A New Approach For The Heat Balance Integral Method Applied to Heat Conduction Problems

2005 ◽  
Author(s):  
Walber Braga ◽  
Marcia Mantelli ◽  
João Azevedo
Keyword(s):  
Heat Conduction ◽  
Heat Balance ◽  
Integral Method ◽  
New Approach ◽  
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.

scholarly journals An alternative integral-balance solutions to transient diffusion of heat (mass) by time-fractional semi-derivatives and semi-integrals: Fixed boundary conditions

2016 ◽  
Vol 20 (6) ◽  
pp. 1867-1878
Author(s):  
Jordan Hristov
Keyword(s):  
Heat Balance ◽  
Neumann Boundary Condition ◽  
Integral Method ◽  
Integration Method ◽  
Neumann Boundary ◽  
New Approach ◽  
Fixed Boundary ◽  
Surface Gradient ◽  
Approximation Errors ◽  
Heat Balance Integral Method

A new approach to integral-balance solutions of the diffusion equation of heat (mass) with constant transport properties by applying time-fractional semi-derivatives and semi-integrals of Riemann-Liouville sense has been developed. The time-fractional semiderivatives and semiintegrals replace the surface gradient (temperature) which in the classical Heat-balance integral method (HBIM) of Goodman and the Double-integration method (DIM) should be expressed through the assumed profile. The application of semiderivatives and semiintegrals reduces the approximation errors to levels less than the ones exhibited by the classical HBIM and DIM. The method is exemplified by solutions of Dirichlet and Neumann boundary condition problems.

Sign in / Sign up

Export Citation Format

Share Document