# Numerical Simulation on Convection and Thermal Radiation of Casson Fluid in an Enclosure with Entropy Generation

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model

_{T}is thermal expansion coefficient. No viscous dissipation or Joule heating are counted.

## 3. Entropy Generation Analysis

## 4. Cup Mixing Temperature and RMSD

_{cup}) and area averaged temperature (T

_{avg}) are given as [32]

## 5. Numerical Technique and Validation

^{−6}. The justification of current computer program is tested against the existing results for buoyant convection in a box [33,34], see Table 1. An agreement between the results provides assurance in the accurateness of the current code to explore the problem.

## 6. Results and Discussion

^{4}. However, the Bejan number declines when raising the values of Rd for Gr = 10

^{6}. There is no difference on Bejan number when changing the values of Casson fluid parameter at high aspect ratios (Ar ≥ 3).

^{6}. However, the opposite trend is found for Gr = 10

^{4}in Figure 10a. The cup mixing temperature augments when increasing the thermal radiation for Gr = 10

^{6}, however, it declines when increasing the radiation for low values of Gr and low values of β (≤0.1). It is seen that the cup mixing temperature behaves nonlinearly with aspect ratio. That is, it is increasing rapidly initially and then declines gradually on raising the size of the box (aspect ratio). Figure 11a–d portrayed the impression of average temperature inside the box with various values of β, Rd, and Ar. The average temperature enhances while reducing the Casson fluid parameter. The average temperature augments when increasing the thermal radiation for Gr = 10

^{4}for all values of Casson fluid parameter, however, it declines when increasing the radiation for higher values of Gr except β = 0.01. It is seen that the average temperature behaves nonlinearly with aspect ratio. That is, it is declining rapidly first (until Ar = 1) and then rises gradually on raising the aspect ratio of the box. The tall and slender cavities behave in different manner.

_{Tcup}inside the box with various values of β, Rd, and Ar. The RMSD

_{Tcup}enhances while reducing the Casson fluid parameter. The RMSD

_{Tcup}augments by increasing the thermal radiation for all values of Casson fluid parameter and Gr. It is perceived that the RMSD

_{Tcup}temperature performs nonlinearly with aspect ratio. RMSD

_{Tcup}declines rapidly first (until Ar = 1/2) for some cases and then rises gradually on raising the aspect ratio of the box. Figure 13a–d demonstrated the impact of RMSD

_{Tavg}inside the box with various values of β, Rd, and Ar. The RMSD

_{Tavg}augments while the Casson fluid parameter falls. The RMSD

_{Tavg}enhances by rising the thermal radiation for all values of Casson fluid parameter and Gr. It is perceived that the RMSD

_{Tavg}achieves nonlinear fashion with aspect ratio. RMSD

_{Tavg}declines rapidly first (until Ar = 0.5) for some cases and then rises gradually on raising the aspect ratio of the box.

## 7. Conclusions

- ○
- Strong thermal layers at boundary are formed along the thermal walls.
- ○
- Thermal stratification found for higher values of β (= 1) for all values of radiation parameter.
- ○
- Skin friction develops with aspect ratio, thermal radiation, and Casson fluid parameter.
- ○
- The kinetic energy enhances with aspect ratio, thermal radiation, and Casson fluid parameter.
- ○
- Averaged heat transfer enhances with thermal radiation and Casson fluid parameter. However, it increases first and then declines when growing the aspect ratio of the box.
- ○
- The Bejan number enhances with Casson fluid parameter and declines with Ar.
- ○
- The cup mixing and average temperature behaves in a nonlinear fashion with aspect ratio of the box.
- ○
- The RMSD
_{Tavg}augments while the Casson fluid parameter falls and it enhances by rising the thermal radiation. - ○
- The RMSD
_{Tcup}enhances while reducing the Casson fluid parameter and it augments by growing the thermal radiation.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Streamlines for diverse values of radiation and Casson fluid parameters with Gr = 10

^{6}, Ar = 1.

**Figure 3.**Isotherms for diverse values of radiation and Casson fluid parameters with Gr = 10

^{6}, Ar = 1.

**Figure 7.**Local Nusselt number for different values of Casson liquid parameter with Rd = 0 and 5 Gr = 10

^{6}, Ar = 1.

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**MDPI and ACS Style**

Alzahrani, A.K.; Sivasankaran, S.; Bhuvaneswari, M.
Numerical Simulation on Convection and Thermal Radiation of Casson Fluid in an Enclosure with Entropy Generation. *Entropy* **2020**, *22*, 229.
https://doi.org/10.3390/e22020229

**AMA Style**

Alzahrani AK, Sivasankaran S, Bhuvaneswari M.
Numerical Simulation on Convection and Thermal Radiation of Casson Fluid in an Enclosure with Entropy Generation. *Entropy*. 2020; 22(2):229.
https://doi.org/10.3390/e22020229

**Chicago/Turabian Style**

Alzahrani, A. K., S. Sivasankaran, and M. Bhuvaneswari.
2020. "Numerical Simulation on Convection and Thermal Radiation of Casson Fluid in an Enclosure with Entropy Generation" *Entropy* 22, no. 2: 229.
https://doi.org/10.3390/e22020229