### Abstract

In the present study, the detailed procedures of Galerkin weighted residual technique of finite element method (FEM) for solving two-dimensional incompressible natural convective flow of nanofluids using nonhomogeneous dynamic model are discussed for the first time. The physical domain is discretized by using unstructured triangular elements. The governing partial differential equations of nanofluids are made dimensionless using the suitable transformation of variables for weak formulations. The method of weighted residuals is used for obtaining the approximate solutions. This approach typically leads to a sparse and indefinite matrix that is difficult to solve efficiently. The formation of an indefinite matrix is avoided in the present work by introducing an artificial compressibility term in the continuity equation. Unequal order interpolation functions are used for pressure, velocity, temperature and concentration variables. The coefficient matrices are calculated using interpolation functions. Assembling of triangular elements in the discretized domain is discussed elaborately. The process of calculating boundary integrals is also discussed. The Newton-Raphson iteration technique along with Euler-backward scheme is used to solve the global matrix. The sample results are obtained for the convective flow of nanofluids in a concentric annulus. It shows that the annulus of having higher thickness is the best performer enhancing convective heat transfer rates.

Original language | English |
---|---|

Pages (from-to) | 251-267 |

Number of pages | 17 |

Journal | Thermal Science and Engineering Progress |

Volume | 6 |

DOIs | |

Publication status | Published - Jun 1 2018 |

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### Keywords

- Annulus
- Artificial compressibility
- Dynamic nanofluid model
- Finite element method
- Shape function

### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes

### Cite this

**Finite element computational procedure for convective flow of nanofluids in an annulus.** / Uddin, M. J.; Rahman, M. M.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Finite element computational procedure for convective flow of nanofluids in an annulus

AU - Uddin, M. J.

AU - Rahman, M. M.

PY - 2018/6/1

Y1 - 2018/6/1

N2 - In the present study, the detailed procedures of Galerkin weighted residual technique of finite element method (FEM) for solving two-dimensional incompressible natural convective flow of nanofluids using nonhomogeneous dynamic model are discussed for the first time. The physical domain is discretized by using unstructured triangular elements. The governing partial differential equations of nanofluids are made dimensionless using the suitable transformation of variables for weak formulations. The method of weighted residuals is used for obtaining the approximate solutions. This approach typically leads to a sparse and indefinite matrix that is difficult to solve efficiently. The formation of an indefinite matrix is avoided in the present work by introducing an artificial compressibility term in the continuity equation. Unequal order interpolation functions are used for pressure, velocity, temperature and concentration variables. The coefficient matrices are calculated using interpolation functions. Assembling of triangular elements in the discretized domain is discussed elaborately. The process of calculating boundary integrals is also discussed. The Newton-Raphson iteration technique along with Euler-backward scheme is used to solve the global matrix. The sample results are obtained for the convective flow of nanofluids in a concentric annulus. It shows that the annulus of having higher thickness is the best performer enhancing convective heat transfer rates.

AB - In the present study, the detailed procedures of Galerkin weighted residual technique of finite element method (FEM) for solving two-dimensional incompressible natural convective flow of nanofluids using nonhomogeneous dynamic model are discussed for the first time. The physical domain is discretized by using unstructured triangular elements. The governing partial differential equations of nanofluids are made dimensionless using the suitable transformation of variables for weak formulations. The method of weighted residuals is used for obtaining the approximate solutions. This approach typically leads to a sparse and indefinite matrix that is difficult to solve efficiently. The formation of an indefinite matrix is avoided in the present work by introducing an artificial compressibility term in the continuity equation. Unequal order interpolation functions are used for pressure, velocity, temperature and concentration variables. The coefficient matrices are calculated using interpolation functions. Assembling of triangular elements in the discretized domain is discussed elaborately. The process of calculating boundary integrals is also discussed. The Newton-Raphson iteration technique along with Euler-backward scheme is used to solve the global matrix. The sample results are obtained for the convective flow of nanofluids in a concentric annulus. It shows that the annulus of having higher thickness is the best performer enhancing convective heat transfer rates.

KW - Annulus

KW - Artificial compressibility

KW - Dynamic nanofluid model

KW - Finite element method

KW - Shape function

UR - http://www.scopus.com/inward/record.url?scp=85046087477&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85046087477&partnerID=8YFLogxK

U2 - 10.1016/j.tsep.2018.04.011

DO - 10.1016/j.tsep.2018.04.011

M3 - Article

AN - SCOPUS:85046087477

VL - 6

SP - 251

EP - 267

JO - Thermal Science and Engineering Progress

JF - Thermal Science and Engineering Progress

SN - 2451-9049

ER -