In the present article, the transient rheological boundary layer flow over a stretching sheet with heat transfer is investigated, a topic of relevance to non‐Newtonian thermal materials processing. Stokes couple stress model is deployed to simulate non‐Newtonian characteristics. Similarity transformations are utilized to convert the governing partial differential equations into nonlinear ordinary differential equations with appropriate wall and free stream boundary conditions. The nondimensional boundary value problem emerging is shown to be controlled by a number of key thermophysical and rheological parameters, namely the rheological couple stress parameter (β), unsteadiness parameter (A), Prandtl number (Pr), buoyancy parameter (λ). The semi‐analytical differential transform method (DTM) is used to solve the reduced nonlinear coupled ordinary differential boundary value problem. A numerical solution is also obtained via the MATLAB built‐in solver “bvp4c” to validate the results. Further validation with published results from the literature is included. Fluid velocity is enhanced with increasing couple stress parameter, whereas it is decreased with unsteadiness parameter. Temperature is elevated with couple stress parameter, whereas it is initially reduced with unsteadiness parameter. The flow is accelerated with increasing positive buoyancy parameter (for heating of the fluid), whereas it is decelerated with increasing negative buoyancy parameter (cooling of the fluid). Temperature and thermal boundary layer thickness are boosted with increasing positive values of buoyancy parameter. Increasing Prandtl number decelerates the flow, reduces temperatures, increases momentum boundary layer thickness, and decreases thermal boundary layer thickness. Excellent accuracy is achieved with the DTM approach.
Numerical analysis is performed to study the transient free convective boundary layer flow of a couple stress fluid past an infinite vertical cylinder, in the absence of body forces and body couples. A set of nondimensional governing equations, namely, the continuity, momentum and energy equations are derived, which are unsteady, non-linear and coupled. The couple stress fluid flow model introduces the length dependent effect based on the material constant and dynamic viscosity. Also, it introduces the biharmonic operator in the Navier-Stokes equations, which is not present in the case of Newtonian fluids. As there are no analytical or direct numerical method available to solve these unsteady, non-linear and coupled equations, they are solved using the CFD techniques. An unconditionally stable Crank-Nicolson type of implicit finite difference scheme is employed to obtain the discretized forms of the governing equations. The discretized equations are solved using the Thomas and pentadiagonal algorithm. The results concerning the velocity and temperature profiles across the boundary layer are illustrated graphically and discussed for different values of Prandtl number. Transient effects of velocity and temperature are analyzed and compared with those of the Newtonian fluids. The heat transfer characteristics are analyzed and compared with those of Newtonian fluids with the help of average skin-friction and Nusselt number and are shown graphically. It is observed that the deviation of transient velocity and temperature profiles from the hot wall of a couple stress fluid is more in comparison with that of Newtonian fluids.
The present numerical study reports the chemically reacting boundary layer flow of a magnetohydrodynamic second-grade fluid past a stretching sheet under the influence of internal heat generation or absorption with work done due to deformation in the presence of a porous medium. To distinguish the non-Newtonian behaviour of the second-grade fluid with those of Newtonian fluids, a very popularly known second-grade fluid flow model is used. The fourth order momentum equation with four appropriate boundary conditions along with temperature and concentration equations governing the second-grade fluid flow are coupled and highly nonlinear in nature.Well-established similarity transformations are efficiently used to reduce the dimensional flow equations into a set of nondimensional ordinary differential equations with the necessary conditions. The standard bvp4c MATLAB solver is effectively used to solve the fluid flow equations to get the numerical solutions in terms of velocity, temperature, and concentration fields. Numerical results are obtained for a different set of physical parameters and their behaviour is described through graphs and tables.The viscoelastic parameter enhances the velocity field whereas the magnetic and porous parameters suppress the velocity field in the flow region. The temperature field is magnified for increasing values of the heat source/sink parameter. However, from the present numerical study, it Heat Transfer-Asian Res. 2019;48:1595-1621.wileyonlinelibrary.com/journal/htj
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