Local non-equilibrium thermal fluctuation,internal noise and dissipation in gaseous heat conduction systems with high values of Prandtl number

By means of a stochastic model suggested in this paper for the systems with local non-equilibrium excited thermal fluctuations, the famous Shannon entropy is extended to include the heat conduction processes controlled externally by boundary constraints of constant temperature gradients at two sides.Meanwhile,using the description of master equation for the continuous Markov processes a balance equation of stochastic entropy production valid for one dimension gaseous heat conduction systems with high values of Prandtl number has been also established.Based on it,a general expression for both the stochastic entropy production and the entropy production of fluctuations have been further deduced by theΩ-expansions.In this formalism,all kinds of stochastic contributions to the dissipation from the non-equilibrium thermal fluctuation and internal noise turn explicit.

Effect of asymmetrical wall heat flux and wall temperature ratio on mixed convection in a vertical micro-porous-channel with internal heat generation

Mixed convective heat transfer in a vertical parallel plate micro-porous channel with internal heat generation and viscous dissipation,varying wall heat flux ratio and wall tem­perature ratio at the boundaries is investigated using the Darcy-Brinkman model under local thermal non-equilibrium assumption.Numerical solution for both fluid and solid temperature distributions are obtained by applying the finite element method.The effect of pertinent param­eters such as Brinkman number,Rayleigh number,Darcy number,inter-phase heat transfer co­efficient,porosity scaled thermal conductivity ratio and solid internal heat generation are discussed.The results indicate that the Nusselt number increases with the increase in the solid internal heat generation as well as Rayleigh number in both wall heat flux ratio and wall tem­perature ratio boundary conditions.It is observed that with the quantitative increase in viscous dissipation parameter Br,Nusselt number Nu increases in the presence of internal heat gener­ation and it decreases in the absence of internal heat generation,for a specific range of values of wall heat flux ratio and wall temperature ratio.Beyond this range Nu increases with the increase in Dr regardless of internal heat generation.For the cases,constant wall temperature and wall heat flux ratios,good correlation is observed in the results obtained with that of available in the literature.