Potential impacts of Cattaneo–Christov model of heat flux on the flow of Carreau–Yasuda fluid with mixed convection over a vertical stationary flat plate

Heat transfer in Carreau–Yasuda fluid with mixed convection, effect of Cattaneo–Christov model of heat flux past a vertical flat plate has been studied in this paper. Using appropriate transformations, governing PDEs are reduced to higher order non-linear non-dimensional ODEs and subsequently these are solved using “bvp4c” package of MATLAB. The Carreau–Yasuda fluid is used to explore the behaviour of fluids having shear-thinning and shear-thickening characters for several values of the parameter called power law exponent involved in the fluid model. The effects of different physical parameters, such as Weissenberg number(We), thermal relaxation parameter(α), Carreau–Yasuda fluid parameter(d), mixed convection parameter(λ) and Prandtl number(Pr) on velocity and temperature has been investigated and depicted through graphs. Results reveals that for lower value of Pr velocity of fluid enhances with higher value of λ and reverse effect is witnessed for larger Pr. Also, velocity rises for shear-thinning fluid(STNF) and decreases for shear-thickening fluid(STKF) with We and d. Temperature exhibits growing behaviour for Cattaneo–Christov model of heat flux near the plate in comparison with Fourier's model, whereas velocity exhibits growing behaviour with α. For larger We, temperature in Carreau–Yasuda model upsurges for STKF and falls for STNF. The surface drag-force displays higher values for both STNF and STKF with growth in $\lambda$. The cooling rate rises/declines with We for STNFs/STKFs.