A scientific report of singular kernel on the rate-type fluid subject to the mixed convection flow

The response of inhomogeneous fluids whose material properties are strongly interconnected with mean normal stress and shear rate; such phenomenon undergo to rate constitutive-type theories within thermodynamical aspects. In this context, the thermodynamic approach for modeling a class of viscoelastic fluids so-called Oldroyd-B fluid is investigated through a singular kernel. This is because role of the singular kernel has become imperative due to the wide applications of rate-type fluid subject to the mixed convection flow. To have the systematical and molecular dynamics of Oldroyd-B fluid, the temperature distribution, velocity profile, and Nusselt numbers have been explored by invoking the Laplace transform on the governing equations. Owing to the strengthening of physical parameters, the enhancement of convective heat transfer is emphasized based on relaxation as well as retardation phenomenon. Additionally, the evaluation of thermal and flow characteristics of Oldroyd-B fluid has resulted in discovering more evolutionary mechanisms of the considered problem of rate-type fluid subject to the mixed convection flow.