Investigation of the Stretching/Shrinking of a Convective-Radiative Radial Fin

Ullah, Sharif; De la Sen, Manuel; Ali, Amir; Din, Zia Ud

doi:https://doi.org/10.1155/2023/2044273

International Journal of Energy Research

On this page

Abstract Introduction Results and Discussion Conclusion Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 2044273 | https://doi.org/10.1155/2023/2044273

Investigation of the Stretching/Shrinking of a Convective-Radiative Radial Fin

Sharif Ullah,¹Manuel De la Sen,²Amir Ali,¹and Zia Ud Din¹

Academic Editor: Mumtaz Ahmad Qaisrani

Received20 May 2023

Revised28 Sept 2023

Accepted27 Oct 2023

Published04 Dec 2023

Abstract

Fins are extended surfaces that increase the surface area for heat transfer between a hot source and an ambient fluid. Heat transfer is increased by adding radial or concentric annular fins to the outside surface of a circular conduit. The fins are used in devices that exchange heat such as car radiators, electrical equipment, and heat exchangers. Based on these applications, the current article examines a stretching/shrinking convective-radiative radial fin. Additionally, parameters such as the Peclet number, surface temperature, and ambient temperature are taken into account. The shooting technique is used to investigate the thermal profile, fin’s tip temperature, and efficiency of the radial fin. It is revealed that the thermal profile enhances with stretching, the Peclet number, surface temperature, and ambient temperature, while declining with radiative and convective parameters. It is observed that the radial fin’s tip temperature versus stretching/shrinking increases with increasing values of the Peclet number and ambient and surface temperatures, but the fin’s tip temperature diminishes with increasing convective and radiative parameters. Additionally, when the radiative and convective parameters increase, efficiency also increases. However, when the Peclet number, surface temperature, and ambient temperature increase, the efficiency decreases. As a result of increasing the convection parameter from 0.1 to 0.3, the temperature distribution increases about 7%, and an increase of 5% in temperature distribution is achieved by increasing the radiation parameter from 0.1 to 0.3, and when the peclet number is increased from 0.3 to 0.8, the temperature distribution decreases by approximately 0.5%. It is also revealed that when the shrinking effect is exposed to a stretching/shrinking moving fin along with the radiative parameter, the thermal performance of the radial fin improves. From the results, it is concluded that stretching/shrinking radial fins improves efficiency and performance. Finally, a comparative study has also been made between the present and published results, and for every case study, superiority of results obtained from the present model is noticed and the degree of supremacy increases with the increase in condensation rate of vapor on fin surfaces.

1. Introduction

In various industrial processes, including nanofluids and cooling fluids, an extended surface (known as the fin) in various geometrical shapes has extensively been used to improve the heat exchange mechanism. The fins have a prominent role in various technological systems and machines, such as air conditioning, computer processors, refrigeration, power plants, electrical chips, automobile radiators, and cryogenic processes [1, 2].

To increase heat transmission and improve the efficiency and performance of several engineering appliances, researchers have analyzed various fin profiles. For example, the thermal exchange analysis of radiating rectangular-shaped fins with convection has been performed by employing computational fluid dynamic enhancement to study the collective properties of fin length, height, and spacing on heat transfer [3]. Similarly, the thermal exchange efficiency of a radiating rectangular fin has been examined, showing that neglecting the thermal radiation effect will reduce the fin’s capacity for dissipating heat and, as a result, their performance [4]. This influence particularly affects fins made of copper and aluminium. The trapezoidal-shaped and exponential-type fins with multiple nonlinearities have been discussed numerically, which revealed that the heat transfer and productivity of the exponential fins are greater than those of the trapezoidal fin [5, 6]. Besides convection, heat transfer through radiation is another prominent kind of mechanism. By considering the radiative parameter, various methods have been developed to determine the thermal dissipation from the different radiative fins. Numerous radiative fins have been studied by the differential transform method (DTM) technique [7–9]. Similarly, a variational iteration method [10], spectral collocation method [11], and the least squares method [12] have also been proposed to study the radiative parameter.

Heat exchange analysis through a porous extended surface is very important and applicable in thermal systems. Porous media are a popular research topic because of how well they transport heat. According to [13], porous materials are widely used in a variety of engineering applications, including heat dissipation, solar thermal collectors, and cooling reactors. Investigating porous cylindrical fins with the Runge-Kutta method has demonstrated that they have a higher thermal transmission rate than solid fins [14]. Furthermore, the author observed that raising the convection parameter increased heat transfer from the fin. An efficient DTM has been proposed in order to analyze the thermal properties of triangular-shaped fins, taking into account porosity at the same time [15, 16]. The DTM has been applied to visualize the heat transfer behaviour of porous exponential fin along with rectangular porous fin [17]. Higher porosity and a dimensionless time parameter result in rapid heat dissipation from the fin to the surrounding air. Furthermore, an exponential profile with a hostile power factor shows a much higher heat transfer rate than a rectangular profile. Various parameters involved in the analysis were considered when analyzing temperature distributions, fin effectiveness, and fin efficiency. Fin performance increases due to the porous constraint. According to [18, 19], a rectangular-shaped porous fin was investigated for heat transfer and validation. It was observed that efficiency increases with increasing porosity, convection, and radiation-surrounding parameters.

Thermal behaviour and effectiveness of stretching/shrinking moving rectangular fin problem with convection have been reported in [20]. It has been demonstrated that stretching reduces fin efficiency while shrinking improves fin efficiency, pointing to important benefits for fin design. The stretching/shrinking mechanism in exponential shape was numerically presented by [21]. The cooling effect of the fin is found to be significantly enhanced by the shrinking mechanism, particularly while the fin is moving. The stretching/shrinking phenomenon was considered for moving fins having different profiles [22, 23]. It is observed that by increasing stretching/shrinking, the Peclet number, surface and ambient temperatures, and convection and radiation parameters, the temperature distribution rises.

Radial or concentric circular fins are used to increase the heat transfer rate from the outside of circular conduits. This type of fins is often used in cross-flow thermal exchangers with finned tube. It can be found in a various heat exchange devices, such as superheaters, refrigeration, computer CPU, car radiators, heat exchangers, and electrical equipment. The thermal aspects of annular fins, its fin efficiency, and its heat transfer were described by [24]. [25] evaluated the thermal characteristics of a wetted annular fin under dehumidifying conditions. With the exact method, [26] studied thermal distribution through annular fin arrays. A DTM study was conducted by [27] to evaluate the extreme heat transfer rate of annular fins under radiation effect. The numerical investigation of a radiating radial-shaped porous fin subject to convection and motion has been conducted [28–30]. It is observed that the higher values of the convective parameter and the radiative parameter improve the rate of heat transfer from the fin surface. The thermal profile is lower for smaller values of the Peclet number and the exponent associated with the convective heat exchange coefficient. The porous media has been considered in radial fins for high thermal capability [31, 32]. The efficiency of radial fins with porous media has been numerically interpreted in [33]. There has been a recent comparison between a wavy fin configuration and a straight fin array [34, 35]. Heat transfer rates between wavy and straight fins were close at low temperatures, according to the results. However, the wavy fin’s efficiency increased by roughly 28% at higher temperatures. Heat transfer is enhanced by radial fins or concentric annular fins attached to the exterior surface of circular conduits. As motivation for these applications, the present study considered stretching/shrinking mechanism in convective-radiative moving radial fin. The governing equation is nondimensionalized by introducing dimensionless parameters and then obtaining the numerical solution by applying the shooting technique to analyze the influence of various parameters on stretching/shrinking moving radial fin [36, 37].

2. Mathematical Formulation

Considering thermal transfer in a stretching/shrinking radial (circular) fin of cross-section area varies with the function (thickness of fin) involving radiation and convection shown in Figure 1. Let the base radius, tip radius, thickness, base temperature, convective coefficient, surface temperature, density, emissivity, permeability, thermal conductivity, Stefan-Boltzmann constant, temperature distribution, and ambient temperature of fin be represented by , , , , , , , , , , , , and , respectively. The fin is subjected to the condition of both moving and stretching/shrinking in horizontal direction with a speed . Here, is the radius, represents the local speed, and denotes the rate of stretching/shrinking.

The energy balanced equation is then given by [20]

Fourier’s law related to conduction is given by [38]

Utilizing Eq. (2) in Eq. (1) and after simplification, we get

The boundary conditions for the base and tip of fin can be written as follows:

Introducing the following dimensionless parameters,

Eq. (3) and Eq. (4) take the following nondimensional form by introducing the above dimensionless terms of Eq. (5): with boundary conditions where is the temperature ratio, is the surface radiation parameter, indicates the Peclet number, is the convection-conduction parameter, and denotes the stretching/shrinking parameter.

The fin’s efficiency states the diminishing in temperature potential between the surrounding and the fin. The fin efficiency is indicated by that can be obtained by the ratio of total thermal exchange of the fin and its maximum thermal exchange. The efficiency for a radial fin is given by

Eq. (6) reveals that the thermal distribution and fin efficiency varies with six parameters, which are radiation parameter , stretching/shrinking parameter , convection parameter , and the Peclet number . We apply the shooting method to solve the problem. A boundary value problem (BVP) is divided into initial value problems (IVPs) using the shooting approach. As a general approach, we shoot out trajectory paths in different directions until we find one with an appropriate boundary value. Our first step is to develop the Dirichlet BVP for a second-order linear differential equation. in the interval . In order to solve this boundary value problem, the functions and are usually combined, since they are solutions to initial value problems. where is an IVP solution. and a solution to another initial value problem is :

3. Results and Discussion

Here, we examine the thermal transfer versus radius of fin, the temperature of the radial fin’s tip , and the radial fin’s efficiency considering stretching/shrinking radiative radial fin along with convection. The thermal profile versus ranges from 0 to 1 for considered physical parameters as shown in Figures 2 and 3.

(a)

(b)

(c)

(a)

(b)

(c)

The thermal profile increases by stretching from 0.3 to 0.5 and decays by enhancing the shrinking from 0.3 to 0.5 of the fin, as demonstrated in Figure 2(a). Figure 2(b) reveals that the thermal profile clearly diminishes when the convective parameter enhances from 0.3 to 0.8, because heat carried from the fin’s surface is exceeded by increasing convection. Hence, the temperature profile steps down. The thermal distribution is further reduced by increasing the radiative parameter from 0.3 to 0.8, as shown in Figure 2(c). In fact, increasing the value of increases heat exchange from the surface to the surrounding air, and thus, the temperature decreases as the radiative parameter increases.

The thermal distribution behaviour is shown in Figures 3(a) and 3(b) by varying the values of ambient temperature () and surface temperature (). When and changes from to , the thermal profile grows because heat exchange through convection from the radial fin’s surface decreases and the temperature rises. Similarly, Figure 3(a) shows the effect of a rising Peclet number, , from 0.5 to 0.9, which enhances the thermal distribution. Physically, increasing the Peclet number means increasing the fin’s speed and decreasing the time for interaction between the surrounding environment and the surface of the radial fin, resulting in a higher temperature. Increasing the convection-conduction number from 0.1 to 0.3 results in an increase of temperature distribution of about 7% as shown in Figure 2(b). According to Figure 2(c), an increase of 5% in temperature distribution is achieved by increasing the radiation-conduction number from 0.1 to 0.3. In the case of increasing surface temperature from 0.3 to 0.8, the temperature distribution decreases by approximately 8% as presented in Figure 3(a). In Figure 3(b), temperature distribution decreases by approximately 8% when surrounding temperature increases from 0.3 to 0.8. Similarly, it is estimated that the temperature distribution decreases by approximately 0.5% when the Peclet number is increased from 0.3 to 0.8 as demonstrated in Figure 3(c).

Furthermore, the effects of various parameters are compared to published work [21]. It can be visualized that the thermal profile of the exponential fin decays by increasing shrinking, while the thermal profile grows by increasing stretching. In the present work, Figure 2(a) demonstrates that fin’s thermal profile drops when shrinking grows from 0.3 to 0.5 but opposite result occurs by enhancing stretching from 0.3 to 0.5. In [23], the thermal profile of the rectangular fin diminishes with increasing convection and radiation parameters but increases with increased surface temperature parameter, the Peclet number, and ambient temperature parameter. Here, Figures 2(b) and 3(c) of the present work reveal the same outcome for the radial fin.

The radial fin’s tip temperature rate versus the behaviour of the nondimensional stretching/shrinking parameter, which ranges from 0 to 1, is illustrated in Figures 4 and 5. These figures clearly show that the tip temperature of a radial fin increases monotonically as the surface thermal distribution of the fin increases. Figure 4(a) reveals the growing rate of the fin’s tip temperature by the behaviour of enhancing the value of from 0.1 to 0.5, while the result is the opposite for increasing and from 0.1 to 0.5. This means the fin’s tip temperature drops, as seen in Figures 4(b) and 5(c). Figures 5(a) and 5(b) anticipated the effect on temperature of the radial fin’s tip versus the stretching/shrinking parameter because of the growing ambient temperature and the surface temperature changes from 0.1 to 0.3. It is visualized that fins’ temperatures ameliorate when the values of and increase.

(a)

(b)

(c)

(a)

(b)

Similarly, the fin’s tip temperature rate of the stretching radial fin versus the behaviour of radiative parameter ranging from 0 to 1 is illustrated in Figures 6 and 7. From these figures, one can see that the fin’s tip temperature continuously drops as the radiative parameter value increases from 0 to 1. Figure 6(a) depicts the behaviour of ; that is, when the value of shrinking changes from 0.1 to 0.3, the fin’s tip temperature drops, and for stretching, the result is incompatible. The consequence of augmenting from 0.1 to 0.3 is to boost the fin’s tip temperature, as visualized in Figure 6(b). The repercussion of increasing from 0.3 to 0.7 leads to the decay of the fin’s temperature, while the converse consequence is for boosting the value of from 0.3 to 0.7 as anticipated in Figures 7(a) and 7(b).

(a)

(b)

(a)

(b)

The efficiency () of the radial fin versus stretching and shrinking parameters ranging from 0 to 1 is shown in Figures 8 and 9 under the influence of the physical parameters considered (, , , , and ). Clearly, these figures show that the efficiency () of fins increases with increased shrinking and decreases with increased stretching. The behaviour of increasing the value of and from 0.1 to 0.5 progressively step up the fin’s efficiency as visualized in Figures 8(a) and 8(b), while the efficiency increases continuously with escalating , , and from to as shown in Figures 8(c), 9(a) and 9(b).

(a)

(b)

(c)

(a)

(b)

Further, the fin’s efficiency versus the outcome of radiative parameter ranging from 0 to 1 is illustrated in Figures 10 and 11. The aforementioned figures present the efficiency of radial fin incrementing rapidly for augmenting and also for enhancing from 0.1 to 0.5 as shown in Figure 10(a). But, the role of escalating , , and from 0.1 to 0.5 is contrasted for the fin’s effectiveness as observed in Figures 10(b), 11(a) and 11(b). The aforesaid behaviour of stretching/shrinking radial fins with radiation showed that the radial fin shrinking effect yielded higher thermal exchange, efficiency, and preferable economic results as compared to stretching radial fins.

(a)

(b)

(a)

(b)

4. Conclusion

The thermal transmission of stretching/shrinking and moving radial fin including convection and radiation effects is performed. The numerical shooting method is used to investigate the thermal profile, fin tip temperature, and efficiency of the radial fin model, and the effects of the included parameters are plotted graphically. It is revealed that the thermal profile enhancement takes place with stretching, the Peclet number, surface temperature, and ambient temperature, while the thermal profile declines with growing radiative and convective parameters. The radial fin’s tip temperature versus stretching/shrinking is elevated by the growing values of the Peclet number, ambient temperature, and surface temperature, but the fin’s tip temperature diminishes with enhanced convective and radiative parameters. The efficiency of the radial fin increases with shrinking and decreases with stretching. Furthermore, the efficiency increases with a growing radiative parameter and convective parameter, but the efficiency decays with an enhanced Peclet number, surface temperature, and ambient temperature. It is concluded that when the shrinking effect is subjected to a stretching/shrinking moving fin along with the radiative parameter, the thermal performance and effectiveness of the considered radial fin are improved and better for desirable economic purposes as compared to stretching radial fin.

Nomenclature

:	Radiation parameter
:	Specific heat coefficient
:	Nondimensional temperature of the fin
:	Nondimensional radius
:	Convective heat coefficient
:	Thermal conductivity number
:	Dimensionless base temperature
:	Density of material (kg/m³)
:	Rate of stretching/shrinking
:	Peclet number
:	Stretching/shrinking parameter
:	Dimensional ambient temperature (K)
:	Radius of fin
:	Dimensional surface temperature (K)
:	Surface emissivity
:	Base radius of fin
:	Fin efficiency
:	Area of fin’s surface (m²)
:	Ratio of thermal conductivity
:	Temperature of fin tip
:	Nondimensional surrounding temperature
:	Thickness of fin
:	Fin base temperature
:	Speed of moving fin
:	Fins length (m)
:	Stefan-Boltzmann constant (W/m²K⁴)
:	Convection parameter
:	Fin temperature (K)
:	Tip radius of fin
:	Nondimensional surface temperature.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors are grateful to the Basque Government for its support through Grants IT1555-22 and KK-2022/00090 and to MCIN/AEI 269.10.13039/501100011033/FEDER, UE for Grants PID2021-1235430B-C21 and PID2021-1235430B-C22.

References

A. D. Kraus, A. Aziz, and J. Welty, Extended Surface Heat Transfer, John Wiley, Inc., New York, NY, USA, 2000.
S. Kalpakjian, Manufacturing Engineering and Technology, Pearson Education, India, 2001.
R. C. Adhikari, D. H. Wood, and M. Pahlevani, “Optimizing rectangular fins for natural convection cooling using CFD,” Thermal Science and Engineering Progress, vol. 17, article 100484, 2020.
View at: Publisher Site | Google Scholar
T. S. Mogaji and F. D. Owoseni, “Numerical analysis of radiation effect on heat flow through fin of rectangular profile,” American Journal of Engineering Research, vol. 6, 2017.
View at: Google Scholar
M. Turkyilmazoglu, “Heat transfer from moving exponential fins exposed to heat generation,” International Journal of Heat and Mass Transfer, vol. 116, pp. 346–351, 2018.
View at: Publisher Site | Google Scholar
Z. U. Din, A. Ali, Z. A. Khan, and G. Zaman, “Investigation of moving trapezoidal and exponential fins with multiple nonlinearities,” Ain Shams Engineering Journal, vol. 14, no. 5, article 101959, 2023.
View at: Publisher Site | Google Scholar
M. Torabi, H. Yaghoobi, and A. Aziz, “Analytical solution for convective-radiative continuously moving fin with temperature-dependent thermal conductivity,” International Journal of Thermophysics, vol. 33, no. 5, pp. 924–941, 2012.
View at: Publisher Site | Google Scholar
S. Mosayebidorcheh and T. Mosayebidorcheh, “Series solution of convective radiative conduction equation of the nonlinear fin with temperature dependent thermal conductivity,” International Journal of Heat and Mass Transfer, vol. 55, no. 23-24, pp. 6589–6594, 2012.
View at: Publisher Site | Google Scholar
A. Aziz, M. Torabi, and K. Zhang, “Convective-radiative radial fins with convective base heating and convective-radiative tip cooling: homogeneous and functionally graded materials,” Energy Conversion and Management, vol. 74, pp. 366–376, 2013.
View at: Publisher Site | Google Scholar
M. Miansari, D. D. Ganji, and M. Miansari, “Application of He's variational iteration method to nonlinear heat transfer equations,” Physics Letters, vol. 372, no. 6, pp. 779–785, 2008.
View at: Publisher Site | Google Scholar
J. Ma, Y. Sun, and B. Li, “Simulation of combined conductive, convective and radiative heat transfer in moving irregular porous fins by spectral element method,” International Journal of Thermal Sciences, vol. 118, pp. 475–487, 2017.
View at: Publisher Site | Google Scholar
A. R. Shateri and B. Salahshour, “Comprehensive thermal performance of convection-radiation longitudinal porous fins with various profiles and multiple nonlinearities,” International Journal of Mechanical Sciences, vol. 136, pp. 252–263, 2018.
View at: Publisher Site | Google Scholar
M. K. Alkam and M. A. Al-Nimr, “Solar collectors with tubes partially filled with porous substrates,” Journal of Solar Energy Engineering, vol. 121, no. 1, pp. 20–24, 1999.
View at: Publisher Site | Google Scholar
S. Saedodin and S. Sadeghi, “Temperature distribution in long porous fins in natural convection condition,” Middle-East Journal of Scientific Research, vol. 13, no. 6, pp. 812–817, 2013.
View at: Google Scholar
M. Hatami, A. Hasanpour, and D. D. Ganji, “Heat transfer study through porous fins (Si₃N₄ and AL) with temperature- dependent heat generation,” Energy Conversion and Management, vol. 74, pp. 9–16, 2013.
View at: Publisher Site | Google Scholar
A. Moradi, T. Hayat, and A. Alsaedi, “Convection-radiation thermal analysis of triangular porous fins with temperature-dependent thermal conductivity by DTM,” Energy Conversion and Management, vol. 77, pp. 70–77, 2014.
View at: Publisher Site | Google Scholar
P. Ndlovu and R. Moitsheki, “Thermal analysis of natural convection and radiation heat transfer in moving porous fins,” Frontiers in Heat and Mass Transfer, vol. 12, 2019.
View at: Publisher Site | Google Scholar
S. Hoseinzadeh, A. Moafi, A. Shirkhani, and A. J. Chamkha, “Numerical validation heat transfer of rectangular cross-section porous fins,” Journal of Thermophysics and Heat Transfer, vol. 33, no. 3, pp. 698–704, 2019.
View at: Publisher Site | Google Scholar
I. Ullah, S. Ullah, A. Ali, S. I. Shah, W. Weera, and M. M. Alam, “Heat transfer analysis from moving convection-radiative triangular porous fin exposed to heat generation,” Case Studies in Thermal Engineering, vol. 38, article 102177, 2022.
View at: Publisher Site | Google Scholar
M. Turkyilmazoglu, “Stretching/shrinking longitudinal fins of rectangular profile and heat transfer,” Energy Conversion and Management, vol. 91, pp. 199–203, 2015.
View at: Publisher Site | Google Scholar
B. J. Gireesha, M. L. Keerthi, and G. Sowmya, “Effects of stretching/shrinking on the thermal performance of a fully wetted convective-radiative longitudinal fin of exponential profile,” Applied Mathematics and Mechanics, vol. 43, no. 3, pp. 389–402, 2022.
View at: Publisher Site | Google Scholar
M. Mosavat, R. Moradi, M. Rahimi Takami, M. Barzegar Gerdroodbary, and D. D. Ganji, “Heat transfer study of mechanical face seal and fin by analytical method,” Engineering Science and Technology, vol. 21, pp. 380–388, 2018.
View at: Google Scholar
Z. U. Din, A. Ali, S. Ullah, G. Zaman, K. Shah, and N. Mlaiki, “Investigation of heat transfer from convective and radiative stretching/shrinking rectangular fins,” Mathematical Problems in Engineering, vol. 2022, Article ID 1026698, 10 pages, 2022.
View at: Publisher Site | Google Scholar
A. Campo and B. Kundu, “Exact analytic heat transfer from an annular fin with stepped rectangular profile,” American Journal of Heat and Mass Transfer, vol. 4, pp. 146–155, 2017.
View at: Publisher Site | Google Scholar
B. Kundu and D. Barman, “Analytical study on design analysis of annular fins under dehumidifying conditions with a polynomial relationship between humidity ratio and saturation temperature,” International Journal of Heat and Fluid Flow, vol. 31, no. 4, pp. 722–733, 2010.
View at: Publisher Site | Google Scholar
B. Kundu, K. S. Lee, and A. Campo, “Exact and approximate analytic methods to calculate maximum heat flow in annular fin arrays with a rectangular step profile,” International Journal of Thermophysics, vol. 33, no. 7, pp. 1314–1333, 2012.
View at: Publisher Site | Google Scholar
B. Kundu and K. S. Lee, “Analytical tools for calculating the maximum heat transfer of annular stepped fins with internal heat generation and radiation effects,” Energy, vol. 76, pp. 733–748, 2014.
View at: Publisher Site | Google Scholar
B. J. Gireesha, G. Sowmya, and M. Nikitha, “Numerical investigation of natural convection and radiation in a moving radial porous fin,” Journal of Engineering and Management, vol. 4, no. 1, 2020.
View at: Publisher Site | Google Scholar
R. S. V. Kumar, I. E. Sarris, G. Sowmya, J. K. Madhukesh, and B. C. Prasannakumara, “Effect of electromagnetic field on the thermal performance of longitudinal trapezoidal porous fin using DTM–Pade approximant,” Heat Transfer, vol. 51, no. 4, pp. 3313–3333, 2022.
View at: Publisher Site | Google Scholar
R. S. Varun Kumar, G. Sowmya, M. C. Jayaprakash et al., “Assessment of thermal distribution through an inclined radiative-convective porous fin of concave profile using generalized residual power series method (GRPSM),” Scientific Reports, vol. 12, no. 1, pp. 1–14, 2022.
View at: Publisher Site | Google Scholar
M. Hatami and D. D. Ganji, “Thermal and flow analysis of microchannel heat sink (MCHS) cooled by Cu-water nanofluid using porous media approach and least square method,” Energy Conversion and Management, vol. 78, pp. 347–358, 2014.
View at: Publisher Site | Google Scholar
R. J. Moitsheki, M. M. Rashidi, A. Basiriparsa, and A. Mortezaei, “Analytical solution and numerical simulation for one-dimensional steady nonlinear heat conduction in a longitudinal radial fin with various profiles,” Heat Transfer—Asian Research, vol. 44, no. 1, pp. 20–38, 2015.
View at: Publisher Site | Google Scholar
M. Hatami and D. D. Ganji, “Investigation of refrigeration efficiency for fully wet circular porous fins with variable sections by combined heat and mass transfer analysis,” International Journal of Refrigeration, vol. 40, pp. 149–154, 2014.
View at: Google Scholar
J. O. Okon and S. O. Effiom, “Numerical simulation of the thermal performance of a wavy fin configuration for a straight fin array,” Scientific African, vol. 16, article e01265, 2022.
View at: Publisher Site | Google Scholar
A. Moradian, M. Ameri, and S. Majidi, “Melting expedition in horizontal triplex tube heat exchangers via radial and combined radial-axial fins,” Journal of Energy Storage, vol. 56, article 106129, 2022.
View at: Publisher Site | Google Scholar
P. M. Patil, I. Pop, and S. Roy, “Unsteady heat and mass transfer over a vertical stretching sheet in a parallel free stream with variable wall temperature and concentration,” Numerical Methods for Partial Differential Equations, vol. 28, no. 3, pp. 926–941, 2012.
View at: Publisher Site | Google Scholar
P. M. Patil, F. S. Hadapad, and A. S. Mikhail, “Mixed convection of silica–molybdenum disulphide/water hybrid nanoliquid over a rough sphere,” Symmetry, vol. 13, no. 2, p. 236, 2021.
View at: Publisher Site | Google Scholar
W. Waseem, M. Sulaiman, S. Islam et al., “A study of changes in temperature profile of porous fin model using cuckoo search algorithm,” Alexandria Engineering Journal, vol. 59, no. 1, pp. 11–24, 2020.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2023 Sharif Ullah et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation

Download other formats

Order printed copies