Computational unsteady flow analysis for third‐grade fluid from an isothermal vertical cylinder through a Darcian porous medium

Abstract

The present study describes a mathematical model for free‐convective laminar incompressible boundary layer flow of a third‐grade fluid of the Reiner‐Rivlin differential type, external to an evenly heated semi‐infinite vertical cylinder through a two‐dimensional porous medium. Assuming a homogenous‐isotropic porous medium, simulation of bulk drag effects at low Reynolds number is conducted with the Darcy model. The resulting partial differential equation boundary value problem is normalized using suitable transformation variables. The highly nonlinear time‐dependent coupled conservation equations along with boundary conditions are resolved computationally with an optimized Crank‐Nicolson finite difference code. Validation with previous studies is included. The heat transport and skin‐friction coefficients are computed for different values of emerging nondimensional parameters. Furthermore, steady‐state and transient fluid flow variables are shown graphically. An enhanced fluid velocity is observed for increased Darcy number and the reverse trend is computed for higher values of third‐grade viscoelastic parameter. Also, the rate of heat transfer is observed to increase with greater Darcy number and a reduction in third‐grade viscoelastic parameter. A key observation which is drawn from the present study is that for third‐grade fluid the flow variables deviate significantly from a hot cylindrical wall as compared with a Newtonian fluid. The study is relevant to thermal polymer coating applications in aerospace materials processing.

Numerical investigation on transient third-grade magnetized nanofluid flow and radiative convection heat transfer from a stationary/moving cylinder: nanomaterial and nanoparticle shape effects

“…The considered flow model is axisymmetric. This axisymmetric thermal convective flow of a viscoelastic third grade nanofluid in the presence of 'transverse radial magnetic field (𝑀 0 )' from the moving cylinder (velocity 𝑢 0 ) is characterized by the subsequent 'momentum' and 'energy' equations [43] including Boussinesq's approximation [44] in the occurrence of thermal radiative flux are presented as [23], [27], [28], [36]:…”

“…In addition, the third-grade model satisfactorily explains fluid such as slurries, biological liquids, certain coolants, lubricants, and of course polymeric coatings. Many excellent studies have been communicated on convective heat transfer of third-grade fluid flows[21][22][23][24][25][26][27]. There have also appeared a number of interesting works which have scrutinized third-grade rheological nanofluid flows.…”