# Electro-Kinetic Pumping with Slip Irreversibility in Heat Exchange of CSP-Powered Bio-Digester Assemblies

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Electro-Kinetic Phenomena

#### 2.1. Slip-Irreversibility

#### 2.2. Electro-Kinetic Pumping

_{d}, where:

## 3. Exergetic Analysis

#### 3.1. CSP-Powered Bio-Digester Subsystems

^{3}of biogas, which consists of 1 m

^{3}of methane. An energy audit of the university cafeteria and the energy input proposed for the integration of the CSP-powered bio-digester project was conducted by Ogedengbe et al. [28]. A multivariate energy consumption model was proposed as a significant design tool, based on an understanding of energy demand and the supply. Figure 5 shows the daily production of methane, based on the system efficiency of Mansour’s system. It implies that 319.77 kg of the food waste daily will produce 31.97 m

^{3}of methane daily from Monday to Saturday, while on Sunday 150.48 kg of food waste will produce 15.48 m

^{3}of methane, resulting in an estimated monthly methane production of 200 m

^{3}.

#### 3.2. Entropy-Based Finite Volume Approach

## 4. Numerical Analysis and Results

Flow parameter | Value |
---|---|

Length of micro-channels (μm) | 2560 |

Square size of micro-channels (μm) | 1.0 |

Dynamic viscosity of gas (Ns/m^{2}) | 0.0000164 |

Density of gas (kg/m^{3}) | 1.2498 |

Density of solid (kg/m^{3}) | 998.2 |

Specific gas constant of gas (J/kg K) | 296.8 |

Specific gas constant of solid (J/kg K) | 390 + 0.9T |

Outlet pressure (Pa) | 100800.0 |

Pressure ratio, P_{in}/P_{out} | 1.34 – 3.34 |

**Figure 6.**Velocity profile validation with slip boundary conditions (using a Non-Inverted Skew Upwind Scheme [NISUS]-based advection code [29]).

**Figure 10.**Entropy distribution with Reynolds number and size pertubation of the micro-channel at pressure ratio of (

**a**) 2.701; (

**b**) 3.00; and (

**c**) 3.34.

## 5. Conclusions

## Acknowledgements

## Nomenclature

${c}_{p}$ | specific heat at constant pressure (J/kg K) |

E | energy (J) |

${h}_{t}$ | specific enthalpy (J/kg) |

$H$ | height of the micro-channel (m) |

$k$ | thermal conductivity (J/kg K) |

${K}_{o}$ | conductivity at the reference temperature (W/mK) |

$\dot{m}$ | mass flow rate (kg/s) |

Pe | Peclet number |

$q$ | heat transfer rate (W) |

${q}^{\prime \prime \prime}$ | Joule heating (J) |

${\dot{Q}}_{O}$ | rate of heat outflow (J/s) |

${\dot{Q}}_{i}$ | rate of heat inflow (J/s) |

$s$ | specific entropy (J/K) |

${\dot{S}}_{gen}$ | entropy production rate (W/m K) |

${t}_{c}$ | thickness of micro-channel at the core section (m) |

${t}_{p}$ | thickness of micro-channel at the passage section (m) |

$T$ | temperature (K) |

$\mathrm{\Delta}T$ | temperature change (K) |

$u,v$ | velocity field (m/s) |

{U} | field variables |

$\dot{W}$ | work rate (J/s) |

${\dot{X}}_{d}^{\u2034}$ | exergy destruction rate (W per unit volume) |

## Greek

$\u03f5$ | applied electric field (V) |

ε | dielectric constant |

${\xi}_{1,}{\xi}_{2}$ | slip coefficients |

$\lambda $ | mean-free path |

$\mu $ | viscosity of fluid (Pa s) |

$\rho $ | density of fluid (kg/m ^{3}) |

$\sigma $ | momentum accommodation coefficient |

$\tau $ | dimensionless temperature difference |

$\mathsf{\psi}$ | induced charge |

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**MDPI and ACS Style**

Ogedengbe, E.O.B.; Rosen, M.A.
Electro-Kinetic Pumping with Slip Irreversibility in Heat Exchange of CSP-Powered Bio-Digester Assemblies. *Entropy* **2012**, *14*, 2439-2455.
https://doi.org/10.3390/e14122439

**AMA Style**

Ogedengbe EOB, Rosen MA.
Electro-Kinetic Pumping with Slip Irreversibility in Heat Exchange of CSP-Powered Bio-Digester Assemblies. *Entropy*. 2012; 14(12):2439-2455.
https://doi.org/10.3390/e14122439

**Chicago/Turabian Style**

Ogedengbe, Emmanuel O.B., and Marc A. Rosen.
2012. "Electro-Kinetic Pumping with Slip Irreversibility in Heat Exchange of CSP-Powered Bio-Digester Assemblies" *Entropy* 14, no. 12: 2439-2455.
https://doi.org/10.3390/e14122439