Here, we adapt the concept of transformational thermodynamics, whereby the flux of temperature is controlled via anisotropic heterogeneous diffusivity, for the diffusion and transport of mass concentration. The n-dimensional, time-dependent, anisotropic heterogeneous Fick's equation is considered, which is a parabolic partial differential equation also applicable to heat diffusion, when convect...

In this study, nanofluids of Chromium (Cr) in water, Ethylene Glycol and Ethanol have been prepared using single step method. The thermal conductivity and diffusivity of these nanofluids were measured via hot wire-photothermal deflection technique. Based on finite difference method (FDM) temperature distribution and photothermal deflection caused by the hot wire inside nanofluids was obtained. ...

In this paper thermal conductivity and thermal diffusivity of a two layer system is examined from the theoretical point of view. We use the one dimensional heat diffusion equation with the appropriate solution in each layer and boundary conditions at the interfaces to calculate the heat transport in this bounded system. We also consider the heat flux at the surface of the samle as boundary cond...

Axial diffusion in a two-dimensional channel of smoothly varying geometry can be approximately described as one-dimensional diffusion in the entropy potential with position-dependent effective diffusivity by means of the modified Fick-Jacobs equation. In this paper, Brownian dynamics simulations are used to study the range of applicability of such a description, as well as the accuracy of the e...

We consider the Moore-Gibson-Thompson equation which arises, e.g., as a linearization of a model for wave propagation in viscous thermally relaxing fluids. This third order in time equation displays, even in the linear version, a variety of dynamical behaviors for their solutions that depend on the physical parameters in the equation. These range from non-existence [3] and instability to expone...

In this thesis, we introduce random differential equations in an abstract framework and study their well-posedness. We study average controllability properties of a random heat equation when the diffusivity is a random variable. We show that the solutions of such random heat equations are both null and approximately controllable in average from an arbitrary open set of the domain and in an arbi...

in this research the drying of four kinds of vegetables was investigated in a vacuum dryer. the effect of temperature on drying rate of samples at various temperatures (30, 35 and 45 °c) was studied. six thin-layer drying models were fitted to drying data and suitable model was selected from them. then effective moisture diffusivity and activation energy of samples were calculated. the diffusio...

We study the behaviour of the solutions of the stationary diffusion equation as a function of a possibly rough (L8-) diffusivity. This includes the boundary behaviour of the solution maps, associating to each diffusivity the solution corresponding to some fixed source function, when the diffusivity approaches infinite values in parts of the medium. In n-dimensions, n ¥ 1, by assuming a weak not...

A head loss concept, new to the stream-aquifer interaction, is introduced for modeling laboratory observations. Using this concept, the equation applicable to fully penetrating streams is modified to account for the head loss at the entrance. The modified model is able to explain and fit the observed laboratory data correctly. Equations are proposed to calculate the hydraulic diffusivity of aqu...