Volume 48, Issue 3

Generalization of the variational formulation of the Onsager–Machlup thermodynamic theory of fluctuation is considered. Within the framework of variational theory, we introduce the time-dependent generalized normal distribution and Hamilton–Jacobi equation. The family of higher-order partial differential equations, which generalize classical Fokker–Planck equation, is considered. It is shown that proposed theory can be used for describing anomalous diffusion.

This computational analysis focuses on the effects of porous layer on the flow dynamics, heat transfer and hydrodynamic forces of hybrid nanofluid in a channel having an open cavity fixed with bottom wall in the presence of partial magnetic field. The set of PDEs governing the dynamics has been transformed to dimensionless form and simulated using higher order finite element method. In particular, P 3 / P 2 ${\mathbb{P}}_{3}/{\mathbb{P}}_{2}$ finite element pair is employed for the spatial discretization and Crank–Nicolson approach is utilized for the temporal discretization. The obtained equations has been linearized with adaptive Newtons method and linearized systems have been computed using the geometric multi-grid technique. The impact of parameters, for instance, Richardson number, thickness of porous layer and nanoparticle fraction is analyzed in the presence of partial magnetic field and porous layer on the hydrodynamic forces like lift and drag forces on the submerged bodies, being the important part of the fluid flow and heat transfer are also be analysed. It is noticed that the drag and lift coefficients are reduced as the nanoparticle fraction is altered while the local- and average-Nusselt number get higher values.

The linear natural convection of a Maxwell viscoelastic fluid with Cattaneo–Christov heat flux constitutive equation, between two thick walls with finite thermal conductivity is investigated. The viscoelastic fluid and the heat flux have different relaxation times. The main interest is on the curves of criticality for different thicknesses ratio D and thermal conductivities ratio X . In the middle range of log  X the curves of criticality stabilize depending on the other parameters of the problem. It is revealed that for some Prandtl numbers the curves of criticality remain higher for small X and lower for large X . However, increasing the Prandtl number this behavior is reversed. It is shown that this has important consequences in the order of the criticality curves when the heat flux relaxation time is increased. Depending on the Prandtl number, an increase of this relaxation time may decrease (destabilize) the curves of criticality until a minimum is reached, after which the curves start to increase (stabilize) again. For two different magnitudes of the viscoelastic relaxation time, the critical Rayleigh number, wavenumber and frequency of oscillation are plotted against log  X for different magnitudes of D and the heat flux relaxation time.

In this paper, we analyze the advanced Feynman’s mechanism from the well-known Feynman’s Lectures on Physics, under the maximum power output, maximum efficient power, and maximum power density criterion. Considering this mechanism like a thermal engine, and using a simplified model, the physical existence regions for these objective functions are shown. We also show their comparison for given values of a defined dimensionless parameter. The behavior for each case of both the general and the normalized forms of the objective functions is compared graphically and the existence of certain intervals of values for the variable parameter used, in which the relation of these objective functions change, is determined. Additionally, it is shown that as the numerical value of the mentioned variable parameter used approaches zero, the area of the region of physical existence of the objective functions is greater. The results of the mentioned comparison are discussed, and appropriate conclusions are included.

We obtain the power and Ω-function of one-qubit Agrawal quantum heat engines solving the Lindbland equation and using the tools of Finite Time Thermodynamics. We prove that these two thermodynamic functions have their maximum values for efficiencies different to zero and the Carnot efficiency. Finally, analyzing the high temperature limit of AQHEs we discover the range of temperatures for which the quantum behaviour is valid.

The proposed study demonstrates the flow phenomenon and thermo-variation of a magnetized stretching sheet induced-radiative nanofluid flow. By incorporating the response surface methodology, the heat transfer rate of the thermally convective flow of nanofluid is optimized. The graphene nanomaterial is used in the water-based nanofluid. A dynamic magnetic field, thermal radiation, and the Cattaneo–Christov heat flux model have used to represent the thermal behavior of the nanofluid. The simulation utilizes experimentally estimated values for the nanomaterial’s thermal conductivity and viscosity. To further reveal the thermal enhancement of the flow, the impact of nanoparticle diameter and the solid-liquid interfacial layer is proposed at the molecular level. The response surface methodology and the sensitivity analysis has used to examine the effects of the nanoparticle volume fraction, Biot number, and magnetic parameter on the rate of heat transfer statistically. A set of equations is formed from the governing partial differential equations by implementing suitable similarity transformations. The bvp4c approach is used to solve the problem numerically. The effect of various parameters has displayed through tables, graphs, and surface plots on heat transfer, mass transfer, and the local Nusselt number. It is discovered that as the Biot number increases, so does the concentration and temperature profile. An excellent accord between the present and previously existing solutions is establishing the validity of the achieved results.

A generalized model for the maximum work rate extractable from the Sun is developed considering a reversible and an endoreversible system to define a more practical upper-bound efficiency for the conversion of solar radiation into work and power. This model is based on a photo-thermal work extractor in communication with a high-temperature radiation reservoir and a low-temperature heat sink. Following the model, a parametric analysis of the concentration acceptance product ( ξ ) and thermal conductance is performed to identify the interdependence of variables for the solar exergy. The results are compared with existing models to provide a practical baseline of work and power extractable from concentrated solar power plants (CSP) technologies. Therefore, it is possible to quantify the irreversibilities of an idealized thermodynamic system operating between the Sun and the absorber (via radiative transfer) and the environment (via convective transfer).

Onsager fluxes proposed by D.G.B. Edelen assume that the same symmetry, nonlinear Onsager reciprocal relations, holds near and far from equilibrium. This assumption leads to exact differential 1-form J ⋅ d X everywhere, where J and X are thermodynamic fluxes and forces, respectively. However, thermodynamic fluxes far from equilibrium are characterized by symmetry breaking, which lead to the inexact differential 1-form. It is shown in this paper that the inexact differential 1-form J ⋅ d X should be represented by multiple independent scalar-valued functions. Generalized Onsager fluxes are obtained based on such representation. Generalized Onsager fluxes do not satisfy the nonlinear Onsager reciprocal relations and contain multiple independent scalar-valued functions, so they are suitable to thermodynamic fluxes far from equilibrium. Generalized Onsager fluxes embody Onsager fluxes as a special case. Therefore, generalized Onsager fluxes provide a unified framework for thermodynamic fluxes near and far from equilibrium.