An Official Journal of the American Society of Thermal and Fluids Engineers

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MIXED CONVECTION HEAT TRANSFER OF VISCOELASTIC FLUID ALONG AN INCLINED PLATE OBEYING THE FRACTIONAL CONSTITUTIVE LAWS

SINOPSIS

The fractional constitutive laws are introduced into the study of mixed convection heat transfer of viscoelastic fluid along an inclined plate. Nonlinear fractional boundary layer governing equations are formulated and solved by a finite difference algorithm combined with the shifted Grünwald–Letnikov formula. The results show that the inclination angle, Prandtl number, and the temperature fractional derivative parameter have remarkable impacts on both temperature and velocity fields, while the effect of the velocity fractional derivative parameter on temperature is ignorable. With decrease of the inclination angle and Prandtl number, the temperature profile rises and the thermal boundary layer becomes thicker significantly. The average Nusselt number increases remarkably with the augmentation of the temperature fractional derivative parameter. For larger velocity fractional derivative parameter, the intersections of velocity profiles demonstrate the strengthened viscoelasticity of the fluid. The average skin friction coefficient increases slowly first and then declines dramatically with the rise of the velocity fractional derivative parameter.