Heat transfer with nonlinear boundary conditions via a variational principle

AIAA Journal ◽  
1971 ◽  
Vol 9 (2) ◽  
pp. 327-330 ◽  
Author(s):  
B. VUJANOVIC ◽  
A. M. STRAUSS
Keyword(s):  
Heat Transfer ◽  
Variational Principle ◽  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions

Closed-form solution for a rectangular stepped fin involving all variable thermal parameters and nonlinear boundary conditions

2016 ◽  
Vol 231 (5) ◽  
pp. 992-1010 ◽  
Author(s):  
Kuljeet Singh ◽  
Ranjan Das ◽  
Rohit K Singla
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Decomposition Method ◽  
Nonlinear Boundary ◽  
Adomian Decomposition Method ◽  
Nonlinear Boundary Conditions ◽  
Thermal Parameters ◽  
Physical Parameters ◽  
Temperature Dependent ◽  
Adomian Decomposition

In this paper, the implementation of the Adomian decomposition method is demonstrated to solve a nonlinear heat transfer problem for a stepped fin involving all temperature-dependent means of heat transfer and nonlinear boundary conditions. Unlike conventional insulated tip assumption, to make the present problem more practical, the fin tip is assumed to disperse heat by convection and radiation. Thermal parameters such as the thermal conductivity, the surface heat transfer coefficient and the surface emissivity are considered to be temperature-dependent. Adomian polynomials are first obtained and then a set of Adomian decomposition method results is validated with pertinent results of the differential transformation method reported in the literature. Effects of different thermo-physical parameters on the temperature distribution and the efficiency have been exemplified. The study reveals that for a given set of conditions, the stepped fin may perform better than the straight fin.

scholarly journals A NEW VARIATIONAL FORMULATION FOR CONVEX HAMILTONIAN SYSTEMS WITH NONLINEAR BOUNDARY CONDITIONS

2011 ◽  
Vol 84 (2) ◽  
pp. 186-204 ◽  
Author(s):  
MARK LEWIS ◽  
ABBAS MOAMENI
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Hamiltonian Systems ◽  
Variational Formulation ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Second Order ◽  
Second Order Hamiltonian Systems ◽  
New Formulation

AbstractA variational principle is established to provide a new formulation for convex Hamiltonian systems. Using this formulation, we obtain some existence results for second-order Hamiltonian systems with a variety of boundary conditions, including nonlinear ones.

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