Purpose In this paper, we present a mathematical model for Marangoni convection boundary layer flow with radiation and different types of nanoparticles, namely, Cu, Al 2 O 3 , and TiO 2 in a water-based fluid. Method The governing equations in the form of partial differential equations have been reduced to a set of ordinary differential equations by applying suitable similarity transformations, which is then solved numerically using the shooting method. Results Numerical results are obtained for the surface-temperature gradient or the heat transfer rate as well as the temperature profiles for some values of the governing parameters, namely, the nanoparticle volume fraction φ , the constant exponent β , and thermal radiation parameter N r . Conclusion The results indicate that the heat transfer rate at the surface decreases as the thermal radiation parameter N r increases. MSC: 76N20, fluid mechanics.
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Mat et al. (2012) studied this question.