson number intensified recirculation zones. Large-eddy simulation (LES) and its comparison with direct numerical simulation (DNS) were reported in an investigation by Jure et al. [36]. LES data were in good agreement with the DNS data for predictions of temperature fluctuations.

## 2. Numerical Approach

#### 2.1. Physical Model

^{2}). Four different velocities are used in this simulation, and the Reynolds numbers are 98.5, 190, 343 and 512.

#### 2.2. Governing Equations

^{−6}, 10

^{−7}and 10

^{−7}, respectively.

## 3. Grid Independence Study and Data Validation

## 4. Results and Discussion

^{2}) and four variations of the Reynolds number (98.5, 190, 343 and 512).

#### 4.1. Nusselt Number

#### 4.2. Flow Characteristics

#### 4.3. Velocity Profile

_{1}= 2.01, X/H

_{2}= 2.51) at the first and second steps for all the studied cases are plotted in Figure 11a–c and Figure 12a–c, respectively. It is noted that velocity diminishes at the first and second steps sharply and then increases due to recirculation flow, which is generated at the regions after the first and second steps. The velocity contours at the first and second steps for a Reynolds number of 512 and case 1 are represented in Figure 13 and Figure 14, respectively. The figures demonstrate the recirculation zone at the first and second steps, which show the heat transfer augmentation.

## 5. Conclusions

- An increase in the local Nusselt number is detected with rises in the Reynolds number, while the critical effects are seen at the start region of the first and second steps.
- The results show that higher local Nusselt numbers occur in cases 1 and 3, compared to case 2, for all types of fluids.
- The maximum average Nusselt number, which represents the thermal performance, can clearly be seen in case 1 for EG, in comparison to water and ammonia.
- A rise in the local skin friction coefficient is apparent at the first and second steps of the downstream section due to the expansion of the passage, which produces the separation flow.
- The velocity decreases rapidly at the first and second steps and then increases. This is due to the recirculation flow, which is generated at the zones after the first and second steps.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

A | Length of the bottom wall before the first step |

B | Length of the bottom wall after the first step |

C | Length of the bottom wall after the second step |

C_{p} | Specific heat |

H | Width of the channel at the entrance |

H_{1} | The step height of the first step |

H_{2} | The step height of the second step |

L | The total length of the channel |

Nu | Nusselt number |

P | Pressure |

Pr | Prandtl number |

Re | Reynolds number |

T | Temperature |

u, v | Axial velocity |

X, y | Cartesian coordinates |

Greek symbols | |

Ρ | Water density |

µ | Dynamic viscosity |

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**Figure 2.**Velocity profile at different positions for (

**a**) X/S = 1, (

**b**) X/S = 3, (

**c**) X/S = 5 and (

**d**) X/S = 7.

**Figure 4.**The effect of the step height on local Nusselt number at Re = 512 for (

**a**) water, (

**b**) ammonia and (

**c**) EG.

**Figure 7.**Distributions of C

_{f}with different Reynolds numbers for (

**a**) water, (

**b**) ammonia and (

**c**) EG.

**Figure 9.**Comparison of average C

_{f}with different Re and step heights for (

**a**) water, (

**b**) ammonia and (

**c**) EG.

Cases | H (cm) | H_{1} (cm) | H_{2} (cm) | a (cm) | b (cm) | c (cm) |
---|---|---|---|---|---|---|

1 | 0.98 | 1 | 1 | 200 | 50 | 50 |

2 | 0.98 | 2 | 1 | 200 | 50 | 50 |

3 | 0.98 | 1 | 2 | 200 | 50 | 50 |

Fluid Type | ρ (kg/m ^{3}) | μ (N s/m ^{2}) | k (W/m K) | C_{p}(J/kg K) |
---|---|---|---|---|

Ammonia (liquid) | 650 | 0.000152 | 0.493 | 4758 |

EG | 1111.4 | 0.0157 | 0.252 | 2415 |

Water | 998.2 | 0.001003 | 0.6 | 4182 |

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**MDPI and ACS Style**

Abdulrazzaq, T.; Togun, H.; Alsulami, H.; Goodarzi, M.; Safaei, M.R.
Heat Transfer Improvement in a Double Backward-Facing Expanding Channel Using Different Working Fluids. *Symmetry* **2020**, *12*, 1088.
https://doi.org/10.3390/sym12071088

**AMA Style**

Abdulrazzaq T, Togun H, Alsulami H, Goodarzi M, Safaei MR.
Heat Transfer Improvement in a Double Backward-Facing Expanding Channel Using Different Working Fluids. *Symmetry*. 2020; 12(7):1088.
https://doi.org/10.3390/sym12071088

**Chicago/Turabian Style**

Abdulrazzaq, Tuqa, Hussein Togun, Hamed Alsulami, Marjan Goodarzi, and Mohammad Reza Safaei.
2020. "Heat Transfer Improvement in a Double Backward-Facing Expanding Channel Using Different Working Fluids" *Symmetry* 12, no. 7: 1088.
https://doi.org/10.3390/sym12071088