Solutions of Heat-Conduction Problem With the Aid of the Inverse Method

1953 ◽  
Vol 20 (4) ◽  
pp. 489-496
Author(s):  
F. S. Weinig
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Heat Flow ◽  
Point Source ◽  
Line Source ◽  
Inverse Method ◽  
Plane Surface ◽  
Heat Conduction Problem ◽  
Potential Equation ◽  
Circular Arc

Abstract Using a known solution of the potential equation for heat conduction it is possible to determine boundaries which fulfill the boundary conditions. This idea was applied to the heat flow with parallel streamlines, from a line source and from a point source. From the parallel flow, fins have been derived on a plane surface having circular arc flanks. From the line source, fins axially and radially on a cylindrical surface and from a point source fins on a sphere are obtained. The improvement of the heat transfer has been found in these examples to depend only on the surface direction at the base of the fins.

Nonlinear Inverse Heat Conduction With a Moving Boundary: Heat Flux and Surface Recession Estimation

1999 ◽  
Vol 121 (3) ◽  
pp. 708-711 ◽  
Author(s):  
V. Petrushevsky ◽  
S. Cohen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fourier Series ◽  
Heat Conduction ◽  
Moving Boundary ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Variable Order ◽  
Inverse Heat Conduction ◽  
One Dimensional

A one-dimensional, nonlinear inverse heat conduction problem with surface ablation is considered. In-depth temperature measurements are used to restore the heat flux and the surface recession history. The presented method elaborates a whole domain, parameter estimation approach with the heat flux approximated by Fourier series. Two versions of the method are proposed: with a constant order and with a variable order of the Fourier series. The surface recession is found by a direct heat transfer solution under the estimated heat flux.

Conservation laws and associated Lie point symmetries admitted by the transient heat conduction problem for heat transfer in straight fins

Open Physics ◽  
2013 ◽  
Vol 11 (8) ◽  
Author(s):  
Partner Ndlovu ◽  
Rasselo Moitsheki
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Conduction ◽  
Conservation Laws ◽  
Linear Function ◽  
Power Law ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Lie Point Symmetries ◽  
Transient Heat Conduction Problem

AbstractSome new conservation laws for the transient heat conduction problem for heat transfer in a straight fin are constructed. The thermal conductivity is given by a power law in one case and by a linear function of temperature in the other. Conservation laws are derived using the direct method when thermal conductivity is given by the power law and the multiplier method when thermal conductivity is given as a linear function of temperature. The heat transfer coefficient is assumed to be given by the power law function of temperature. Furthermore, we determine the Lie point symmetries associated with the conserved vectors for the model with power law thermal conductivity.

scholarly journals Validation of accuracy and stability of numerical simulation for 2-D heat transfer system by an entropy production approach

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 97-104
Author(s):  
Ali Brohi ◽  
Haochun Zhang ◽  
Kossi Min-Dianey ◽  
Muhammad Rafique ◽  
Muhammad Hassan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Heat Conduction ◽  
Entropy Production ◽  
Heat Conduction Problem ◽  
Current Approach ◽  
Transfer System ◽  
Heat Transfer System ◽  
The Stability ◽  
Accuracy And Stability

The entropy production in 2-D heat transfer system has been analyzed systematically by using the finite volume method, to develop new criteria for the numerical simulation in case of multidimensional systems, with the aid of the CFD codes. The steady-state heat conduction problem has been investigated for entropy production, and the entropy production profile has been calculated based upon the current approach. From results for 2-D heat conduction, it can be found that the stability of entropy production profile exhibits a better agreement with the exact solution accordingly, and the current approach is effective for measuring the accuracy and stability of numerical simulations for heat transfer problems.

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