Constant wall heat flux boundary conditions in micro-channels filled with porous material with internal heat generation under local thermal non-equilibrium conditions

Forced convection heat transfer in a micro-channel filled with a porous material saturated with rarefied gas with internal heat generation is studied analytically in this work. The study is performed by analysing the boundary conditions for constant wall heat flux under local thermal non-equilibrium (LTNE) conditions. Invoking the velocity slip and temperature jump, the thermal behaviour of the porous-fluid system is studied by considering thermally and hydrodynamically fully-developed conditions. The flow inside the porous material is modelled by the Darcy–Brinkman equation. Exact solutions are obtained for both the fluid and solid temperature distributions for two primary approaches models A and B using constant wall heat flux boundary conditions. The temperature distributions and Nusselt numbers for models A and B are compared, and the limiting cases resulting in the convergence or divergence of the two models are also discussed. The effects of pertinent parameters such as fluid to solid effective thermal conductivity ratio, Biot number, Darcy number, velocity slip and temperature jump coefficients, and fluid and solid internal heat generations are also discussed. The results indicate that the Nusselt number decreases with the increase of thermal conductivity ratio for both models. This contrasts results from previous studies which for model A reported that the Nusselt number increases with the increase of thermal conductivity ratio. The Biot number and thermal conductivity ratio are found to have substantial effects on the role of temperature jump coefficient in controlling the Nusselt number for models A and B. The Nusselt numbers calculated using model A change drastically with the variation of solid internal heat generation. In contrast, the Nusselt numbers obtained for model B show a weak dependency on the variation of internal heat generation. The velocity slip coefficient has no noticeable effect on the Nusselt numbers for both models. The difference between the Nusselt numbers calculated using the two models decreases with an increase of the temperature jump coefficient.

Stable oxygen isotopes in irish oaks: potential for reconstructing local and regional climate

The long Irish oak tree-ring chronology, developed for archaeological dating and radiocarbon calibration, is the longest of any in northwest maritime Europe, spanning most of the Holocene (7,272 years). Unfortunately, the rings widths do not carry a strong climate signal and the record hasnever been satisfactorily applied for dendroclimatic reconstruction. This pilot study explores the potential for extracting a climate signal from Irish oaks by comparing the stable oxygen isotopes ratios from 10 oak tree cores (Quercus robur and Quercus petraea L.) collected across the Armagh region of NE Ireland with local and regional climatic and stable isotopic data. Statistically significant correlations between isotope ratios and the amount of summer precipitation (r = -0.44) point to the isotopic composition of summer rainfall as the dominant signal. Including the Armagh data into an extended regional oxygen isotope series did not reduce the correlation coefficient with regional precipitation (r = -0.68, p < 0.01). Correlations of this magnitude in dendro-hydroclimatology are typically restricted to trees growing at their ecological limits. This research suggests that there is considerable potential for including living trees and ancient timbers from Ireland into a regional composite to reconstruct the summer hydroclimate of Britain and Ireland.