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.
Highlights
In numerous present day technologies, non-Newtonian fluids are attaining invaluable attraction because of their indispensable implications
A capable and simple model, which records the flow history and provides an adequate approximation of viscoelastic nature of fluids is recognized as Oldroyd-B model
In the light of above investigations, this study is an attempt to analyze the profiles of unsteady free convective flow of Oldroyd-B fluid over a static vertical plate and radiative heat transfer with Newtonian heating at boundary
Summary
In numerous present day technologies, non-Newtonian fluids are attaining invaluable attraction because of their indispensable implications. Tiwana et al [17] evaluated the influence of ramped temperature and ramped boundary motion on transient MHD convection flow of Oldroyd-B model. This study is an attempt to fulfill this gap by analyzing the role of Newtonian heating and nonlinear heat flux in unsteady naturally convective motion of Oldroyd-B fluid past a vertically static plate. Ahmed [30] analyzed the effects of heat source, Hall current, MHD, thermal diffusion, and porosity of medium on transient natural convective motion over an upright plate. In the light of above investigations, this study is an attempt to analyze the profiles of unsteady free convective flow of Oldroyd-B fluid over a static vertical plate and radiative heat transfer with Newtonian heating at boundary. Current velocity, temperature and velocity of some limiting fluids’ cases are graphically portrayed to get a clear insight of physical features of considered model
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