Department of Mathematics, Amrita Vishwa Vidya Peetham Coimbatore, India.
A mathematical investigation on the combined effect of oscillation and conjugation on the enhancement of heat transfer in a heat pipe called Dream Pipe is carried out, when viscoelastic fluids (CPyCl/NaSal) are employed as the heat carriers. Closed-form solutions for the momentum and heat equations are presented. The physical and thermal properties of the polymer solution used are obtained by experiments. The effects of thermal conductivity and thickness of the wall, fluid thickness, Womersley number (α), Deborah number and Prandtl number on the enhancement of heat transfer are examined. Results obtained in the present analysis are in excellent agreement with those of the existing literature. The effective thermal diffusivity (κe) is maximized at optimum α where the fluid flow exhibits a resonant behavior. Several maxima occur in κe for several resonant frequencies and the dramatic increase in κe due to oscillation for the viscoelastic fluid is 5.63 x 109 times higher than that obtained by the molecular motion. This increase is much higher than that (1.84 x 104 times) obtained for the Newtonian fluid. κe is increased with increasing wall thermal conductivity and thickness in the viscous regime whereas in the elastic regime the effect of conjugation is saturated. In the viscous regime, a maximum increase of 50.63% in κe is obtained by optimizing the wall thickness. Also κe increases with increasing molar ratio of concentrations of counterion to surfactant. A maximum heat flux of 4.54 x 1010 W/m2 is achieved using a viscoelastic fluid with thermally conducting wall and this highest heat flux is 207 times higher than that (2.19 x 108 W/m2) obtained with the Newtonian fluid (liquid metal). Hence, viscoelastic fluids are preferable to liquid metals as working fluids in the Dream Pipe. The new insights gained by the present investigation are useful while designing viscoelastic Dream Pipes and micro channel heat exchangers.