Finite Element Analysis of Viscoelastic Nanofluid Flow with Energy Dissipation and Internal Heat Source/Sink Effects

Abstract

A numerical study is conducted of laminar viscoelastic nanofluid polymeric boundary layer stretching sheet flow. Viscous dissipation, surface transpiration (suction/injection), internal heat generation/absorption and work done due to deformation are incorporated using a second grade viscoelastic non-Newtonian nanofluid with non-isothermal associated boundary conditions. The nonlinear boundary value problem is solved using a higher order finite element method. The influence of viscoelasticity parameter, Brownian motion parameter, thermophoresis parameter, Eckert number, Lewis number, Prandtl number, internal heat generation and also wall suction on thermofluid characteristics is evaluated in detail. Validation with earlier non-dissipative studies is also included. The hp-finite element method achieves the desired accuracy at $$p=8$$ with comparatively less CPU cost per iteration (with less degrees of freedom, DOF) as compared to lower order finite element methods. The simulations have shown that greater polymer fluid viscoelasticity $$({k}_{1})$$ accelerates the flow. A rise in Brownian motion parameter (Nb) and thermophoresis parameter (Nt) elevates temperatures and reduce the heat transfer rates (local Nusselt number function). Increasing Eckert number increases temperatures whereas increasing Prandtl number (Pr) strongly lowers temperatures. Increasing internal heat generation $$({Q} > 0)$$ elevates temperatures and reduces the heat transfer rate (local Nusselt number function) whereas heat absorption $$({Q} < 0)$$ generates the converse effect. Increasing suction $$({f}_{w}>0)$$ reduces velocities and temperatures but elevates enhances mass transfer rates (local Sherwood number function), whereas increasing injection $$({f}_{w}<0)$$ accelerate the flow, increases temperatures and depresses wall mass transfer rates. The study finds applications in rheological nano-bio-polymer manufacturing.