Design of selective emitting media within a cylindrical tube for conversion of wasted heat energy to electrical energy

Abstract

Thermophotovoltaic (TPV) energy conversion is the conversion of heat energy to electrical energy via light. This manuscript focuses on the geometric design of emitting material within an exhaust tube to convert wasted heat energy to light, and achieve an optimal amount of irradiance at the PV diode cells. Due to the large value of the absorption coefficient for the selectively emitting erbia-doped nanofibers under discussion, the diffusion approximation to the equation of radiation transfer is used. This approximate equation is solved for emission from hot-spot sources within the emitting material. Several geometric distributions of the emitting material are considered. Within an axisymmetric geometry all erbia-doped nanofibers, all quartz wool, and mixtures of disk-shaped or cylindrical shell shaped distributions of nanofibers and wool are investigated. Within a polar geometry all erbia-doped nanofibers, all quartz wool, and mixtures of spoke-shaped or cylindrical shell shaped distributions are investigated. In both geometries the mixture distributions consist of alternating thin layers of emitting and non-emitting material. Homogenization techniques are applied to these distributions to define expressions for the effective absorption and scattering coefficients for these spatially distributed emitting structures. The effective expressions are input into the diffusion approximation that is solved for the spectral irradiance. The net radiation obtained from these emitting structures is examined to optimize the geometry of the TPV material to maximize emission with use of minimal TPV material. Results show that disk-shaped bands or spokes allow for maximum irradiation in the radial direction toward the diode collectors. A large volume fraction of erbia-doped nanofibers is optimal when hot spots are close to the diodes. Smaller volume fractions work better when hot spots are away from the diodes due to reabsorption of emitted light by the emitting material.