Abstract
Non-Newtonian flow from a wedge constitutes a fundamental problem in chemical<br /> engineering systems and is relevant to processing of polymers, coating systems, etc. Motivated by such applications, the homotopy analysis method (HAM) was employed to<br /> obtain semi-analytical solutions for thermal convection boundary layer flow of incompressible micropolar fluid from a two-dimensional body (wedge). Viscous dissipation<br /> and heat sink effects were included. The non-dimensional boundary value problem<br /> emerges as a system of nonlinear coupled ordinary differential equations, by virtue of<br /> suitable coordinate transformations. The so-called Falkner-Skan flow cases are elaborated. Validation of the HAM solutions was achieved with earlier simpler models, as well as with a Nakamura finite difference method for the general model. The micropolar model employed simulates certain polymeric solutions quite accurately, and features rotary motions of micro-elements. Primary and secondary shear stress, wall couple stress, Nusselt number, microrotation velocity, and temperature were computed for the effect of<br /> vortex viscosity parameter (micropolar rheological), Eckert number (viscous dissipation),<br /> Falkner-Skan (pressure gradient) parameter, micro-inertia density, and heat sink parameter. The special cases of Blasius and stagnation flow were also addressed. It was observed from the study that the temperature and thermal boundary layer thickness are both suppressed with increasing wedge parameter and wall heat sink effect, which is beneficial to temperature regulation in polymer coating dynamics. Further, strong reverse spin was generated in the microrotation with increasing vortex viscosity, which resulted in<br /> increase in angular momentum boundary layer thickness. Also, both primary and secondary skin friction components were reduced with increasing wedge parameter. Nusselt number was also enhanced substantially with greater wedge parameter.
Highlights
The flow from a two-dimensional wedge is a classical problem in viscous fluid mechanics and boundary layer theory, often referred to as Falkner-Skan flow1
It was observed from the study that the temperature and thermal boundary layer thickness are both suppressed with increasing wedge parameter and wall heat sink effect, which is beneficial to temperature regulation in polymer coating dynamics
Rashidi et al.12 used numerical shooting and homotopy methods to elaborate the effects of pressure-gradient parameter and viscoelasticity on heat transfer characteristics in third grade differential fluid flow from a non-isothermal wedge
Summary
The flow from a two-dimensional wedge is a classical problem in viscous fluid mechanics and boundary layer theory, often referred to as Falkner-Skan flow. Rashidi et al. used numerical shooting and homotopy methods to elaborate the effects of pressure-gradient parameter and viscoelasticity on heat transfer characteristics in third grade differential fluid flow from a non-isothermal wedge. HAM, presently a very popular method in computational engineering sciences, was employed to develop solutions for the nonlinear, dissipative thermal convection boundary layer flow from a wedge with heat absorption effects. Where u denotes translational velocity along the x-direction, v is the translational velocity along the y-direction, N is the angular velocity (microrotation) component in the x-y plane, g = (m+k/2) j is the Eringen spin gradient viscosity, T is fluid temperature, cp denotes specific heat at constant pressure (isobaric), k is thermal conductivity of the micropolar fluid, and Q is the heat sink parameter (negative). Equations [4] – [8] are thereby reduced to the following ninth order system of coupled, non-linear ordinary differential equations, describing the dimensionless linear and angular velocity fields and temperature field: primary momentum
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