scholarly journals Analytical Solutions for Steady Heat Transfer in Longitudinal Fins with Temperature-Dependent Properties

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Partner L. Ndlovu ◽  
Raseelo J. Moitsheki
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Power Law ◽  
Analytical Solutions ◽  
Physical Parameters ◽  
Transform Method ◽  
Fin Efficiency ◽  
Analytical Series

Explicit analytical expressions for the temperature profile, fin efficiency, and heat flux in a longitudinal fin are derived. Here, thermal conductivity and heat transfer coefficient depend on the temperature. The differential transform method (DTM) is employed to construct the analytical (series) solutions. Thermal conductivity is considered to be given by the power law in one case and by the linear function of temperature in the other, whereas heat transfer coefficient is only given by the power law. The analytical solutions constructed by the DTM agree very well with the exact solutions even when both the thermal conductivity and the heat transfer coefficient are given by the power law. The analytical solutions are obtained for the problems which cannot be solved exactly. The effects of some physical parameters such as the thermogeometric fin parameter and thermal conductivity gradient on temperature distribution are illustrated and explained.

Exact solution of a nonlinear fin problem of temperature-dependent thermal conductivity and heat transfer coefficient

2020 ◽  
Vol 98 (7) ◽  
pp. 700-712 ◽  
Author(s):  
Sheng-Wei Sun ◽  
Xian-Fang Li
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Temperature Distribution ◽  
Transfer Coefficient ◽  
Power Law ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Special Cases ◽  
Temperature Dependent Thermal Conductivity

This paper studies a class of nonlinear problems of convective longitudinal fins with temperature-dependent thermal conductivity and heat transfer coefficient. For thermal conductivity and heat transfer coefficient dominated by power-law nonlinearity, the exact temperature distribution is obtained analytically in an implicit form. In particular, the explicit expressions of the fin temperature distribution are derived explicitly for some special cases. An analytical expression for fin efficiency is given as a function of a thermogeometric parameter. The influences of the nonlinearity and the thermogeometric parameter on the temperature and thermal performance are analyzed. The temperature distribution and the fin efficiency exhibit completely different behaviors when the power-law exponent of the heat transfer coefficient is more or less than negative unity.

Exact Closed-Form Solution of the Nonlinear Fin Problem With Temperature-Dependent Thermal Conductivity and Heat Transfer Coefficient

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Mahdi Anbarloei ◽  
Elyas Shivanian
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Exact Analytical Solution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Temperature Dependent Thermal Conductivity

In the current paper, the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient is revisited. In this problem, it has been assumed that the heat transfer coefficient is expressed in a power-law form and the thermal conductivity is a linear function of temperature. It is shown that its governing nonlinear differential equation is exactly solvable. A full discussion and exact analytical solution in the implicit form are given for further physical interpretation and it is proved that three possible cases may occur: there is no solution to the problem, the solution is unique, and the solutions are dual depending on the values of the parameters of the model. Furthermore, we give exact analytical expressions of fin efficiency as a function of thermogeometric fin parameter.

scholarly journals A Convenient Method for the Accurate Calculation of Fin Efficiency of H-Type Fins Based on Linear Nomograms and Fitting Formulae

Energies ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 456
Author(s):  
Yongshi Feng ◽  
Xin Wu ◽  
Cai Liang ◽  
Zhongping Sun
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Surface Heat ◽  
Surface Heat Transfer ◽  
Fin Efficiency ◽  
Surface Heat Transfer Coefficient ◽  
Fin Thickness

Fin efficiency, as a measure of the effectiveness of the heat transfer enhancement, is of great importance in studying the heat transfer performance of H-type finned tube banks. The fin efficiency of square fins is adopted by most researchers as an alternative to that of H-type fins, which can create certain errors in the fin efficiency of H-type fins. For this paper, the linear nomograms and fitting formulae of fin efficiency of H-type fins are obtained by the definition method of fin efficiency based on numerous numerical simulations, and the results calculated by this method are verified by experimental data. On this basis, the effects of three geometric parameters (slit width, fin height, and fin thickness) and two thermal parameters (surface heat transfer coefficient and fin thermal conductivity) on the fin efficiency of H-type fins are also investigated and compared to those of square fins. The results indicate that the fin efficiency of H-type fins increases with the increment of fin thickness and thermal conductivity, and decreases with the increase of slit width, fin height, and surface heat transfer coefficient. Accordingly, the linear nomograms and fitting formulae for the fin efficiency of H-type fins, which are well compatible with experimental data, can help to facilitate further theoretical research and engineering application.

Development of a New Correlation and Post Processing of Heat Transfer Coefficient and Pressure Drop of Functionalized COOH MWCNT Nanofluid by Artificial Neural Network

2018 ◽  
Vol 14 (2) ◽  
pp. 104-112 ◽  
Author(s):  
Mohammad Hemmat Esfe ◽  
Somchai Wongwises ◽  
Saeed Esfandeh ◽  
Ali Alirezaie
Keyword(s):  
Neural Network ◽  
Heat Transfer ◽  
Thermal Conductivity ◽  
Artificial Neural Network ◽  
Heat Transfer Coefficient ◽  
Pressure Drop ◽  
Transfer Coefficient ◽  
Regression Coefficient ◽  
New Correlation ◽  
The Neural Network

Background: Because of nanofluids applications in improvement of heat transfer rate in heating and cooling systems, many researchers have conducted various experiments to investigate nanofluid's characteristics more accurate. Thermal conductivity, electrical conductivity, and heat transfer are examples of these characteristics. Method: This paper presents a modeling and validation method of heat transfer coefficient and pressure drop of functionalized aqueous COOH MWCNT nanofluids by artificial neural network and proposing a new correlation. In the current experiment, the ANN input data has included the volume fraction and the Reynolds number and heat transfer coefficient and pressure drop considered as ANN outputs. Results: Comparing modeling results with proposed correlation proves that the empirical correlation is not able to accurately predict the experimental output results, and this is performed with a lot more accuracy by the neural network. The regression coefficient of neural network outputs was equal to 99.94% and 99.84%, respectively, for the data of relative heat transfer coefficient and relative pressure drop. The regression coefficient for the provided equation was also equal to 97.02% and 77.90%, respectively, for these two parameters, which indicates this equation operates much less precisely than the neural network. Conclusion: So, relative heat transfer coefficient and pressure drop of nanofluids can also be modeled and estimated by the neural network, in addition to the modeling of nanofluid’s thermal conductivity and viscosity executed by different scholars via neural networks.

Experimental Convective Heat Transfer With Nanofluids

2008 ◽  
Author(s):  
S. Kabelac ◽  
K. B. Anoop
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Turbulent Regime ◽  
Heat Transfer Characteristics ◽  
Forced Convective Heat Transfer ◽  
Transfer Characteristics

Nanofluids are colloidal suspensions with nano-sized particles (<100nm) dispersed in a base fluid. From literature it is seen that these fluids exhibit better heat transfer characteristics. In our present work, thermal conductivity and the forced convective heat transfer coefficient of an alumina-water nanofluid is investigated. Thermal conductivity is measured by a steady state method using a Guarded Hot Plate apparatus customized for liquids. Forced convective heat transfer characteristics are evaluated with help of a test loop under constant heat flux condition. Controlled experiments under turbulent flow regime are carried out using two particle concentrations (0.5vol% and 1vol %). Experimental results show that, thermal conductivity of nanofluids increases with concentration, but the heat transfer coefficient in the turbulent regime does not exhibit any remarkable increase above measurement uncertainty.

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