Natural convection inside a C-shaped nanofluid-filled enclosure with localized heat sources

2014 ◽  
Vol 24 (8) ◽  
pp. 1954-1978 ◽  
Author(s):  
M.A. Mansour ◽  
M.A. Bakeir ◽  
A. Chamkha
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Difference Method ◽  
Volume Fraction ◽  
Cu Nanoparticles ◽  
Content Type ◽  
The Finite Difference Method

Purpose – The purpose of this paper is to investigate natural convection fluid flow and heat transfer inside C-shaped enclosures filled with Cu-Water nanofluid numerically using the finite difference method. Design/methodology/approach – In this investigation, the finite difference method is employed to solve the governing equations with the boundary conditions. Central difference quotients were used to approximate the second derivatives in both the X and Y directions. Then, the obtained discretized equations are solved using a Gauss-Seidel iteration technique. Findings – It was found from the obtained results that the mean Nusselt number increased with increase in Rayleigh number and volume fraction of Cu nanoparticles regardless aspect ratio of the enclosure. Moreover the obtained results showed that the rate of heat transfer increased with decreasing the aspect ratio of the cavity. Also, it was found that the rate of heat transfer increased with increase in nanoparticles volume fraction. Also at low Rayleigh numbers, the effect of Cu nanoparticles on enhancement of heat transfer for narrow enclosures was more than that for wide enclosures. Originality/value – This paper is relatively original for considering C-shaped cavity with nanofluids.

Studi Perpindahan Panas Material pada Sistem Koordinat Segitiga

2017 ◽  
Vol 1 ◽  
pp. 114
Author(s):  
Imam Basuki ◽  
C Cari ◽  
A Suparmi
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
The Finite Difference Method ◽  
The Mathematical Model

<p class="Normal1"><strong><em>Abstract: </em></strong><em>Partial Differential Equations (PDP) Laplace equation can be applied to the heat conduction. Heat conduction is a process that if two materials or two-part temperature material is contacted with another it will pass heat transfer. Conduction of heat in a triangle shaped object has a mathematical model in Cartesian coordinates. However, to facilitate the calculation, the mathematical model of heat conduction is transformed into the coordinates of the triangle. PDP numerical solution of Laplace solved using the finite difference method. Simulations performed on a triangle with some angle values α and β</em></p><p class="Normal1"><strong><em> </em></strong></p><p class="Normal1"><strong><em>Keywords:</em></strong><em>  heat transfer, triangle coordinates system.</em></p><p class="Normal1"><em> </em></p><p class="Normal1"><strong>Abstrak</strong> Persamaan Diferensial Parsial (PDP) Laplace  dapat diaplikasikan pada persamaan konduksi panas. Konduksi panas adalah suatu proses yang jika dua materi atau dua bagian materi temperaturnya disentuhkan dengan yang lainnya maka akan terjadilah perpindahan panas. Konduksi panas pada benda berbentuk segitiga mempunyai model matematika dalam koordinat cartesius. Namun untuk memudahkan perhitungan, model matematika konduksi panas tersebut ditransformasikan ke dalam koordinat segitiga. Penyelesaian numerik dari PDP Laplace diselesaikan menggunakan metode beda hingga. Simulasi dilakukan pada segitiga dengan beberapa nilai sudut  dan  </p><p class="Normal1"><strong> </strong></p><p class="Normal1"><strong>Kata kunci :</strong> perpindahan panas, sistem koordinat segitiga.</p>

scholarly journals Mathematical modeling of air duct heater using the finite difference method

2011 ◽  
Vol 13 (4) ◽  
pp. 47-52
Author(s):  
M. Sarafraz ◽  
S. Peyghambarzadeh ◽  
A. Marahel
Keyword(s):  
Mathematical Modeling ◽  
Heat Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Convection Heat Transfer ◽  
Convection Heat ◽  
Transfer Coefficients ◽  
Design And Optimization ◽  
The Finite Difference Method

Mathematical modeling of air duct heater using the finite difference method In this research, mathematical modeling of a duct heater has been performed using energy conservation law, Stefan-Boltzman law in thermal radiation, Fourier's law in conduction heat transfer, and Newton's law of cooling in convection heat transfer. The duct was divided to some elements with equal length. Each element has been studied separately and air physical properties in each element have been used based on its temperature. The derived equations have been solved using the finite difference method and consequently air temperature, internal and external temperatures of the wall, internal and external convection heat transfer coefficients, and the quantity of heat transferred have been calculated in each element and effects of the variation of heat transfer parameters have been surveyed. The results of modelling presented in this paper can be used for the design and optimization of heat exchangers.

A gradient-based shape optimization scheme via isogeometric exact reanalysis

2018 ◽  
Vol 35 (8) ◽  
pp. 2696-2721 ◽  
Author(s):  
Chensen Ding ◽  
Xiangyang Cui ◽  
Guanxin Huang ◽  
Guangyao Li ◽  
K.K. Tamma ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Shape Optimization ◽  
Difference Method ◽  
Computer Aided Design ◽  
Content Type ◽  
Optimization Framework ◽  
Computer Aided ◽  
Gradient Based ◽  
The Finite Difference Method

PurposeThis paper aims to propose a gradient-based shape optimization framework in which traditional time-consuming conversions between computer-aided design and computer-aided engineering and the mesh update procedure are avoided/eliminated. The scheme is general so that it can be used in all cases as a black box, no matter what the objective and/or design variables are, whilst the efficiency and accuracy are guaranteed.Design/methodology/approachThe authors integrated CAD and CAE by using isogeometric analysis (IGA), enabling the present methodology to be robust and accurate. To overcome the difficulty in evaluating the sensitivities of objective and/or constraint functions by analytic method in some cases, the authors adopt the finite difference method to calculate these sensitivities, thereby providing a universal approach. Moreover, to further eliminate the inefficiency caused by the finite difference method, the authors advance the exact reanalysis method, the indirect factorization updating (IFU), to exactly and efficiently calculate functions and their sensitivities, which guarantees its generality and efficiency at the same time.FindingsThe proposed isogeometric gradient-based shape optimization using our IFU approach is reliable and accurate, as well as general and efficient.Originality/valueThe authors proposed a gradient-based shape optimization framework in which they first integrate IGA and the proposed exact reanalysis method for applicability to structural response and sensitivity analysis.

scholarly journals Thermal Behavior of the Natural Convection of Air Confined in a Trapezoidal Cavity

2021 ◽  
pp. 69-80
Author(s):  
Windé Nongué Daniel Koumbem ◽  
Issaka Ouédraogo ◽  
Noufou Bagaya ◽  
Pelega Florent Kieno
Keyword(s):  
Natural Convection ◽  
Heat Flow ◽  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Thermal Behavior ◽  
Systems Of Equations ◽  
Constant Heat ◽  
The Finite Difference Method ◽  
Mass Transfers

The thermal behavior of air by natural convection in a confined trapezoidal cavity, one of the walls of which is subjected to a constant heat flow in hot climates, has been analyzed numerically. The heat and mass transfers are carried out by the classical equations of natural convection. These equations are discretized using the Finite Difference Method and the algebraic systems of equations thus obtained are solved with the Thomas and Gauss algorithms. We analyze the influence of the number on the current and isothermal lines as well as the effects of the aspect ratio A = l / H and the angle of inclination φ. In particular, we have shown that convective exchanges in the cavity are preponderant for high Ra numbers. Also we have watches the increase in the values ​​of the isothermal lines and the decrease in the intensity of the streamlines for the low values ​​of A and of the angle φ.

NUMERICAL COMPUTATIONS OF CONDUCTIVITY IN CONTINUUM PERCOLATION FOR OVERLAPPING SPHEROIDS

2010 ◽  
Vol 21 (06) ◽  
pp. 709-729 ◽  
Author(s):  
SHIGEKI MATSUTANI ◽  
YOSHIYUKI SHIMOSAKO ◽  
YUNHONG WANG
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Percolation Model ◽  
Continuum Percolation ◽  
Laplace Equations ◽  
The Finite Difference Method ◽  
The Continuum

By numerically solving the generalized Laplace equations by means of the finite difference method, we investigated isotropic electric conductivity of a three-dimensional continuum percolation model consisting of overlapped spheroids of revolution in continuum. Since the computational results strongly depend upon parameters in the discretization methods of the finite difference method, we explored the dependences in details to construct the computational scheme which can represent the continuum percolation model well. Using the discrete scheme, we obtained the conductivity curves, σ =c (p -pc)t, depending upon aspect ratio of the conductive spheroids for the volume fraction p. We found the fact that the critical exponent t is not universal, which depends upon the shape of spheroids with a range varying from 1.58 ± 0.08 to 1.94 ± 0.18 whereas 1.85 is reported as the standard one of cubic lattice case [A. B. Harris, Phys. Rev. B28, 2614 (1983)]. We also discussed its relation to the nonuniversality in the broad distribution continuum percolation models.

Numerical Simulation by FDM of Unsteady Heat Transfer in Cylindrical Coordinates

2016 ◽  
Vol 851 ◽  
pp. 322-325
Author(s):  
Cláudia Narumi Takayama Mori ◽  
Estaner Claro Romão
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Exact Solutions ◽  
Difference Method ◽  
Transfer Problem ◽  
Cylindrical Coordinates ◽  
Unsteady Heat Transfer ◽  
The Finite Difference Method

In this paper the heat transfer problem in transient and cylindrical coordinates will be solved by the Crank-Nicolson method in conjunction the Finite Difference Method. To validate the formulation will study the numerical efficiency by comparisons of numerical results compared with two exact solutions.

A Software Tool for Determining Steady-State Temperature Distributions in a Square Domain by the Finite-Difference Method

2007 ◽  
Vol 35 (4) ◽  
pp. 305-315
Author(s):  
K. A. Oladejo ◽  
D. A. Adetan ◽  
O. A. Bamiro
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Computer Aided Design ◽  
Linear Equations ◽  
Analytical Techniques ◽  
Software Tool ◽  
Transfer Equations ◽  
The Finite Difference Method

This paper presents the development of an interactive program (called SSTDD) to solve two-dimensional conduction heat transfer equations in a square domain using the finite-difference method. The development of the tool (based on a computer-aided design package), on a Visual BASIC 6.0 platform, involved the application of the heat transfer equations and the appropriate boundary conditions to a square domain. The finite-difference method was used to express the elliptic differential equation in a form suitable for numerical solution. The system of linear equations generated was solved by the Gauss–Seidel iterative technique. The SSTDD model was tested by using problems solved by conventional analytical techniques. The results generated by the model and the analytical method were in good agreement. Hence the model can be used to solve practical engineering problems, with good accuracy, and also as a demonstration tool to students in the area of design and heat transfer of mechanical engineering.

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