An asymptotic-preserving semi-Lagrangian algorithm for the time-dependent anisotropic heat transport equation

2014 ◽  
Vol 272 ◽  
pp. 719-746 ◽  
Author(s):  
L. Chacón ◽  
D. del-Castillo-Negrete ◽  
C.D. Hauck
Keyword(s):  
Transport Equation ◽  
Heat Transport ◽  
Time Dependent ◽  
Asymptotic Preserving ◽  
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 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.

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