Radiation Heat Transfer in Fluidized Beds: A Comparison of Exact and Simplified Approaches

Radiation heat transfer at heat exchanger walls in fluidized beds has never been examined through a complete formulation of the problem. In this paper a wall-to-bed heat transfer model is proposed to account for particle convection, gas convection, and radiation exchange in a variable porosity medium. Momentum, energy, and intensity equations are solved in order to determine the velocity, temperature, radiative heat flux profiles and heat transfer coefficients. The discrete-ordinates method is used to compute the radiative intensity equation and the radiative flux divergence in the energy equation. Both the gray and the non-gray assumptions are considered, as well as dependent and independent scattering. The exact solution obtained is compared with several simplified approaches. Large differences are shown for small particles at high temperature but the simplified solutions are valid for large particle beds. The dependency of radiative contribution on controlling parameters is discussed.