## THERMAL SCIENCE

International Scientific Journal

### ANALYTICAL INVESTIGATION OF NONLINEAR MODEL ARISING IN HEAT TRANSFER THROUGH THE POROUS FIN

**ABSTRACT**

In this letter simple analytical methods called homotopy perturbation method(HPM), variation iteration method(VIM) and perturbation method(PM) are employed to approach temperature distribution of porous fins. also energy balance and Darcy's model used to formulate the heat transfer equation. To study the thermal performance, a type case considered is finite-length fin with insulated tip. The obtained results from variation iteration method (VIM) are compared with other analytical techniques proposed before. These methods are homotopy perturbation method and perturbation method (PM). Also BVP is applied as a numerical method for validation. The obtained results shows that the VIM is more accurate, stable and more appropriate than other techniques. Also it is found that this method is powerful mathematical tools and can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering specially some heat transfer equations.

**KEYWORDS**

PAPER SUBMITTED: 2011-12-17

PAPER REVISED: 2012-04-23

PAPER ACCEPTED: 2012-05-04

**THERMAL SCIENCE** YEAR

**2014**, VOLUME

**18**, ISSUE

**Issue 2**, PAGES [409 - 417]

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