Thermally Symmetric Nonlinear Heat Transfer in Solids

1981 ◽  
Vol 103 (4) ◽  
pp. 745-752 ◽  
Author(s):  
M. Imber
Keyword(s):  
Heat Transfer ◽  
Thermal Properties ◽  
Analytical Solutions ◽  
Solution Method ◽  
Equivalent Linearization ◽  
Temperature Dependent ◽  
Numerical Examples ◽  
Nonlinear Heat Transfer ◽  
Composite Wall ◽  
Thermal Conductivities

Material thermal properties are temperature dependent, and this effect cannot be disregarded at elevated design temperatures. Based upon the principle of equivalent linearization, analytical solutions are developed for thermally symmetric planar solids. The solution method is, in turn, extended to a composite wall whose individual thermal conductivities are also temperature dependent. As a demonstration of the method’s accuracy several numerical examples are shown.

Heat Transfer of Thin Fins With Temperature-Dependent Thermal Properties and Internal Heat Generation

1967 ◽  
Vol 89 (2) ◽  
pp. 155-162 ◽  
Author(s):  
H. M. Hung ◽  
F. C. Appl
Keyword(s):  
Heat Transfer ◽  
Thermal Properties ◽  
Temperature Distribution ◽  
Heat Generation ◽  
Analytical Study ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Numerical Examples

An analytical study of the temperature distribution along thin fins with temperature-dependent thermal properties and internal heat generation is presented. The analysis utilizes a recently published bounding procedure which yields analytical and continuous bounding functions for the temperature distribution. Several numerical examples are considered. Tabular and graphical results are given. The effects of variable thermal properties and internal heat generation are also shown.

scholarly journals Survey of Some Exact and Approximate Analytical Solutions for Heat Transfer in Extended Surfaces

2021 ◽  
Author(s):  
Raseelo Joel Moitsheki ◽  
Partner Luyanda Ndlovu ◽  
Basetsana Pauline Ntsime
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Thermal Properties ◽  
Analytical Solutions ◽  
Nonlinear Problems ◽  
Transient Heat Transfer ◽  
Temperature Dependent ◽  
Approximate Analytical Solutions ◽  
Extended Surfaces ◽  
Insight Into

In this chapter we provide the review and a narrative of some obtained results for steady and transient heat transfer though extended surfaces (fins). A particular attention is given to exact and approximate analytical solutions of models describing heat transfer under various conditions, for example, when thermal conductivity and heat transfer are temperature dependent. We also consider fins of different profiles and shapes. The dependence of thermal properties render the considered models nonlinear, and this adds a complication and difficulty to solve these model exactly. However, the nonlinear problems are more realistic and physically sound. The approximate analytical solutions give insight into heat transfer in fins and as such assist in the designs for better efficiencies and effectiveness.

ANALYTICAL SOLUTIONS OF NON-FOURIER PENNES AND CHEN–HOLMES EQUATIONS

2012 ◽  
Vol 05 (04) ◽  
pp. 1250022 ◽  
Author(s):  
WEIPING ZHU ◽  
FANGBAO TIAN ◽  
PENG RAN
Keyword(s):  
Heat Transfer ◽  
Analytical Solutions ◽  
Laplace Transformation ◽  
Solution Method ◽  
Thermal Relaxation ◽  
Blood Perfusion ◽  
Good Alternative ◽  
Tissue Temperature ◽  
Particular Solution ◽  
Insight Into

The analytical solutions of non-Fourier Pennes and Chen–Holmes equations are obtained using the Laplace transformation and particular solution method in the present paper. As an application, the effects of the thermal relaxation time τ, the blood perfusion wb, and the blood flow velocity v on the biological skin and inner tissue temperature T are studied in detail. The results obtained in this study provide a good alternative method to study the bio-heat and a biophysical insight into the understanding of the heat transfer in the biotissue.

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