Forced Convection Heat Transfer of a Giesekus Fluid in Circular Micro-Channels Subjected to a Constant Wall Temperature

Abstract

Abstract In this paper, an exact analytical solution for forced convective heat transfer of nonlinear viscoelastic fluid in isothermal circular micro-channel is presented. The nonlinear Giesekus constitutive equation is used to model the Giesekus fluid heat transfer in micro-channel with constant wall temperature, which is the main innovative aspect of the current study. This constitutive equation is a powerful tool and able to model the fractional viscometric functions, extensional viscosity, and elastic property. The solution of temperature profile and Nusselt number is obtained based on the Frobenius method. The effects of Weissenberg number, mobility factor, slip coefficient, and Navier index on temperature distribution, velocity profile, and Nusselt number are investigated in detail. The results show that the increases in both slip coefficient and Navier index cause the increases in slip velocity and maximum dimensionless temperature at the wall and the micro-channel center, respectively. Moreover, the Nusselt number has an upward trend with increases in slip coefficient and Navier index parameters. The results are indicated that the flow and temperature fields have a complex relation with mobility factor which controls the level of the nonlinearity of the Giesekus model. Additionally, three correlations for Nusselt number of Giesekus flow in micro-channel are presented.