Paper cit04-0427 the graetz problem for a fene-p fluid in a pipe.

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Author	Oliveira, Paulo Jorge Coelho, Paulo Martins Pinho, Fernando Tavares De
Abstract	Abstract. The development of the thermal boundary layer in a pipe for a FENE-P fluid is investigated using the method of separation of variables. The ensuing Sturm-Liouville problem is then solved for the eignevalues by means of an adequate solver, while the ordinary differential equations for the eigenfunctions and their derivatives are calculated with a fourth order Runge-Kutta method. Solutions are presented for two different boundary conditions and viscous dissipation effects are included: imposed wall temperature and imposed wall heat flux. The physical properties are considered to be independent of temperature, the fluid dynamics is fully-developed and axial conduction is neglected. Results are presented for the Nusselt number and normalized temperature as a function of the Brinkman number, which quantifies the intensity of viscous dissipation, and of numbers accounting for elastic effects, such as the Weissenberg number and the extensibility parameter.
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Subject Keyword	Fene-p Fluid Pipe Paper Cit04-0427 Graetz Problem Adequate Solver Normalized Temperature Physical Property Viscous Dissipation Effect Wall Temperature Elastic Effect Sturm-liouville Problem Viscous Dissipation Weissenberg Number Different Boundary Condition Axial Conduction Fluid Dynamic Nusselt Number Wall Heat Flux Fene-p Fluid Brinkman Number Ordinary Differential Equation Extensibility Parameter Fourth Order Runge-kutta Method Thermal Boundary Layer
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