scholarly journals Reply to Comment on  Exact analytical solution for the generalized Lyapunov exponent of the two-dimensional Anderson localization 

2004 ◽  
Vol 16 (9) ◽  
pp. 1683-1685 ◽  
Author(s):  
V N Kuzovkov ◽  
V Kashcheyevs ◽  
W von Niessen
Keyword(s):  
Lyapunov Exponent ◽  
Analytical Solution ◽  
Anderson Localization ◽  
Exact Analytical Solution ◽  
Two Dimensional

scholarly journals The exact analytical solution for the gas lubricated bearing in the slip and continuum flow regime

2012 ◽  
Vol 91 (105) ◽  
pp. 83-93 ◽  
Author(s):  
Nevena Stevanovic ◽  
Vladan Djordjevic
Keyword(s):  
Analytical Solution ◽  
Flow Rate ◽  
Gas Flow ◽  
Exact Analytical Solution ◽  
The Other ◽  
Two Dimensional ◽  
Lubrication Equation ◽  
Continuum Flow ◽  
Independent Variable ◽  
The Continuum

The exact analytical solution for the compressible two-dimensional gas flow in the microbearing is presented. The general slip-corrected Reynolds lubrication equation is derived and it is shown that it possesses an exact analytical solution. It is obtained by a suitable transformation of the independent variable, and it provides the pressure distribution in the bearing as well as the mass flow rate through it. By neglecting the rarefaction effect, this solution is also applicable to the continuum gas flow in the bearing, which also does not exist in the open literature. The obtained analytical solution can be usefully applied for testing the other, experimental or numerical results.

scholarly journals The exact analytical solution of the dual-phase-lag two-temperature bioheat transfer of a skin tissue subjected to constant heat flux

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Hamdy M. Youssef ◽  
Najat A. Alghamdi
Keyword(s):  
Heat Flux ◽  
Analytical Solution ◽  
Exact Analytical Solution ◽  
Constant Heat Flux ◽  
Bioheat Transfer ◽  
Skin Tissue ◽  
Phase Lag ◽  
Dual Phase ◽  
Constant Heat ◽  
Two Temperature

Abstract This work is dealing with the temperature reaction and response of skin tissue due to constant surface heat flux. The exact analytical solution has been obtained for the two-temperature dual-phase-lag (TTDPL) of bioheat transfer. We assumed that the skin tissue is subjected to a constant heat flux on the bounding plane of the skin surface. The separation of variables for the governing equations as a finite domain is employed. The transition temperature responses have been obtained and discussed. The results represent that the dual-phase-lag time parameter, heat flux value, and two-temperature parameter have significant effects on the dynamical and conductive temperature increment of the skin tissue. The Two-temperature dual-phase-lag (TTDPL) bioheat transfer model is a successful model to describe the behavior of the thermal wave through the skin tissue.

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