# Entropy Generation via Ohmic Heating and Hall Current in Peristaltically-Flowing Carreau Fluid

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{1}and y = W

_{2}because of the viscous dissipation effect. In addition, reducing the operating temperature minimizes the entropy.

## 1. Introduction

## 2. Mathematical Model and Analysis

#### 2.1. Flow Characteristics

#### 2.2. Fluid Model

#### 2.3. Development Problem

## 3. Analysis of Entropy Generation

## 4. Solution Methodology

#### 4.1. Zeroth Order System and Boundary Conditions

#### 4.2. First-Order System and Boundary Conditions

## 5. Discussion and Results

#### 5.1. Analysis of Entropy Generation $\left({N}_{ts}\right)$ and Bejan Number $\left({B}_{e}\right)$

#### 5.2. Analysis of Temperature

#### 5.3. Analysis of Velocity

#### 5.4. Analysis of the Pressure Gradient and the Rate of Heat Transfer

#### 5.5. Trapping Phenomenon

#### 5.6. Analysis of Entropy Generation Due to Heat Diffusion and Viscous Dissipation

## 6. Conclusions

- Entropy generation is not zero at the centerline y = 0.
- Heat irreversibility, at the bulk fluid region, is dominant, while at the edges, magnetic and viscous irreversibility dominates.
- The entropy generation profile is parabolic.
- Entropy production boosts for increasing values of the Hartman number and Brinkman number.
- Increasing the value of $\xi $, which is the temperature difference parameter, reduces both the entropy generation and Bejan number.
- Due to the resistive nature of the magnetic field ${B}_{0}$, the velocity profile decreases for the Hartman number, while for temperature, it increases.
- The velocity decreases due to the fluid’s Weissenberg number.
- The pressure gradient increases in a wider region for both the Hall parameter and the Hartman number.
- The number of closed circular stream lines encircling the bolus increases with an increase in the values of the Hall parameter.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Entropy generation ${N}_{ts}$ versus y for different values of ${M}_{f},{m}_{e},{B}_{r}\mathrm{and}\xi $ (

**a**–

**d**).

**Figure 3.**Bejan number ${B}_{e}$ versus $y$ for various ${M}_{f},{m}_{e},{B}_{r}\mathrm{and}\xi $ (

**a**–

**d**).

**Figure 4.**Temperature $\theta $ versus $y$ for different values of ${M}_{f},{m}_{e},{B}_{r},B{i}_{1},B{i}_{2}\mathrm{and}n$ (

**a**–

**f**).

**Figure 5.**(

**a**–

**c**) Velocity $u$ versus $y$ for different values of ${M}_{f},{m}_{e}\mathrm{and}{W}_{e}$.

**Figure 6.**(

**a**–

**c**) Pressure gradient $dp/dx$ versus x for different values of ${M}_{f},{m}_{e},\mathrm{and}{W}_{e}$.

**Figure 7.**(

**a–d**) Rate of heat transfer for different values of ${M}_{f},{m}_{e},{B}_{r}\mathrm{and}B{i}_{2}$.

**Figure 11.**(

**a**,

**b**) Entropy generation rate due to heat diffusion for different values of ${M}_{f}$ and ${W}_{e}$.

**Figure 12.**(

**a**,

**b**) Entropy generation rate due to the viscous dissipation effect for different values of ${M}_{f}$ and ${W}_{e}$.

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**MDPI and ACS Style**

Noreen, S.; Abbas, A.; Hussanan, A. Entropy Generation via Ohmic Heating and Hall Current in Peristaltically-Flowing Carreau Fluid. *Entropy* **2019**, *21*, 529.
https://doi.org/10.3390/e21050529

**AMA Style**

Noreen S, Abbas A, Hussanan A. Entropy Generation via Ohmic Heating and Hall Current in Peristaltically-Flowing Carreau Fluid. *Entropy*. 2019; 21(5):529.
https://doi.org/10.3390/e21050529

**Chicago/Turabian Style**

Noreen, Saima, Asif Abbas, and Abid Hussanan. 2019. "Entropy Generation via Ohmic Heating and Hall Current in Peristaltically-Flowing Carreau Fluid" *Entropy* 21, no. 5: 529.
https://doi.org/10.3390/e21050529