Abstract
We present an analytical solution for the thermal transport in fluid-particle systems that include a spatially and temporally constant volumetric heat source. Our solution enables the rapid calculation of temperature profiles in systems undergoing chemical reactions or phase change phenomena. Also, we propose a map that helps in deciding in which situations the simple solution of Schumann (1929) [15] is enough to calculate fluid and particle temperatures.
Highlights
The thermal design of process equipment in various industrial applications, such as solar power plants (Behar et al, 2013), thermal energy storage (Van Lew et al, 2011), and reactive systems (Li et al, 2016) is an essential engineering task
We extend the analytical solution presented by Schumann (1929) to consider a constant heat source in the solid phase
Considering the intrinsic limitations of a numerical solution, it appears that an analytical solution for heat exchange in the fluidparticle system with a heat source would be helpful
Summary
The thermal design of process equipment in various industrial applications, such as solar power plants (Behar et al, 2013), thermal energy storage (Van Lew et al, 2011), and reactive systems (Li et al, 2016) is an essential engineering task. A number of attempts to derive analytical solutions were successful for certain simplified situations: Schumann (1929) presented such a solution for transient heat transfer in a one-dimensional packed bed Even though his solution is valid only for perfectly insulated systems without heat source, it has been extensively used by various researchers (Anderson et al, 2015; Cascetta et al, 2014; Li et al, 2014; Valmiki et al, 2012; Van Lew et al, 2011; Xu et al, 2012; Xu et al, 2015). We extend the analytical solution presented by Schumann (1929) to consider a constant heat source in the solid phase This will be realized via solving the set of heat transfer equations for the gas and solid phase in the packed bed using Laplace transformation. Considering the intrinsic limitations of a numerical solution, it appears that an analytical solution for heat exchange in the fluidparticle system with a heat source would be helpful
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