No abstract

Please cite this article in press as: A. Singh, E.B. Tadmor, Thermal parameter identification for non-Fourier heat transfer from molecular dynamics, J. Comput. Phys. (2015), http://dx. AbstractFourier's law leads to a diffusive model of heat transfer in which a thermal signal propagates infinitely fast and the only material parameter is the thermal conductivity. In micro-and nano-scale systems, non-Fourier effects involving coupled diffusion and wavelike propagation of heat can become important. An extension of Fourier's law to account for such effects leads to a Jeffreys-type model for heat transfer with two relaxation times. We propose a new Thermal Parameter Identification (TPI) method for obtaining the Jeffreys-type thermal parameters from molecular dynamics simulations. The TPI method makes use of a nonlinear regression-based approach for obtaining the coefficients in analytical expressions for cosine and sine-weighted averages of temperature and heat flux over the length of the system. The method is applied to argon nanobeams over a range of temperature and system sizes. The results for thermal conductivity are found to be in good agreement with standard Green-Kubo and direct method calculations. The TPI method is more efficient for systems with high diffusivity and has the advantage, that unlike the direct method, it is free from the influence of thermostats. In addition, the method provides the thermal relaxation times for argon. Using the determined parameters, the Jeffreys-type model is able to reproduce the molecular dynamics results for a short-duration heat pulse where wavelike propagation of heat is observed thereby confirming the existence of second sound in argon. An implementation of the TPI method in MATLAB is available as part of the online supplementary material.

Global absolute and convective stability analysis of flow past a circular cylinder with symmetry conditions imposed along the centreline of the flow field is carried out. A stabilized finite element formulation is used to solve the eigenvalue problem resulting from the linearized perturbation equation. All the computations carried out are in two dimensions. It is found that, compared to the unrestricted flow, the symmetry conditions lead to a significant delay in the onset of absolute as well as convective instability. In addition, the onset of absolute instability is greatly affected by the location of the lateral boundaries and shows a non-monotonic variation. Unlike the unrestricted flow, which is associated with von Kármán vortex shedding, the flow with centreline symmetry becomes unstable via modes that are associated with low-frequency large-scale structures. These lead to expansion and contraction of the wake bubble and are similar in characteristics to the low-frequency oscillations reported earlier in the literature. A global linear convective stability analysis is utilized to find the most unstable modes for different speeds of the disturbance. Three kinds of convectively unstable modes are identified. The ones travelling at very low streamwise speed are associated with large-scale structures and relatively low frequency. Shear layer instability, with relatively smaller scale flow structures and higher frequency, is encountered for disturbances travelling at relatively larger speed. For low blockage a new type of instability is found. It travels at relatively high speed and resembles a swirling flow structure. As opposed to the absolute instability, the convective instability appears at much lower Re and its onset is affected very little by the location of the lateral boundaries. Analysis is also carried out for determining the convective stability of disturbances that travel in directions other than along the free stream. It is found that the most unstable disturbances are not necessarily the purely streamwise travelling ones. Disturbances that move purely in the cross-stream direction can also be convectively unstable. The results from the linear stability analysis are confirmed by carrying out direct time integration of the linearized disturbance equations. The disturbance field shows transient growth by several orders of magnitude confirming that such flows act as amplifiers. Direct time integration of the Navier–Stokes equation is carried out to track the time evolution of both the large-scale low-frequency oscillations and small-scale shear layer instabilities. The critical Re for the onset of convective instability is compared with earlier results from local analysis. Good agreement is found.

No abstract

PurposeTo provide a general equation for finding out viscosity of lubricating oils at different temperatures and ages.Design/methodology/approachBased on previous works and a case study on field, a general equation was formulated which relates viscosity‐temperature‐age of lubricant.FindingsThe equation is very simple and a good consistency was found.Practical implicationsThis equation will help the designers/manufacturers to recommend the correct grade of lubricating oil.Originality/valueThis type of relationship was never reported earlier.