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International Heat Transfer Conference 6

ISSN: 2377-424X (online)
ISSN: 2377-4371 (flashdrive)


A.R. Chandrupatla
Gas Turbine Research Establishment, Bangalore, India

V.M.K. Sastri
Heat Transfer and Thermal Power Laboratory Department of Mechanical Engineering Indian Institute of Technology, Madras - 600 036

DOI: 10.1615/IHTC6.1450
pages 323-328


A numerical method is used to solve the energy equation for laminar incompressible non-Newtonian fluid flow in a duct of square cross section with simultaneously developing temperature and velocity profiles for constant and uniform wall temperature, peripherally as well as axially. The power-law model characterises the non-Newtonian behavior.

Finite-difference representations are developed for the equations of mathematical model and numerical solutions are obtained assuming uniform inlet velocity and temperature distributions. Forced convective heat transfer information as a function of the pertinent non-dimensional numbers is presented.

Like the numerical solutions for a fully developed velocity profile, the logarithmic mean Nusselt number for each flow behavior index is found to decrease from a maximum at the entry plane to a limiting value at large distances from the entry plane. The results show the strong effect of the Prandtl number on the logarithmic mean Nusselt number, with fully developed and uniform velocity profiles representing the lower and upper limits respectively. Comparisons are made with the available analytical solutions for Newtonian fluid and with experimental data.

In order to ascertain the validity of the' heat transfer parameters arrived at from the numerical analysis and to check the numerical results, experiments were conducted. The case of a constant and uniform wall temperature, peripherally as well as axially, was investigated experimentally where simultaneous development of velocity and temperature profiles for laminar flow of a non-Newtonian fluid is taking place in the entrance region of a square duct. Water was selected as the working Newtonian fluid and dilute polymer solutions of РАМ (Polyacrylamide - molecular weight 4 × 106 and 7−8 × 106) and PEO (Polyethyleneoxide - molecular weight 4 × 106) were selected as working non-Newtonian fluids. Good qualitative agreement is seen between present experimental and numerical results over the range of Graetz numbers 10 to 200. The measured Nusselt numbers are greater than the numerical, results for all Graetz numbers for all cold liquids.

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