Natural convection flow of second-grade fluid along a vertical heated surface with variable heat flux

In this paper, we have investigated the effects of free convection flow of a viscoelastic second-grade fluid along vertical flat surface with variable heat flux. The boundary-layer equations for the momentum and the energy transport are reduced to local non-similarity equations using appropriate transformations. Solutions of the reduced equations are obtained employing the implicit finite difference (Keller–Box) method for fluids having Prandtl number, Pr, equals 10, 50 and 100. Results are obtained and discussed in terms of the local skin-friction and local rate of heat transfer coefficients. Skin-friction and local heat transfer coefficients for values of surface heat flux gradient, m, 1.0, 1.5 and 2.0 are also obtained against the local streamwise variable ξ. Effect of the local streamwise variable, ξ, on the velocity and temperature profiles for different values of m, Pr and De, the Deborah number, have been shown graphically. Effects of the aforementioned physical parameters on streamlines as well as on isotherms have also been shown graphically.