Abstract
Abstract In this article, we study the nonlinear steady thermal convection of an incompressible third-grade non-Newtonian fluid from a horizontal circular cylinder. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-differences Keller Box technique. The influence of a number of emerging non-dimensional parameters, namely the third-grade fluid parameter (ϕ), the material fluid parameters (ϵ1, ϵ2), Prandtl number (Pr), Biot number (y), thermal radiation (F) and dimensionless tangential coordinate (ξ) on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation is achieved. It is found that the velocity, skin friction and Nusselt number (heat transfer rate) reduce with increasing third grade fluid parameter (ϕ), whereas the temperature is enhanced. Increasing material fluid parameter (ϵ1) reduces the velocity and heat transfer rate but enhances the temperature and skin friction. The study is relevant to chemical materials processing applications and low density polymer materials processing.
Highlights
The dynamics of non-Newtonian uids has been a popular area of research owing to ever-increasing applications in chemical and process engineering
In this article, we study the nonlinear steady thermal convection of an incompressible third-grade nonNewtonian uid from a horizontal circular cylinder
The in uence of a number of emerging non-dimensional parameters, namely the third-grade uid parameter (φ), the material uid parameters (ε, ε ), Prandtl number (Pr), Biot number (γ), thermal radiation (F) and dimensionless tangential coordinate (ξ ) on velocity and temperature evolution in the boundary layer regime are examined in detail
Summary
The dynamics of non-Newtonian uids has been a popular area of research owing to ever-increasing applications in chemical and process engineering. Examples of such uids include coal-oil slurries, shampoo, paints, clay coating and suspensions, grease, cosmetic products, custard, physiological liquids (blood, bile, synovial uid), fabricarion, pharmacology, polymer synthesis and food processing. In these applications, the working uid is generically rheological in nature and the constitutive relationship between stress and rate of strain is non-linear in comparison to the Navier-Stokes equaitons.
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