In this study, the effect of magnetic field on an incompressible ferrofluid flow along a vertical wavy surface saturated in a porous medium is investigated. Ferrofluid is made by incorporating magnetic particles, in this case cobalt, at the nanoscale level into a base fluid. For the study of porous medium two well-known models, namely, Darcy and non-Darcy, are used. The mathematical model in terms of governing partial differential equations which are based on conservation laws in mechanics according to the assumption is developed, and this model is converted into a dimensionless form by suitable transformations. Due to the complex non-linear partial differential equations, the numerical solution is calculated by using an implicit finite difference scheme. The impact of involved parameters, namely, magnetic parameter, nanoparticle volume fraction parameter, the amplitude of the wavy surface, and the Grashof number, on Nusselt and average Nusselt numbers are studied through graphs and tables.
The results show that for large values of the magnetic parameter, both the Nusselt number and the average Nusselt number decrease in ferrofluid flow. The value of the Nusselt number in the Darcy model is higher than the value of the Nusselt number in the non-Darcy model.
Thermodynamic performance analysis of microscopic Feynman’s engine has always been a hot topic, since it can reveal the operating mechanism of the system and give out the suggestions of performance improvement. The present work explores the optimal performance regions of the ratchet operating, respectively, as heat engine and refrigerator. The major purpose is to obtain the optimal performance bunds and provide theoretical guidelines for the designs of practical microscopic ratchet engine systems. Based on an irreversible Feynman’s ratchet engine, the optimal power output versus thermal efficiency performance and the optimal cooling load versus COP performance in different operation modes are analyzed. The effects of irreversible heat leakage and major design parameters are also explored. By further introducing the ecological function, efficient power, and figure of merit criteria, performance characteristics of ratchet device with different optimization indexes are analyzed and compared with each other. The optimal performance regions concerning different optimization criteria are obtained. The results show that by reasonably selecting design parameters, Feynman’s ratchet can attain the optimal operation conditions for different design purposes.
First, the special-relativistic Theory of Irreversible Processes for a multi-component fluid is formulated. It is based on (i) the balance equations of the particle number and the energy-momentum for the total system (i. e., the mixture of the components) as well as the sub-systems (i. e., the components) and (ii) the dissipation inequality and the Gibbs equation for the mixture. In order to allow for reactions between the single components, in contrast to the total system, the sub-systems are assumed to be open, which means that their particle number and energy-momentum are not constrained by conservation laws. Without making any assumptions on the thermodynamic behavior of the interacting components, one arrives at a thermodynamic description of the mixture showing now heat conduction and viscosity. In particular, this makes it possible to calculate the entropy production and, thus, to identify thermodynamic currents and forces. In a second part, the post-Newtonian limit of this theory is calculated to show that for the mixture there result relations known from classical Extended Thermodynamics that partly are corrected by entrainment terms. The mathematical origin and physical consequences of these terms are discussed.
The main aim of this research work is to show the simultaneous effects of ferro-particles () and thermal radiation on the natural convection of non-Newtonian nanofluid flow between two vertical flat plates. The studied nanofluid is created by dispersing ferro-particles () in sodium alginate (SA), which is considered as a non-Newtonian base fluid. Resolution of the resulting set of coupled non-linear second order differential equations characterizing dynamic and thermal distributions (velocity/temperature) is ensured via the Adomian decomposition method (ADM). Thereafter the obtained ADM results are compared to the Runge–Kutta–Feldberg based shooting data. In this investigation, a parametric study was conducted showing the influence of varying physical parameters, such as volumic fraction of nanoparticles, Eckert number () and thermal radiation parameter (N), on the velocity distribution, the skin friction coefficient, the heat transfer rate and the temperature distribution. Results obtained also show the advantages of ferro-particles over other types of standard nanoparticles. On the other hand, this investigation demonstrates the accuracy of the adopted analytical ADM technique.
Canonical statistical mechanics hinges on two quantities, i. e., state degeneracy and the Boltzmann factor, the latter of which usually dominates thermodynamic behaviors. A recently identified phenomenon (supradegeneracy) reverses this order of dominance and predicts effects for equilibrium that are normally associated with non-equilibrium, including population inversion and steady-state particle and energy currents. This study examines two thermodynamic paradoxes that arise from supradegeneracy and proposes laboratory experiments by which they might be resolved.
Rheo-NMR velocimetry was used to study shear banding of a 6 wt.% cetylpyridinium chloride (CPCl) worm-like micelle solution under shear startup conditions with and without pre-shear. 1D velocity profiles across the fluid gap of a concentric cylinder Couette shear cell were measured every 1 s following shear startup for four different applied shear rates within the stress plateau. Fitting of the velocity profiles allowed calculation of the shear banding characteristics (shear rates in the high and low shear band, the interface position and apparent slip at the inner rotating wall) as the flow transitioned from transient to steady state regimes. Characteristic timescales to reach steady state were obtained and found to be similar for all shear banding characteristics. Timescales decreased with increasing applied shear rate. Large temporal fluctuations with time were also observed and Fourier transform of the time and velocity autocorrelation functions quantified the fluctuation frequencies. Frequencies corresponded to the elastically driven hydrodynamic instabilities, i.e. vortices, that are known to occur in the unstable high shear band and were dependent upon both applied shear rate and the pre-shear protocol.