Application of perturbation techniques to heat-transfer problems with variable thermal properties
Abstract
The paper considers the application of regular parameter perturbation technique to obtain approximate solutions of heat-transfer problems with temperature-dependent thermal properties. For pure conduction, linearly varying thermal conductivity and heat capacity are considered and two examples are solved. Next, a conducting-convecting fin is treated with convective heat-transfer coefficient proportional to the fourth root of the temperature increment for fin cooled by natural convection and inversely proportional to the fourth root of the temperature increment for fin heated by laminar condensation. Finally, a two-parameter perturbation is used to solve for temperature distribution in a conducting-convecting-radiating fin with temperature-dependent thermal conductivity. On comparing the perturbation solutions with corresponding numerical solutions, the accuracy is found to be good.
- Publication:
-
International Journal of Heat and Mass Transfer
- Pub Date:
- March 1976
- DOI:
- 10.1016/0017-9310(76)90030-2
- Bibcode:
- 1976IJHMT..19..271A
- Keywords:
-
- Conductive Heat Transfer;
- Convective Heat Transfer;
- Cooling Fins;
- Perturbation Theory;
- Dirichlet Problem;
- Heat Transfer Coefficients;
- Radiative Heat Transfer;
- Specific Heat;
- Temperature Distribution;
- Thermal Conductivity;
- Fluid Mechanics and Heat Transfer