# Develop a New Correlation between Thermal Radiation and Heat Source in Dual-Tube Heat Exchanger with a Twist Ratio Insert and Dimple Configurations: An Experimental Study

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## Abstract

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## 1. Introduction

_{2}in DPHE were researched experimentally, with influences on the SCO

_{2}of pressure, mass flux, and buoyancy force studied extensively. On the other hand, the study showed that increasing the gas-side pressure significantly reduced both the overall and gas-side temperature gradient ratio. Moreover, the study showed that water-side discharge, as opposed to gas-side flow rate, was the most important factor in the heat transfer rate. Furthermore, Tala et al. [53] established the forecasting of thermal performance and genetic algorithm-based scientific correlation. Several investigators have explored various kinds of TTs in experimental and modelling studies, according to the literature analysis. However, few studies are observed on evaluating thermal performance in a dual-pipe heat exchanger using TT with a dimple configuration insert. The goal of this research is to in-vestigate HT and ‘f’ properties of twisted tape with dimple configuration inserts of differ-ent parameters at the same dimple diameter (D) to dimple diameter to depth ratio (D/H) in a horizontal DPHE. The influence of the dimple configuration on HT and pressure drop (ρ) is investigated experimentally in this work. With cold/hot water as a working fluid, “Re” ranged from 6000 to 14,000. The experimentally acquired results of thermal performance enhancement and pressure decrease were assessed and extensively discussed.

- Developing new correlations for Performance Evaluation Criteria (PEC) in terms of Nusselt number (Nu), friction factor (f), Reynolds number (Re), Dimple diameter (D
_{d}), Hole diameter (D_{h}) for given set of flow and geometrical parameters.

- Providing a dimple protrusion surface only on front face with a hole configuration placed adjacent to it over the tube length of 1500 mm.

## 2. Methodology

## 3. Experimental Set-Up

_{d}). The employed twisted tapes fabrication diagram is depicted in below Figure 2.

## 4. Data Analysis [54]

- Twisted factor is spatial measurement amidst successive points of a geometrical configuration on co-planes measured parallel to twisted tape axis (i.e., 50% of the twisted ratio) divided by Total Hydraulic (T
_{d}). ‘TR’ or ‘y’ are typical abbreviations used for it.

- 2.
- Reynolds Number (Re) is the ratio of the fluid’s dynamic viscosity to compound of the tube’s (Hd), median fluid flow rate, and volume. Re is symbol used for it.

- 3.
- Nusselt Number—It is a proportionality between product of convective heat transfer rate factor and tube diameter (H
_{d}) to electrical properties.

- 4.
- Friction factor is proportionality between the product of tube’s total pressure decrease and corresponding Inner Tube Diameter equals the square of the average fluid velocity in the tube multiplied by density, characteristic linear dimension, and inner tube diameter. It is shown in use by ‘f’.

- 5.
- Thermal enhancement efficiency is to measure performance evaluation criteria (PEC) or Thermal figure of merit factor or Overall efficiency $\left(\eta \right)$ when pumping power is constant. It is defined as the ratio of Nu ratio $\left({{\displaystyle N}}_{uT}/{{\displaystyle N}}_{u0}\right)$ [Ratio of $\left({{\displaystyle N}}_{uT}\right)$ to $\left({{\displaystyle N}}_{u0}\right)$] to that of cubic root of friction factors ratio ${\left({{\displaystyle f}}_{T}/{{\displaystyle f}}_{0}\right)}^{{\scriptscriptstyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}$ [Ratio of friction factor with twisted tape insert (f
_{T}) to that of friction factor without twisted tape or plane tube (f_{0})] and calibrated using mathematical correlation: Thermal figure of merit factor or Overall efficiency $\left(\eta \right)$ or of performance evaluation criteria It fortifies stability of ‘Nu’ and (f) and also core emphasis will be put forth on modification of twisted tape(s) shapes.

_{e}) = Inner Tube Diameter, (u) = average fluid velocity, (ρ) = fluid density, (µ) = dynamic viscosity of fluid, (k) = thermal conductivity, (h) = convective heat transfer coefficient., (ΔP) = Pressure Drop, and (L

_{C}) = Characteristic Linear Length. The majority mean temperature for warm and chilled water is considered to be the average value of in and out temperature equation represents a number of formulae used in the current work.

## 5. Results and Discussions

#### 5.1. Validation of Experimental Setup

_{o}is unquestionably a meaning in relation to other inducing fundamentals, is to procedure dimple diameter to depth ratio (D/H) as a deterioration examination parameter and draw a graph among ln(A

_{o}) and (D/H) shown in Figure 3. This correlation was discovered using a second order deterioration investigation and optimal curve for the full summary.

_{0}) with the dimple Natural log scale diameter ln Diameter was visually shown in Figure 5, and the regression produced this equation as

_{0}) with the dimple Natural log scale diameter ln(D) was visually shown in Figure 6, and the regression produced this equation as

_{0}, may be used to write the final correlation

_{o}is greatly influenced by other geometrical factors. Now, using factor (D/H), rate of $\frac{f}{{\mathrm{Re}}^{-0.1521}}={A}_{0}$ is graphically shown in Figure 8, on a log-log scale as a purpose of (D/H).

_{0}) with the Diameter (D) ln(D) remained distinctly designed arranged usual graph shown in Figure 9, measurement and deterioration created this calculation.

_{0}, the final correlation can be expressed and shown in Figure 10.

#### 5.1.1. Impact of Dimple Diameter (D) and Dimple Diameter to Depth Ratio (D/H) on Heat Transfer

#### 5.1.2. Effect of Dimple Diameter and Dimple Diameter (D) to Depth Ratio (D/H) on Friction Factor

## 6. Conclusions

- i.
- According to the conclusions derived from this research, twisted tape inserts with dimple configurations significantly increased the values of the Nusselt number (Nu) and Reynolds number (Re) after a certain limit of Reynolds number (Re) in the experiments evaluated;
- ii.
- Correlations were developed for Nusselt number and friction factor and these correlations may be helpful for further applications;
- iii.
- This analysis makes it possible to investigate many different aspects in double-pipe heat exchangers with twisted tape inserts, and the following areas of research are suggested for future research:
- Experimental study of ‘Nu’ and ‘f’ in DPHE using dimpled configuration twisted tape with selected Nano fluid.
- Experimental study of heat transfer and friction factor in double pipe heat exchanger using conical dimpled configuration twisted tape.
- Analysis of Nusselt number and friction factor(f) in DPHE using dimpled configuration twisted strip with diverse twist ratio.
- Experimental study of ‘Nu’ and ‘f’ in DPHE using dimpled twisted tape of different length and at different locations.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Acronym | Description | Unit |

C_{P} | Specific heat at constant pressure | J/kg K |

C_{V} | Specific heat at constant volume | J/kg K |

e | Internal energy | J/kg |

E_{0} | Total energy | J/kg |

h | Enthalpy | J/kg |

k | Turbulent kinetic energy | J/kg = m^{2}/s^{2} |

p | Static pressure | Pa |

R | Specific gas constant | J/kg K |

t | Time | S |

T | Static temperature | K |

U^{*} | Friction velocity | m/s |

u_{i} | Velocity | m/s |

ε | Turbulence dissipation | J/kgs |

$\mu $ | Dynamic viscosity | N s/m^{2} |

V | Kinematic viscosity | M^{2/s} |

ρ | Density | Kg/m^{3} |

ω | Specific dissipation | s^{−1} |

Dimensionless parameters | ||

Parameter | Description | Description |

Nu | Nusselt number | hL/k |

Pr | Prandtl number | uC_{p/k} |

Re | Reynolds number | ρV L/μ |

Subscript | ||

t | Turbulent property | |

0 | Stagnation/total property | |

Superscript | ||

conv | Convective part | |

diff | Diffusive part | |

lam | Laminar part |

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**Figure 1.**Experiment Set-up. 1. Heater 2. Hot water tank 3. RTD-hot water in tank 4. Ball valve 5. Hot water pump 6. Hot water control valve 7. Flow meter (Turbine flow meter) 8. RTD-Hot water inlet 9. RTD-Hot water outlet 10. RTD-cold water inlet 11. RTD-Cold water outlet 12. U-Tube manometer 13. Cold water recover 14. Thermocouples 15. Data logger 16. Flow meter (Turbine flow meter) 17. Cold water control valve 18. Cold water pump 19. Ball valve 20. Cold water tank.

**Figure 11.**Experimental validation of Nusselt number Vs Reynolds number at various values of D/H ratio’s (1.5, 3 and 4.5) and different Dimple Diameter (2, 4 and 6 mm).

**Figure 12.**Experimental validation of Friction factor Vs Reynolds number at various values of D/H ratio’s (1.5, 3 and 4.5) and different Dimple Diameter (2, 4 and 6 mm).

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## Share and Cite

**MDPI and ACS Style**

Heeraman, J.; Kumar, R.; Chaurasiya, P.K.; Gupta, N.K.; Dobrotă, D.
Develop a New Correlation between Thermal Radiation and Heat Source in Dual-Tube Heat Exchanger with a Twist Ratio Insert and Dimple Configurations: An Experimental Study. *Processes* **2023**, *11*, 860.
https://doi.org/10.3390/pr11030860

**AMA Style**

Heeraman J, Kumar R, Chaurasiya PK, Gupta NK, Dobrotă D.
Develop a New Correlation between Thermal Radiation and Heat Source in Dual-Tube Heat Exchanger with a Twist Ratio Insert and Dimple Configurations: An Experimental Study. *Processes*. 2023; 11(3):860.
https://doi.org/10.3390/pr11030860

**Chicago/Turabian Style**

Heeraman, Jatoth, Ravinder Kumar, Prem Kumar Chaurasiya, Naveen Kumar Gupta, and Dan Dobrotă.
2023. "Develop a New Correlation between Thermal Radiation and Heat Source in Dual-Tube Heat Exchanger with a Twist Ratio Insert and Dimple Configurations: An Experimental Study" *Processes* 11, no. 3: 860.
https://doi.org/10.3390/pr11030860