A variant of the heat balance integral method and a new proof of the exponentially fast asymptotic behavior of the solutions in heat conduction problems with absorption

1990 ◽  
Vol 28 (12) ◽  
pp. 1253-1259 ◽  
Author(s):  
Domingo Alberto Tarzia
Keyword(s):  
Asymptotic Behavior ◽  
Heat Conduction ◽  
Heat Balance ◽  
Integral Method ◽  
Heat Balance Integral Method ◽  
The Heat Balance

scholarly journals Heat-balance integral to fractional (half-time) heat diffusion sub-model

2010 ◽  
Vol 14 (2) ◽  
pp. 291-316 ◽  
Author(s):  
Jordan Hristov
Keyword(s):  
Diffusion Equation ◽  
Heat Balance ◽  
Integral Method ◽  
Time Derivative ◽  
Heat Diffusion ◽  
Half Time ◽  
Heat Diffusion Equation ◽  
Parabolic Profile ◽  
Heat Balance Integral Method ◽  
The Heat Balance

The fractional (half-time) sub-model of the heat diffusion equation, known as Dirac-like evolution diffusion equation has been solved by the heat-balance integral method and a parabolic profile with unspecified exponent. The fractional heat-balance integral method has been tested with two classic examples: fixed temperature and fixed flux at the boundary. The heat-balance technique allows easily the convolution integral of the fractional half-time derivative to be solved as a convolution of the time-independent approximating function. The fractional sub-model provides an artificial boundary condition at the boundary that closes the set of the equations required to express all parameters of the approximating profile as function of the thermal layer depth. This allows the exponent of the parabolic profile to be defined by a straightforward manner. The elegant solution performed by the fractional heat-balance integral method has been analyzed and the main efforts have been oriented towards the evaluation of fractional (half-time) derivatives by use of approximate profile across the penetration layer.

Research on Heat Conductivity with a Time-Varying Heat Source

2014 ◽  
Vol 698 ◽  
pp. 637-642
Author(s):  
Anton Eremin ◽  
Ekaterina Stefanyuk ◽  
Liubov Abisheva
Keyword(s):  
Heat Conduction ◽  
Heat Source ◽  
Heat Balance ◽  
Integral Method ◽  
Approximate Analytical Solution ◽  
Heat Conduction Problem ◽  
Time Varying ◽  
Heat Sources ◽  
Plate Temperature ◽  
The Heat Balance

Using additional boundary conditions in the integral method of the heat balance, an approximate analytical solution to the heat conduction problem for an endless plate with time-varying heat sources has been found. It is shown that with any heat source capacity an unlimited plate temperature increase takes place in the course of time.

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