scholarly journals Exact analytical solution for the Kissinger equation: Determination of the peak temperature and general properties of thermally activated transformations

2014 ◽  
Vol 598 ◽  
pp. 51-58 ◽  
Author(s):  
J. Farjas ◽  
P. Roura
Keyword(s):  
Analytical Solution ◽  
Exact Analytical Solution ◽  
Peak Temperature ◽  
Kissinger Equation ◽  
Thermally Activated ◽  
General Properties

ANALYTICAL METHOD FOR DETERMINING THE THICKNESS OF DEPOSITS ON THE INTERNAL SURFACES OF HEAT EXCHANGERS

2019 ◽  
Vol 9 (1) ◽  
pp. 20-24
Author(s):  
Olga Yu. KURGANOVA ◽  
Igor V. KUDINOV ◽  
Ruslan M. KLEBLEEV ◽  
Ekaterina V. STEFANYUK ◽  
Tatiana E. GAVRILOVA
Keyword(s):  
Analytical Solution ◽  
Outer Surface ◽  
Analytical Method ◽  
Exact Analytical Solution ◽  
Large Diameter ◽  
Experimental Studies ◽  
Sediment Layer ◽  
Internal Surfaces ◽  
Pipeline Wall

Using the exact analytical solution of the stationary thermal conductivity problem for a two layer flat wall under inhomogeneous boundary conditions of the first and third kind, an analytical method for thickness determination of the sediment layer on the inner surface of the pipeline wall by the temperature known from the experiment on its outer surface is developed. The thickness of the deposits is found from the solution of the inverse problem by substituting the experimental value of the temperature of the outer surface of the wall into the formula of an accurate analytical solution. According to the results of theoretical studies, the thickness of the deposits was equal to 1.3 cm. Due to the large diameter of the pipeline (0.6 m) and the insignificant thickness of the two layer wall (0.016 m), it was assumed to be flat. The thickness of the deposits according to experimental studies was equal to 1.1 cm. Therefore, the discrepancy between the results of theoretical and experimental studies is 15.3%. The sequence of obtaining a solution to a similar problem for a cylindrical wall is also presented.

scholarly journals PURE BENDING OF ELASTIC CURVE OF A BEAM

2021 ◽  
Vol 4 (4) ◽  
pp. 36-43
Author(s):  
Vyacheslav Ogarkov ◽  
Aleksei Aksenov ◽  
Sergei Malyukov ◽  
Aleksandr Knyazev ◽  
Nikolai Borodin
Keyword(s):  
Analytical Solution ◽  
Poisson’S Ratio ◽  
Exact Analytical Solution ◽  
Poisson's Ratio ◽  
Curved Beam ◽  
Pure Bending ◽  
Elastic Curve

The problem of pure bending of an elastic curved beam with a given moment M is considered. It is proved that the values of stresses and strains found in this paper depend on the value of the Poisson's ratio μ. An exact analytical solution to this problem is obtained with the determination of unambiguous expressions for stresses and deformations.

scholarly journals POLAR-SYMMETRIC DEFORMATION OF AN ELASTIC CYLINDER UNDER TEMPERATURE-HUMIDITY EXPOSURE

2020 ◽  
Vol 3 (3) ◽  
pp. 81-93
Author(s):  
Vyacheslav Ogarkov ◽  
Aleksei Aksenov ◽  
Sergei Malyukov
Keyword(s):  
Analytical Solution ◽  
Radial Displacement ◽  
Exact Analytical Solution ◽  
Technical Problem ◽  
Incompressible Material ◽  
Elastic Cylinder ◽  
Symmetric Deformation ◽  
Temperature And Humidity ◽  
Special Case

The actual scientific and technical problem of polar-symmetric deformation of an elastic cylinder under conditions of temperature and humidity influences is considered. An exact analytical solution to this problem is obtained with the determination of unambiguous expressions for stresses, deformations and radial displacement. The obtained solution allows solving this problem for an incompressible material with μ = 1/2 as a special case.

Analytical solution for the Kissinger equation

2009 ◽  
Vol 24 (10) ◽  
pp. 3095-3098 ◽  
Author(s):  
Pere Roura ◽  
Jordi Farjas
Keyword(s):  
Activation Energy ◽  
Analytical Solution ◽  
Kinetic Analysis ◽  
Relative Error ◽  
Structural Relaxation ◽  
Amorphous Materials ◽  
Reaction Rate ◽  
Large Range ◽  
Peak Temperature ◽  
Kissinger Equation

An analytical solution for the Kissinger equation relating the activation energy, E, with the peak temperature of the reaction rate, Tm, has been found. It is accurate (relative error below 2%) for a large range of E/RTm values (from 15 to above 60) that cover most experimental situations. The possibilities opened by this solution are outlined by applying it to the analysis of some particular problems encountered in structural relaxation of amorphous materials and in kinetic analysis.

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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