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Transport of heat and mass and the thermodynamics of porous microreactors with thermal diffusion and radiation effects are investigated analytically. The examined configuration includes an axisymmetric, thickwall microchannel with an iso-flux thermal boundary condition imposed on the external surfaces. The microchannel is filled with porous materials and accommodates a zeroth order homogenous chemical reaction. Internal radiative heat transfer is modelled in addition to heat convection and conduction, while the local thermal non-equilibrium approach is taken within the porous section of the system. The transport of species is coupled with that of heat via the inclusion of thermodiffusion or Soret effect. Two-dimensional heat and mass transfer differential equations are solved analytically. The results are subsequently used to predict the thermodynamic irreversibilities inside the reactor and a thorough analysis of local and total entropy generation rates is performed. Also, the changes in Nusselt number, calculated on the internal walls of the microreactor, versus various parameters are reported. It is shown that the radiation effects can impact the temperature of the solid phase of the porous medium and lead to alteration of Nusselt number. It is further observed that the transfer of mass is the main source of irreversibility in the system. The findings are of particular use for the design and analysis of the microreactors with homogenous chemical reactions and can be also used for the validation of computational models.

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Microreactors for chemical synthesis and combustion have already attracted significant attention. Exothermic catalytic activity features heavily in these devices and thus advective-diffusive transport is of key importance in their analyses. Yet, thermal modelling of the heat generated by catalytic reactions on the internal surfaces of porous microreactors has remained as an important unresolved issue. To address this, the diffusion of heat of catalytic reactions into three phases including fluid, porous solid and solid walls is investigated by extending an existing interface model of porous media under local thermal non-equilibrium. This is applied to a microchannel fully filled with a porous material, subject to a heat flux generated by a catalytic layer coated on the porous-wall boundary. The finite wall thickness and viscous dissipation of the flow kinetic energy are considered, and a twodimensional analytical model is developed, examining the combined heat and mass transfer and thermodynamic irreversibilities of the system. The analytical solution is validated against the existing theoretical studies on simpler configurations as well as a computational model of the microreactor in the limit of very large porosity. In keeping with the recent findings, the wall thickness is shown to strongly influence the heat and mass transport within the system. This remains unchanged when the symmetricity of the microchannel is broken through placing walls of unequal thicknesses, while deviation from local thermal equilibrium is significantly intensified in this case. Importantly, the Nusselt number is shown to have a singular point, which remains fixed under various conditions. NomenclatureInterfacial area per unit volume of porous media, (m -1 ) Prandtl number Biot number Wall heat flux ratio ′ Modified Brinkman number ′′ Total catalytic heat flux (W m -2 ) Mass species concentration (kg m -3 ) 1 ′′ Lower wall heat flux (W m -2 ) 0 Inlet concentration (kg m -3 ) 2 ′′ Upper wall heat flux (W m -2 ) Specific heat capacity (J K -1 kg -1 ) Reynolds number Mass diffusion coefficient (m 2 s -1 ) Specific gas constant (J K -1 kg -1 ) Darcy number Shape factor of the porous medium Coefficient of thermal mass diffusion (m K -1 kg -1 s -1 ) ̇′ ′′ Volumetric entropy generation due to mass diffusion (W K -1 m -3 ) ℎ 1 Half-thickness of the microchannel to lower wall (m) ′ ′′ Volumetric entropy generation due to fluid friction (W K -1 m -3 ) ℎ 2 Half-thickness of the microchannel to upper wall (m) ̇′ ′′ Volumetric entropy generation in the fluid (W K -1 m -3 ) ℎ 3 Half-height of microchannel (m) ′ ′′ Volumetric entropy generation in the porous solid (W K -1 m -3 ) ℎ Interstitial heat transfer coefficient (W K -1 m -2 ) ̇1 ′′′ Volumetric entropy generation rate from lower wall (W K -1 m -3 )