scholarly journals Closure to “Discussion of ‘An Exact Solution of the Inverse Problem in Heat Conduction Theory and Applications’” (1964, ASME J. Heat Transfer, 86, pp. 380–381)

1964 ◽  
Vol 86 (3) ◽  
pp. 381-382
Author(s):  
O. R. Burggraf
Keyword(s):  
Heat Transfer ◽  
Inverse Problem ◽  
Exact Solution ◽  
Heat Conduction ◽  
Conduction Theory

An Exact Solution of the Inverse Problem in Heat Conduction Theory and Applications

1964 ◽  
Vol 86 (3) ◽  
pp. 373-380 ◽  
Author(s):  
O. R. Burggraf
Keyword(s):  
Inverse Problem ◽  
Exact Solution ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Approximate Solutions ◽  
Convergent Series ◽  
Single Location ◽  
Leading Term ◽  
The One ◽  
Direct Problems

An inverse problem in unsteady heat conduction is one for which boundary conditions are prescribed internally, the surface conditions being unknown. By specifying the boundary conditions at a single location, an exact solution is obtained as a rapidly convergent series with the well-known, lumped capacitance approximation as the leading term. Specific forms of the series are determined for sample inverse problems: solid slab, cylinder, sphere, and transpiration-cooled slab. The solution also is applied to direct problems, involving two-point boundary conditions. By truncating the series, approximate solutions of simple form result. The one-term and two-term approximations compare well with exact solutions.

Nonlocal and Nonequilibrium Heat Conduction in the Vicinity of Nanoparticles

1996 ◽  
Vol 118 (3) ◽  
pp. 539-545 ◽  
Author(s):  
G. Chen
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Particle Temperature ◽  
Approximate Expression ◽  
Mean Free Path ◽  
Boltzmann Transport ◽  
Host Medium ◽  
Conduction Theory ◽  
Fourier Heat Conduction ◽  
Thermal Phenomena

Heat transfer around nanometer-scale particles plays an important role in a number of contemporary technologies such as nanofabrication and diagnosis. The prevailing method for modeling thermal phenomena involving nanoparticles is based on the Fourier heat conduction theory. This work questions the applicability of the Fourier heat conduction theory to these cases and answers the question by solving the Boltzmann transport equation. The solution approaches the prediction of the Fourier law when the particle radius is much larger than the heat-carrier mean free path of the host medium. In the opposite limit, however, the heat transfer rate from the particle is significantly smaller, and thus the particle temperature rise is much larger than the prediction of the Fourier conduction theory. The differences are attributed to the nonlocal and nonequilibrium nature of the heat transfer processes around nanoparticles. This work also establishes a criterion to determine the applicability of the Fourier heat conduction theory and constructs a simple approximate expression for calculating the effective thermal conductivity of the host medium around a nanoparticle. Possible experimental evidence is discussed.

3D Unsteady Heat Transfer in Multi-Connected Domains via LSFEM: A Case Study

2015 ◽  
Vol 775 ◽  
pp. 93-97
Author(s):  
Estaner Claro Romão
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Exact Solution ◽  
Finite Element ◽  
Heat Conduction ◽  
Least Squares ◽  
Unsteady Heat Transfer ◽  
Future Studies ◽  
Comparison Of The Results

This paper aims in particular to do a case study of the numerical efficiency of the application of LSFEM (Least Squares Finite Element Method) in the solution of heat conduction problems in multi-connected domains. To demonstrate this study two cases (the first with exact solution for comparison of results) are presented in the same multi-connected geometry, of easy construction, to facilitate the comparison of the results of this paper with future studies of other researchers.

scholarly journals An Exact Solution to a Problem in Heat Transfer

1961 ◽  
Vol 14 (2) ◽  
pp. 317 ◽  
Author(s):  
CHJ Johnson
Keyword(s):  
Heat Transfer ◽  
Exact Solution ◽  
Heat Conduction ◽  
Heat Transport ◽  
Solid Body ◽  
Analytical Solutions ◽  
Heat Conduction Equation ◽  
Transport Equations ◽  
Temperature History ◽  
Moving Fluid

In order to determine the complete temperature history in problems concerning the transfer of heat from a moving fluid to a solid body one is obliged, in general, to solve both the flow and heat transport equations for the fluid and the heat conduction equation for the solid. Analytical solutions to this problem cannot in general be given owing to the (non-linear) way in which the flow and heat transport equations for the fluid are coupled.

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