The response of inhomogeneous fluids whose material properties are strongly interconnected with mean normal stress and shear rate; such phenomenon undergo to rate type constitutive theories within thermodynamical aspects. In this context, the thermodynamic approach for modeling a class of viscoelastic fluids so called Oldroyd-B fluid is investigated by means of singular kernel. This is because, role of singular kernel has become imperative due to the wide applications of rate type fluid subject to the mixed convection flow. In order to have the systematical and molecular dynamics of Oldroyd-B fluid, the temperature distribution, velocity profile and Nusslet number 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 on the basis of relaxation as well as retardation phenomenon. Additionally, the evaluation of thermal and flow characteristics of Oldroyd-B fluid have resulted to discover more evolutionary mechanisms of the considered problem of rate type fluid subject to the mixed convection flow.