Heat Transfer Analysis of Unsteady Natural Convection Flow of Oldroyd-B Model in the Presence of Newtonian Heating and Radiation Heat flux

Abstract

The main focus of this theoretical inspection is to explore the control of Newtonian heating on heat transfer for an unsteady natural convection flow of Oldroyd-B fluid confined to an infinitely long, vertically static plate. Partial differential equations are constructed effectively to describe the fluid flow and heat transfer. Some appropriate dimensionless quantities and Laplace transformation are employed as basic tools to evaluate the solutions of these differential equations. However, due to the complex nature of velocity field, solution is approximated by using Durbin's numerical Laplace inverse algorithm. This solution is further validated by obtaining the velocity solution through algorithms proposed by Stehfest and Zakian. The temperature and velocity gradient are also determined to anticipate the heat transfer rate and skin friction at wall. Some well known results in literature are also deduced from the considered model. Conclusively, to have a deep understanding of the physical mechanism of considered model, and influence of implanted parameters, some outcomes are elucidated with the assistance of tables and graphs. As a result, it is found that under the effect of Newtonian heating, freely convective viscous fluid has greater velocity than Oldroyd-B fluid, Maxwell fluid and second grade fluid. INDEX TERMS Free convection, Laplace transform, Newtonian heating, Oldroyd-B model, thermal radiation. NOMENCLATURE ρ Fluid density (kgm −3) g Acceleration due to gravity (ms −2) β Coefficient of thermal expansion (K −1) T Fluid temperature (K) x, y, z Spatial variables (m) u, v, w Velocity components (ms −1) The associate editor coordinating the review of this manuscript and approving it for publication was Hamid Mohammad-Sedighi. µ Dynamic viscosity (kgms −1) λ Relaxation time (s) λ r Retardation time (s) S Shear stress (Nm −2) ν Kinematic viscosity (m 2 s −1) k Thermal conductivity (Wm −1 K −1) c p Specific heat (Jkg −1 K −1) σ 1 Stefan-Boltzmann coefficient (Wm −2 K −4) K 1 Rosseland absorption constant (m −1) T ∞ Ambient temperature (K)

Numerical Simulation for Bioconvection of Unsteady Stagnation Point Flow of Oldroyd-B Nanofluid with Activation Energy and Temperature-Based Thermal Conductivity Past a Stretching Disk

“…The improvement of dual stratification in the nonlinear radiative movement of Oldroyd-B nano liquid was explained by Irfan et al [24]. Anwar et al [25] evaluated the consequence of Newtonian thermal conductivity by the unsteady natural convectional movement of Oldroyd-B nanofluid contained in an infinite, vertical stationary plate. Interested readers may refer to [26,27] for more works on Oldroyd-B fluid.…”