Nonlinear heat-transport equation beyond Fourier law: application to heat-wave propagation in isotropic thin layers

2016 ◽  
Vol 29 (2) ◽  
pp. 411-428 ◽  
Author(s):  
A. Sellitto ◽  
V. Tibullo ◽  
Y. Dong
Keyword(s):  
Wave Propagation ◽  
Transport Equation ◽  
Heat Transport ◽  
Heat Wave ◽  
Thin Layers ◽  
Fourier Law ◽  
Heat Transport Equation

scholarly journals Exact Solution of Heat Transport Equation for a Heterogeneous Geothermal Reservoir

Energies ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 2935 ◽  
Author(s):  
Sayantan Ganguly
Keyword(s):  
Temperature Distribution ◽  
Transport Equation ◽  
Heat Transport ◽  
Transport Processes ◽  
Geothermal Reservoir ◽  
Transient Temperature ◽  
Thermal Front ◽  
Transient Temperature Distribution ◽  
Heat Transport Equation ◽  
Geothermal Aquifer

An exact integral solution for transient temperature distribution, due to injection-production, in a heterogeneous porous confined geothermal reservoir, is presented in this paper. The heat transport processes taken into account are advection, longitudinal conduction and conduction to the confining rock layers due to the vertical temperature gradient. A quasi 2D heat transport equation in a semi-infinite porous media is solved using the Laplace transform. The internal heterogeneity of the geothermal reservoir is expressed by spatial variation of the flow velocity and the effective thermal conductivity of the medium. The model results predict the transient temperature distribution and thermal-front movement in a geothermal reservoir and the confining rocks. Another transient solution is also derived, assuming that longitudinal conduction in the geothermal aquifer is negligible. Steady-state solutions are presented, which determine the maximum penetration of the cold water thermal front into the geothermal aquifer.

scholarly journals Influence of the composition gradient on the propagation of heat pulses in functionally graded nanomaterials

2019 ◽  
Vol 475 (2221) ◽  
pp. 20180499 ◽  
Author(s):  
B.-Y. Cao ◽  
M. Di Domenico ◽  
B.-D. Nie ◽  
A. Sellitto
Keyword(s):  
Theoretical Model ◽  
Heat Transport ◽  
Functionally Graded ◽  
Thin Layers ◽  
Composition Gradient ◽  
Graded Materials ◽  
Heat Transport Equation ◽  
Acceleration Waves ◽  
Heat Pulses ◽  
Special Case

A theoretical model to describe heat transport in functionally graded nanomaterials is developed in the framework of extended thermodynamics. The heat-transport equation used in our theoretical model is of the Maxwell–Cattaneo type. We study the propagation of acceleration waves in functionally graded materials (FGMs). In the special case of functionally graded Si 1− c Ge c thin layers, we point out the influence of the composition gradient on the propagation of heat pulses. A possible use of heat pulses as exploring tool to infer the inner composition of FGMs is suggested.

scholarly journals Heat-pulse propagation along nonequilibrium nanowires in thermomass theory

2016 ◽  
Vol 7 (2) ◽  
pp. 39-55
Author(s):  
Antonio Sellitto ◽  
Patrizia Rogolino ◽  
Isabella Carlomagno
Keyword(s):  
Temperature Gradient ◽  
Transport Equation ◽  
Heat Transport ◽  
Pulse Propagation ◽  
Heat Pulse ◽  
Average Temperature ◽  
Temperature Ranges ◽  
Heat Transport Equation ◽  
Heat Pulses ◽  
Theoretical Proposal

AbstractWe analyze the consequences of the nonlinear terms in the heat-transport equation of the thermomass theory on heat pulses propagating in a nanowire in nonequilibrium situations. As a consequence of the temperature dependence of the speeds of propagation, in temperature ranges wherein the specific heat shows negligible variations, heat pulses will shrink (or extend) spatially, and will increase (or decrease) their average temperature when propagating along a temperature gradient. A comparison with the results predicted by a different theoretical proposal on the shape of a propagating heat pulse is made, too.

scholarly journals Non-local effects in radial heat transport in silicon thin layers and graphene sheets

2011 ◽  
Vol 468 (2141) ◽  
pp. 1217-1229 ◽  
Author(s):  
A. Sellitto ◽  
D. Jou ◽  
J. Bafaluy
Keyword(s):  
Heat Transport ◽  
Local Equilibrium ◽  
Mean Free Path ◽  
Thin Layers ◽  
Graphene Sheets ◽  
Fourier Law ◽  
Local Effects ◽  
Radial Heat ◽  
Non Local ◽  
The Mean

We explore non-local effects in radially symmetric heat transport in silicon thin layers and in graphene sheets. In contrast to one-dimensional perturbations, which may be well described by means of the Fourier law with a suitable effective thermal conductivity, two-dimensional radial situations may exhibit a more complicated behaviour, not reducible to an effective Fourier law. In particular, a hump in the temperature profile is predicted for radial distances shorter than the mean-free path of heat carriers. This hump is forbidden by the local-equilibrium theory, but it is allowed in more general thermodynamic theories, and therefore it may have a special interest regarding the formulation of the second law in ballistic heat transport.

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