Significance of Convection and Internal Heat Generation on the Thermal Distribution of a Porous Dovetail Fin with Radiative Heat Transfer by Spectral Collocation Method
Abstract
:1. Introduction
2. Mathematical Formulation
Definition | Nondimensional Parameters |
---|---|
Convective–conductive parameter | |
Radiation number | |
Fin taper ratio | |
Heat generation parameter | |
Porosity parameter | |
Relative thermal conductivity | |
Heat generation number | |
Radiation–conduction parameter | |
Temperature ratio parameter |
3. Spectral Collocation Method Formulation
4. Results and Discussions
5. Conclusions
- SCM has an excellent agreement with the findings of available research, and to achieve precise results, only a few collocation points are required; thus, the technique is very effective in computation. This high level of accuracy suggests that the SCM is a viable alternative to other methods for solving fin problems with high nonlinearities.
- The thermal distribution through DF declines monotonically from the fin base to its tip, and the heat transfer rate in a porous fin is higher when compared to a nonporous fin.
- The temperature of the DF upsurges as the heat-generating number rises, which result in reduced heat flux.
- An increase in magnitude of the porosity parameter causes lower thermal dispensation and higher thermal flux in the fin.
- As the scale of the radiation number and convective–conductive parameter improves, the thermal distribution becomes lower and heat flux enhances through the dovetail fin.
- The increased magnitude of the temperature ratio parameter causes a decrement in the temperature distribution of the fin.
- The increment in the radiative–conductive variable leads to the upsurge of thermal dispersion and lessening of heat flux.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Kinematic viscosity | Heat generation parameter (dimensionless) | ||
Acceleration due to gravity | Fin’s thickness | ||
Fin taper ratio(dimensionless) | Temperature | ||
Heat transfer rate | Fin’s semithickness | ||
Fin’s width | Nondimensional temperature | ||
Convective heat transfer coefficient | Average velocity of the liquid passing through the fin | ||
Heat generation at ambient temperature | Specific heat | ||
Temperature ratio parameter (dimensionless) | Convection–conduction parameter (dimensionless) | ||
Stefan–Boltzmann constant | Thermal conductivity | ||
Radiation number (dimensionless) | Heat generation | ||
Emissivity | Porosity parameter (dimensionless) | ||
Fin’s length | Rosseland extinction coefficient | ||
Density | Heat generation number (dimensionless) | ||
Fin axial coordinate | Thermal expansion coefficient | ||
Length (dimensionless) | Subscripts | ||
Porosity | Ambient | ||
Mass flow rate | Base | ||
Radiation–conduction parameter (dimensionless) | Fluid | ||
Cross-sectional area | Solid | ||
Permeability | Effective properties |
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0 | 0.66972 | 0.32422 | ||||||
0.1 | 0.66394 | 0.33463 | ||||||
0 | 0.66264 | 0.33536 | ||||||
0.3 | 0.66652 | 0.33318 | ||||||
2 | 0.66394 | 0.33463 | ||||||
5 | 0.5071 | 0.47356 | ||||||
2 | 0.59196 | 0.3729 | ||||||
4 | 0.50587 | 0.40026 | ||||||
0.1 | 0.72743 | 0.28435 | ||||||
0.3 | 0.66394 | 0.33463 | ||||||
0 | 0.68813 | 0.31494 | ||||||
7 | 0.65494 | 0.34165 | ||||||
0.5 | 0.67332 | 0.32714 | ||||||
0.7 | 0.68322 | 0.32122 |
Gorila and Bakier [46] | Present Result | |||
---|---|---|---|---|
1 | 0.1 | 0.01 | 0.68610 | 0.68613 |
0.1 | 0.70210 | 0.70210 | ||
0.5 | 0.83890 | 0.83892 | ||
10 | 0.01 | 2.1763 | 2.1765 | |
0.1 | 2.6413 | 2.6415 | ||
0.5 | 5.4420 | 5.4423 | ||
10 | 0.1 | 0.01 | 2.5616 | 2.5616 |
0.1 | 2.5660 | 2.5660 | ||
0.5 | 2.6100 | 2.6100 | ||
10 | 0.01 | 3.2791 | 3.2792 | |
0.1 | 3.6059 | 3.6060 | ||
0.5 | 5.9690 | 5.9693 |
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Sowmya, G.; Lashin, M.M.A.; Khan, M.I.; Kumar, R.S.V.; Jagadeesha, K.C.; Prasannakumara, B.C.; Guedri, K.; Bafakeeh, O.T.; Mohamed Tag-ElDin, E.S.; Galal, A.M. Significance of Convection and Internal Heat Generation on the Thermal Distribution of a Porous Dovetail Fin with Radiative Heat Transfer by Spectral Collocation Method. Micromachines 2022, 13, 1336. https://doi.org/10.3390/mi13081336
Sowmya G, Lashin MMA, Khan MI, Kumar RSV, Jagadeesha KC, Prasannakumara BC, Guedri K, Bafakeeh OT, Mohamed Tag-ElDin ES, Galal AM. Significance of Convection and Internal Heat Generation on the Thermal Distribution of a Porous Dovetail Fin with Radiative Heat Transfer by Spectral Collocation Method. Micromachines. 2022; 13(8):1336. https://doi.org/10.3390/mi13081336
Chicago/Turabian StyleSowmya, G., Maha M. A. Lashin, M. Ijaz Khan, R. S. Varun Kumar, K. C. Jagadeesha, B. C. Prasannakumara, Kamel Guedri, Omar T Bafakeeh, El Sayed Mohamed Tag-ElDin, and Ahmed M. Galal. 2022. "Significance of Convection and Internal Heat Generation on the Thermal Distribution of a Porous Dovetail Fin with Radiative Heat Transfer by Spectral Collocation Method" Micromachines 13, no. 8: 1336. https://doi.org/10.3390/mi13081336
APA StyleSowmya, G., Lashin, M. M. A., Khan, M. I., Kumar, R. S. V., Jagadeesha, K. C., Prasannakumara, B. C., Guedri, K., Bafakeeh, O. T., Mohamed Tag-ElDin, E. S., & Galal, A. M. (2022). Significance of Convection and Internal Heat Generation on the Thermal Distribution of a Porous Dovetail Fin with Radiative Heat Transfer by Spectral Collocation Method. Micromachines, 13(8), 1336. https://doi.org/10.3390/mi13081336