Comparative Analysis of Fin Heat Transfer Using Simulation ... … · the nonlinear heat transfer...
Transcript of Comparative Analysis of Fin Heat Transfer Using Simulation ... … · the nonlinear heat transfer...
Contemporary Engineering Sciences, Vol. 11, 2018, no. 61, 3013 - 3020
HIKARI Ltd, www.m-hikari.com
https://doi.org/10.12988/ces.2018.87308
Comparative Analysis of Fin Heat Transfer
Using Simulation Software
Jose Di Filippo Buitrago, Álvaro Garzón Campo
and Guillermo Valencia Ochoa
Research Group on Energy Efficient Management - kaí, Faculty of Engineering
University of Atlántico, km 7 Antigua via Puerto Colombia
Copyright © 2018 Jose Di Filippo Buitrago, Álvaro Garzón Campo and Guillermo Valencia
Ochoa. This article is distributed under the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
Abstract
Engineering education software has become a key factor in completing the
objectives of an education program and achieving a student's results. This article
presents the validation of the Profiles Fins program by comparing it with the
results obtained by the already known Solidworks® that allows to determine the
temperature distribution, heat transfer coefficient, efficiency and effectiveness of
the different types of fins. The variation of these values with respect to their
change in fin geometry was analyzed to give as results which present the best heat
dissipation percentages.
Keywords: heat transfer fins, simulation software, Profile Fins, comparative
analysis
1. Introduction
Because of the size reduction, performance improvement and cost minimization in
fin fabrication, the industry and its researchers are continually striving to find the
optimal structure and design. [1] that maximizes the rate of heat dissipation.
Ghasemi and others.[2] They used the differential transformation method to solve
the nonlinear heat transfer equation [3] in the longitudinal fin with temperature-
dependent internal heat generation and thermal conductivity [4]. Campo y
Celentano[5] briefly evaluated the maximum heat transfer attributes of the
optimum straight ends with the quarter-circle profile proposed by Isachenko and
others. In terms of three descriptive parameters: the thermal conductivity k, the
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average coefficient of convection h ~, and the semi-thickness at the base R. Dogan
et al. [6] numerically researched the natural convection in a stationary state and
the radiation heat transfer of various thin sets of fins onto a horizontal baseplate.
Kundu and Wongwises [7] performed a complete thermal analysis on a
rectangular fin [8] with its primary surface taking into consideration the heat
exchange (radiation) with the environment together with the convective mode of
heat transfer. Yaici and Ghorab [9] presented the results of three-dimensional
computational fluid dynamics (CFD) simulations to investigate the effect of poor
distribution of incoming airflow on the thermohydraulic performance of fin heat
exchangers and plate tubes. Moitsheki and Bradshaw-Hajek [10] They considered
a heat conduction model that emerges in transient heat transfer through
longitudinal fins of a heterogeneous (functionally classified) material. In this case,
the thermal conductivity depends on the spatial variable. The heat transfer
coefficient is temperature dependent and is given by the power law function. The
resulting nonlinear partial differential equation is analyzed using both classical
and non-classical symmetry techniques. Ndlovu and Moitsheki [19] derived
approximate analytical solutions (series) for temperature distribution in
rectangular and convex longitudinal parabolic fins with temperature-dependent
thermal conductivity and heat transfer coefficient. The transitory heat conduction
problem is solved for the first time using the two-dimensional differential
transformation method (DTM 2D). Senapati and others[20] found that with the
addition of fins to the heated isothermal surface of a tube, heat transfer increases
for laminar flow and turbulent flow, heat transfer first increases and achieves a
maximum value, then begins to decrease.
A software will be used to simulate the heat transference present in fins by
varying their geometry, to validate the Profile Fins software and idealize the fin
geometry supported in SolidWorks and the results it produces.
2. Methodology
2.1.Fundamental equations
Depending on the specific geometry of each fin, its heat transfer capacity is
defined.
�̇�𝑐𝑜𝑛𝑑, 𝑥 = �̇�𝑐𝑜𝑛𝑑, 𝑥 + ∆𝑥 + �̇�𝑐𝑜𝑛𝑣 (1)
In the special case of a constant cross-section and constant thermal conductivity,
𝑑2𝜃
𝑑𝑥2 − 𝑎2𝜃 = 0 where 𝑎2 =ℎ𝑝
𝑘𝐴𝑐 (2)
At the tip of the fin there are several boundary conditions, including specific
temperature, negligible heat loss, convection or convection and combined
radiation.
Comparative analysis of fin heat transfer using simulation software 3015
For a fin of sufficiently long and uniform cross section (Ac = constante) CF flipper tip: 𝜃(𝐿) = 𝑇(𝐿) − 𝑇∞ when L → ∞
�̇�𝑙𝑜𝑛𝑔 𝑓𝑖𝑛 − 𝑘𝐴𝑐𝑑𝑇
𝑑𝑥|
𝑥=0= √ℎ𝑝𝑘𝐴𝑐 (𝑇𝑏 − 𝑇∞) (3)
Negligible heat loss from the tip of the fin (isolated fin tip),
�̇�𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑒𝑑 𝑓𝑖𝑛 𝑡𝑖𝑝 = 0
CF flipper tip: 𝑑𝜃
𝑑𝑥|
𝑥=𝐿= 0
�̇�𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑒𝑑 𝑓𝑖𝑛 𝑡𝑖𝑝= −𝑘𝐴𝑐
𝑑𝑇
𝑑𝑥|
𝑥=0= √ℎ𝑝𝑘𝐴𝑐(𝑇𝑏 − 𝑇∞) (4)
Convection (combined convection and radiation) from the tip of the fin
Corrected fin length
𝐿𝑐 = 𝐿 +𝐴𝑐
𝑝 (5)
𝐿𝐶,𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑓𝑖𝑛 = 𝐿 + 𝑡
2 Y 𝐿𝑐,𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 𝑓𝑖𝑛 = 𝐿 +
𝐷
4 (6)
Fin Efficiency To consider the effect of this decrease in temperature on heat
transfer, a fin efficiency is defined as,
𝑛𝑓𝑖𝑛 =�̇�𝑓𝑖𝑛
�̇�𝑓𝑖𝑛,𝑚á𝑥
(7)
2.2.Fin design and analysis with simulation software
The fins were designed with the help of Solidworks simulation software in 2D and
3D plane, using commands such as lines, midpoint lines, arc, circumference, 3D
extrusion, etc. The fins were designed with the following specifications: length
l=100 mm, width b=60 mm and thickness y=20 mm. The specifications of each
fin is shown in Error! Reference source not found..
3016 Jose Di Filippo Buitrago et al.
Error! Reference source not found.studied in the software
After the design is created, the next step is to analyze the fin for heat transfer
using Solidworks Simulation software. The type of analysis was first selected as
thermal analysis for the stationary heat transfer process. The material of the piece
was assigned, then the thermal load was applied, in this case, temperature through
the plate and convective properties of the environment, the unit system was used
as customization length in mm, temperature in k and thermal energy in J.
Now from the adjustment of the 3D mesh was established a mesh size of 60% to
fine. The design mesh was generated as shown in Error! Reference source not
found.a. In this assignment the material has thermal conductivity, heat transfer
convection coefficient for fluid, surface temperature and ambient temperature as:
Thermal conductivity, k = 200 W / m. k, Convection coefficient of heat transfer, h
= 40 W / m2. K, Temperature of the surface of the wall to which the fin was
attached to 328, 15 K, and ambient temperature to 303,15 K. With the help of the
Profile Fins simulation software, the respective simulations were carried out under
the same conditions that were used in the Solidworks software for both material
and environment. Error! Reference source not found. 2a and Error! Reference
source not found.2b displays the software Profile Fins.
Type of fin Efficiency Fin Area
rectangular straight
𝑛𝑓𝑖𝑛 =tanh 𝑚𝐿𝑐
𝑚𝐿𝑐
𝑚 = 2ℎ/𝑘𝑡
𝐿𝑐 = 𝐿 +𝑡
2
𝐴𝑓𝑖𝑛 = 2𝑤𝐿𝑐
Straight triangular
𝑛𝑓𝑖𝑛 =1
𝑚𝐿
𝑙1(2𝑚𝐿)
𝑙0(2𝑚𝐿)
𝑚 = 2ℎ/𝑘𝑡
𝐴𝑓𝑖𝑛 = 2𝑤 𝐿2 + (𝑡/2)2
Rectangular profile circular
𝑛𝑓𝑖𝑛
= 𝑐2
𝑘1(𝑚𝑟1)𝐼1(𝑚𝑟1)𝐼1 𝑚𝑟1 𝑘1(𝑚𝑟2𝑐)
𝑙0 𝑚𝑟1 𝑘1 𝑚𝑟2𝑐 + 𝑘0(𝑚𝑟1)𝐼1(𝑚𝑟2𝑐)
𝑚 = 2ℎ/𝑘𝑡
𝑟2𝑐 = 𝑟2 +𝑡
2
𝐴𝑓𝑖𝑛 = 2𝜋(𝑟22𝑐 − 𝑟2
1)
Straight parabolic
𝑛𝑓𝑖𝑛 =2
1 + (2𝑚𝐿)2 + 1
𝑚 = 2ℎ/𝑘𝑡
𝐴𝑓𝑖𝑛 = 𝑤𝐿[𝐶1 + (𝐿/𝑡)ln(𝑡
/𝐿) + 𝐶1)]
𝐶1 = 1 + (𝑡/𝐿)2
Rectangular profile
herringbone
𝑛𝑓𝑖𝑛 =tanh 𝑚𝐿𝑐
𝑚𝐿𝑐
𝑚 = 4ℎ/𝑘𝐷
𝐿𝑐 = 𝐿 +𝐷
4
𝐴𝑓𝑖𝑛 = 𝜋𝐷𝐿𝑐
Comparative analysis of fin heat transfer using simulation software 3017
a) b)
Error! Reference source not found., b) Rectangular fin interface.
3. Results and discussion
There are infinite parameters, variables and factors that influence the way in
which each fin dissipates heat. Using software simulation (Profile Fins and
Solidworks) the temperature distribution was found in each geometric variation
and compared when it changed its border condition. Error! Reference source not
found.a shows how SW shows the heat on the fin surface and how it is conducted
from the heat source outwards.
Error! Reference source not found., b) Cylindrical fin.
By varying the surface fin geometry and under the same conditions, Error!
Reference source not found. 3b shows that heat is dissipated at a slightly lower
temperature in a cylindrical fin. Profile Fins, being a specialized software for this
type of simulation, shows us a more realistic result that does not differ from the
one shown in Solidworks but shows the temperature distribution as a function of
the distance from the base of the fin to the tip. In Error! Reference source not
found.4 it is clearly seen that applying the border condition C. F. Mechanisms
combined has a greater heat dissipation, however, it is observed that there is a
similarity between the graph corresponding to Solidworks and the
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border condition of insulated tip used in Profile Fins. Error! Reference source
not found.4b shows that for parabolic geometry fins, contradictory results were
found between the two softwares, due to the configuration of the profile Fins
software.
a) b)
Error! Reference source not found., b) Parabolic fin.
Conclusion
The ProfileFins tool was successfully introduced in the mechanical engineering
classes where its analysis capability was validated depending on the geometry of
each fin. Three different extended geometries were studied with the help of the
two programs and the surface area equations, the heat distribution was observed
observing and concluding that there is a greater heat dissipation with rectangular
fins, the operation of the ProfileFins software is validated, noting that it has an
adequate behavior to the comparison made with Solidworks, besides being much
more specific offering more detailed information of the heat distribution behavior.
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Received: July 19, 2018; Published: August 8, 2018