Exact and numerical solutions of a fully developed generalized second-grade incompressible fluid with power-law temperature-dependent viscosity
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Date
2006-03
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Abstract
We compute exact and numerical solutions of a fully developed flow of a generalized second-grade fluid, with power-law temperature-dependent viscosity (μ=θ-M), down an inclined plane. Analytical solutions are found for the case when M=m+1, m≠1, m being a constant that models shear thinning (m<0) or shear thickening (m>0). The exact solutions are given in terms of Bessel functions. The numerical solutions indicate that both the velocity and the temperature increase with decreasing Froude number and that there is a critical value of Fr below which temperature “overshoots” its free surface value of unity. This phenomena is not reported in the work of Massoudi and Phuoc [Fully developed flow of a modified second grade fluid with temperature dependent viscosity, Acta Mech. 150 (2001) 23–37.] for viscosity that depends exponentially on temperature.
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Full text can be accessed at
http://www.sciencedirect.com/science/article/pii/S0020746205000910
Keywords
Non-Newtonian fluids, Second-grade fluid, Temperature-dependent viscosity, Super-temperature
Citation
Soh, C.W. and Mureithi, E.W., 2006. Exact and numerical solutions of a fully developed generalized second-grade incompressible fluid with power-law temperature-dependent viscosity. International Journal of Non-Linear Mechanics, 41(2), pp.271-280.