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**Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity, non-uniform heat source and radiation.**
*(English)*
Zbl 1145.76469

Summary: An analysis has been carried out to study the magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid over a flat sheet with a linear velocity in the presence of thermal radiation and non-uniform heat source. The thermal conductivity is assumed to vary as a linear function of temperature. The basic equations governing the flow and heat transfer are in the form of partial differential equations, the same have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformation. The transformed equations are solved analytically by regular perturbation method. Numerical solution of the problem is also obtained by the efficient shooting method, which agrees well with the analytical solution. The effects of various physical parameters such as viscoelastic parameter, Chandrasekhar number, Prandtl number, variable thermal conductivity parameter, Eckert number, thermal radiation parameter and non-uniform heat source/sink parameters which determine the temperature profiles are shown in several plots and the heat transfer coefficient is tabulated for a range of values of said parameters. Some important findings reported in this work reveals that combined effect of variable thermal conductivity, radiation and non-uniform heat source have significant impact in controlling the rate of heat transfer in the boundary layer region.

### MSC:

76W05 | Magnetohydrodynamics and electrohydrodynamics |

80A20 | Heat and mass transfer, heat flow (MSC2010) |

### Keywords:

viscoelastic liquid; stretching sheet; variable thermal conductivity; radiation; non-uniform heat source; Prandtl number
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\textit{M. Subhas Abel} and \textit{N. Mahesha}, Appl. Math. Modelling 32, No. 10, 1965--1983 (2008; Zbl 1145.76469)

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