Effect of aspect ratio on entropy generation in a rectangular cavity with differentially heated vertical walls

TLDR: In this article, the entropy generation in rectangular cavities with the same area but different aspect ratios is numerically investigated and the variation of the total entropy generation and average Bejan number for the whole cavity volume at different aspects ratios for different values of the Rayleigh number and irreversibility distribution ratio are also evaluated.

About: This article is published in International Communications in Heat and Mass Transfer.The article was published on 2008-07-01 and is currently open access. It has received 291 citations till now. The article focuses on the topics: Bejan number & Rayleigh number.

Figures

Fig. 4. Isotherm, streamline and entropy generation contours for a cavity with AR=1, Φ=10−4 and Ra=105 a) isotherms b) streamlines c) local entropy generation due to heat transfer d) local entropy generation due to fluid friction e) local entropy generation f) local Bejan number.

Fig. 5. Isotherm, streamline and entropy generation contours for a cavity with AR=16, Φ=10−4 and Ra=105 a) isotherms b) streamlines c) local entropy generation due to heat transfer d) local entropy generation due to fluid friction e) local entropy generation f) local Bejan number.

Fig. 6. Variation of total entropy generation and Bejan number with aspect ratio for different values of Ra number and Φ=10−4 a) total entropy generation due to heat transfer b) total entropy generation due to fluid friction, c) total entropy generation d) average Bejan number.

Fig. 1. A schematic view of the considered problem.

Fig. 8. The changes of total entropy generation with Rayleigh number for cavities with different aspect ratios a) Φ=10−4, b) Φ=10−2.

Fig. 7. Variation of total entropy generation and Bejan number with aspect ratio for different values of Ra number and Φ=10−2 a) total entropy generation due to heat transfer b) total entropy generation due to fluid friction, c) total entropy generation d) average Bejan number.

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Effect of aspect ratio on entropy generation in a rectangular cavity with differentially heated vertical walls" ?

In the present study, entropy generation in rectangular cavities with the same area but different aspect ratios is numerically investigated. The present results are compared with reported solutions and excellent agreement is observed. The study is performed for 10bRab10, 10bφb10, and Pr=0. 

Q2. What is the behavior of St.h.t with aspect ratio?

For low Rayleigh numbers (i.e., Ra=102, 103), St.h.t almost varies linearly with aspect ratio; though a non-linear behavior appears for high Rayleigh number due to development of the fluid flow. 

Q3. How are the energy and vorticity equations solved?

The energy and vorticity equations are solved line by line by employing the ADI method, whereas the stream function equation is solved point by point. 

Q4. What is the second law of thermodynamics applied to cavity problems?

The second law of thermodynamics has been applied to cavity problems to determine entropy generations due to heat and flow transport in the cavity and consequently minimize the entropy generation. 

Q5. What is the effect of the increase of the bejan number?

An increase of the irreversibility ratio pulls down the average Bejan number curves since the fluid friction irreversibility is increased. 

Q6. What is the entropy generation rate in an inclined square enclosure?

Based on that study, the local heat transfer irreversibility and the local fluid friction irreversibility change by the inclination angle and the minimum entropy generation depends considerably on the inclination. 

Q7. What is the value of the average Bejan number?

For low Ra numbers (i.e., Rab104), the value of the average Bejan number is greater than 1/2 (BeavN1/2), which shows the strong heat transfer irreversibility in the major part of the cavity. 

Q8. What is the maximum value of local entropy generation due to heat transfer?

Themaximum local entropy generation due to heat transfer is (Sl.h.t)max=2.27 while the maximum value of local fluid friction entropy generation is (Sl.f.f)max=0.25. 

Q9. What is the entropy generation rate for the cavity with different aspect ratio?

8. For Ra=100, the total entropy generationincreases from theminimum aspect ratio (AR=1) to the maximum aspect ratio (AR=16) with the same order. 

Q10. What is the entropy generation rate in a square enclosure?

The isotherms, streamlines and their corresponding local entropy generation maps are plotted to supply useful information for minimizing the entropy generation in rectangular cavities. 

Q11. Who solved the transient state of entropy generation in a square cavity?

The transient state of entropy generation for laminar natural convection in a square cavity with heated vertical walls was numerically solved by Magherbi et al.☆