An upper bound estimate for a class of conduction heat transfer problems with nonlinear boundary conditions

2000 ◽  
Vol 27 (7) ◽  
pp. 955-964 ◽  
Author(s):  
Rogério Martins Saldanha da Gama
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Upper Bound ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Conduction Heat Transfer ◽  
Upper Bound Estimate ◽  
Transfer Problems

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.

Sign in / Sign up

Export Citation Format

Share Document