An analytical model is developed to study the Darcy flows in viscoelastic convection from an inclined plate as a simulation of electro-conductive polymer materials processing with Biot number effects. The Jeffery’s viscoelastic model describes the non-Newtonian characteristics of the fluid and provides a good approximation for polymers, which constitutes a novelty of the present work. The normalized nonlinear boundary value problem is solved computationally with the Keller Box implicit finite difference technique. Extensive solutions for velocity, surface temperature, skin friction and heat transfer rate are visualized numerically and graphically for various thermophysical parameters. Validation is conducted with earlier published work for the case of a vertical plate in the absence of non-Newtonian effects. The boundary layer flow is accelerated with increase in Deborah number, whereas temperatures are decelerated slightly. Temperatures are boosted with increase in inclination parameter, whereas velocity is lowered. A reverse trend is seen for increasing mixed convection parameter. Increase in Biot number enhances both velocity and temperature. Increasing Darcy number is found to enhance velocity, whereas it suppresses temperature. This particle study finds applications in different industries like reliable equipment design, nuclear plants, gas turbines and different propulsion devices. © 2020, Akadémiai Kiadó, Budapest, Hungary.