This paper presents a study of the thermal characteristics and entropy generation of a porous microchannel with thick walls featuring uneven thicknesses. Two sets of asymmetric boundary conditions are considered. The first includes constant temperatures at the surface of the outer walls, with the lower wall experiencing a higher temperature than the upper wall. The second case imposes a constant heat flux on the lower wall and a convection boundary condition on the upper wall. These set thermal models for microreactors featuring highly exothermic or endothermic reactions such as those encountered in fuel reforming processes. The porous system is considered to be under local thermal nonequilibrium (LTNE) condition. Analytical solutions are, primarily, developed for the temperature and local entropy fields and then are extended to the total entropy generation within the system. It is shown that the ratio of the solid to fluid effective thermal conductivity and the internal heat sources are the most influential parameters in the thermal and entropic behaviors of the system. In particular, the results demonstrate that the internal heat sources can affect the entropy generation in a nonmonotonic way and that the variation of the total entropy with internal heat sources may include extremum points.

S. (2016) On the effects of internal heat sources upon forced convection in porous channels with asymmetric thick walls. International Communications in Heat and Mass Transfer, 73, pp. 100-110. (doi:10.1016/j.icheatmasstransfer.2016.02.016) This is the author's final accepted version.There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it.http://eprints.gla.ac.uk/116241/ literature, it is demonstrated that the inclusion of internal heat sources leads to deviations from the local 19 thermal equilibrium. Nonetheless, the results imply that the extent of these deviations depends on the 20 thermal boundary conditions and also the specific phase in which heat is generated or consumed. 21

Approximate analytical methods, such as the multiple scales (MS) and direct normal form (DNF) techniques, have been used extensively for investigating nonlinear mechanical structures, due to their ability to offer insight into the system dynamics. A comparison of their accuracy has not previously been undertaken, so is addressed in this paper. This is achieved by computing the backbone curves of two systems: the single-degree-of-freedom Duffing oscillator and a non-symmetric, two-degree-of-freedom oscillator. The DNF method includes an inherent detuning, which can be physically interpreted as a series expansion about the natural frequencies of the underlying linear system and has previously been shown to increase its accuracy. In contrast, there is no such inbuilt detuning for MS, although one may be, and usually is, included. This paper investigates the use of the DNF detuning as the chosen detuning in the MS method as a way of equating the two techniques, demonstrating that the two can be made to give identical results up to order. For the examples considered here, the resulting predictions are more accurate than those provided by the standard MS technique. Wolfram Mathematica scripts implementing these methods have been provided to be used in conjunction with this paper to illustrate their practicality. Electronic supplementary material The online version of this article (10.1007/s11071-018-4534-1) contains supplementary material, which is available to authorized users.

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Modelling the dynamics of nonlinear systems poses a much more challenging problem than for their linear counterparts; as such, analytical solutions are rarely achievable and numerical or analytical approximations are often necessary to understand the system's behaviour. While numerical techniques are undoubtedly accurate, it is possible to gain a greater understanding of the processes underpinning the workings of the dynamics. Therefore, it is valuable to investigate the accuracy and practicality of the aforementioned analytical approximation techniques and compare the results with numerical which are known to be accurate. In this paper, the unforced, undamped dynamics (known as backbone curves) of a non-symmetric twomass oscillator will be calculated using the second-order normals forms (SONF), harmonic balance, and multiple scales techniques. The results of these will then be compared to responses found using numerical continuation. Furthermore, the forced responses will be approximated using the SONF and harmonic balance techniques.