## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Mathematical modelling of the conjugate natural convection in a closed system with the radiant heating source under conditions of radiant energy distribution by Lambert's cosine law

**ABSTRACT**

Various types of emitters are often used as energy sources in real engineering systems and technological processes. Investigations of heat transfer basic laws in such systems are of interest. We conducted mathematical modelling of conjugate heat transfer in a closed rectangular cavity under conditions of radiant energy source operating. Two - dimensional problem of conjugate natural convection in vorticity-stream function-temperature dimensionless variables has been numerically solved by means of the finite difference method. Radiant energy distribution along the gas-wall interfaces was set by Lamberts' cosine law. We obtained fields of temperature and stream functions in a wide range of governing parameters (Rayleigh number 104 ≤ Ra ≤ 106, the length of radiant heating source 0.15 ≤ D ≤ 0.6 ). Then we analyzed how heat-retaining properties of finite thickness heat-conducting walls made of different materials affect the heat transfer intensity. Differential characteristics distribution showed significant nonuniformity and nonstationarity of the conjugate heat transfer process under study.

**KEYWORDS**

PAPER SUBMITTED: 2016-01-20

PAPER REVISED: 2016-08-04

PAPER ACCEPTED: 2016-10-24

PUBLISHED ONLINE: 2016-11-06

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