### Abstract

A numerical study of a conjugate turbulent natural convection with thermal surface radiation inside a square cavity with heat-conducting solid walls and a local heat source has been performed. Two-dimensional equations for conservation of mass, momentum and energy using k–ε turbulence model with a heat conduction equation inside the solid walls and corresponding boundary conditions have been solved using the finite difference method. The developed numerical method can be widely used in some engineering problems, such as the simulation of heat and mass transfer in heat-generating elements in power engineering. Discrete heater has been simulated by a heat source of constant temperature centrally located on the bottom wall. Numerical solutions have been obtained for Ra = 10^{9} and different values of surface emissivity (0≤ɛ˜<1) and thermal conductivity ratio (10 ≤ λ_{1,2} ≤ 1000). It has been found that an increase in surface emissivity and thermal conductivity ratio leads to a growth of the average total Nusselt number, while a rise of surface emissivity only illustrates a reduction of the average convective Nusselt number. The obtained numerical results are useful for predicting the convective and radiative heat transfer in domain similar to the one under consideration.

Original language | English |
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Pages (from-to) | 1339-1351 |

Number of pages | 13 |

Journal | Applied Mathematics and Computation |

Volume | 321 |

DOIs | |

Publication status | Published - 15 Mar 2018 |

### Keywords

- Finite difference method
- Heat conduction
- Local heater
- Solid walls
- Surface radiation
- Turbulent natural convection

### ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics

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## Cite this

*Applied Mathematics and Computation*,

*321*, 1339-1351. https://doi.org/10.1016/j.amc.2017.11.010