Prandtl Number Effects on the Rheological and Thermal Behaviour of Forced Convection Turbulent Flow of the Ostwald De Waele Fluids

The present study establishing a better understanding of the rheological and thermal behavior of forced convection turbulent flow of the Ostwald de Waele fluids and shedding further light on the transfer mechanism of the turbulent energy via examining the effects of the Prandtl numbers and the flow behavior index of the shear-thinning fluid on the mean thermal quantities and the thermal turbulence characteristics. A fully developed turbulent flow of shear-thinning fluid through a heated pipe has been investigated numerically in the present study, employing a large eddy simulation (LES) with an extended Smagorinsky model. The flow behavior index has been chosen to be 0.75 over a Prandtl number range of (3, 5, 7, 30, and 70) at a fixed simulation Reynolds number equals 5500. A uniform constant heat flux has been imposed at the wall as a thermal boundary condition, and the working fluids have been assumed to be thermally independent. The numeric resolution was chosen to be 65³ gridpoints in axial, radial and circumferential directions, respectively, with a domain length of 20R in the axial direction. The mathematical model was implemented in the laboratory code; the computational procedure is based on a finite difference scheme and second-order accuracy in space and time. The time advancement employed a fractional step method. A third-order Runge-Kutta explicit scheme and a Crank-Nicholson implicit scheme were used to evaluate the convective and diffusive terms. The finding suggests that the impact of Prandtl numbers providing crucial insights into the prevalent heat transfer processes inside fluid flows. The investigation shows a recurrent inverse connection for lower Prandtl numbers, indicating that convective heat transport is dominant. When the Prandtl number increased, an obvious trend occurs, indicating the increasing importance of thermal diffusion over convective processes.