Nonlinear three-dimensional stretched flow of an Oldroyd-B fluid with convective condition, thermal radiation, and mixed convection

doi:10.1007/s10483-017-2219-6

Abstract

Abstract:

The effect of non-linear convection in a laminar three-dimensional Oldroyd-B fluid flow is addressed. The heat transfer phenomenon is explored by considering the non-linear thermal radiation and heat generation/absorption. The boundary layer assumptions are taken into account to govern the mathematical model of the flow analysis. Some suitable similarity variables are introduced to transform the partial differential equations into ordinary differential systems. The Runge-Kutta-Fehlberg fourth-and fifth-order techniques with the shooting method are used to obtain the solutions of the dimensionless velocities and temperature. The effects of various physical parameters on the fluid velocities and temperature are plotted and examined. A comparison with the exact and homotopy perturbation solutions is made for the viscous fluid case, and an excellent match is noted. The numerical values of the wall shear stresses and the heat transfer rate at the wall are tabulated and investigated. The enhancement in the values of the Deborah number shows a reverse behavior on the liquid velocities. The results show that the temperature and the thermal boundary layer are reduced when the nonlinear convection parameter increases. The values of the Nusselt number are higher in the non-linear radiation situation than those in the linear radiation situation.

Key words: truncated shallow spherical shell with variable thickness, nonlinear stability, step-by-step loading method, spline collocation method, convective boundary condition, heat source/sink, Oldroyd-B fluid, nonlinear thermal convection, nonlinear thermal radiation

2010 MSC Number:

76A05

B. MAHANTHESH, B. J. GIREESHA, S. A. SHEHZAD, F. M. ABBASI, R. S. R. GORLA. Nonlinear three-dimensional stretched flow of an Oldroyd-B fluid with convective condition, thermal radiation, and mixed convection. Applied Mathematics and Mechanics (English Edition), 2017, 38(7): 969-980.

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