Abstract
The unsteady free convection boundary layer flow of a thermomicropolar fluid along a vertical plate with effect of micropolar heat conduction has been investigated. The governing equations are transformed into a new form using a method of transformed coordinates. We then use an explicit finite difference scheme to solve the transformed equations. Here, the governing equations have been reduced to the forms that are valid for entire, small, and large time regimes, by using stream-function formulation. The results obtained for the above mentioned three time regimes are compared and found to be in excellent agreement. Moreover, the effects of the physical parameters such as the viscosity parameter, K, and the heat conduction parameter, α*, are presented in terms of the transient shear stress, couple stress, and surface heat transfer coefficient as well as transient velocity profiles, angular velocity profiles, and temperature profiles.
Highlights
The concept of a micropolar fluid to model fluids with microstructures which cannot be adequately is described by the classical Stokesian theory introduced by Eringen [1, 2]
The steady boundary layer flow of micropolar fluids at the stagnation point of a 2-dimensional body has been considered by Peddieson and McNitt [4]
We have analyzed the problem of unsteady natural convection laminar boundary layer flow of thermomicropolar viscous incompressible fluid along a nonuniformly heated vertical surface
Summary
The concept of a micropolar fluid to model fluids with microstructures which cannot be adequately is described by the classical Stokesian theory introduced by Eringen [1, 2]. Examples of such fluids are animal blood, liquid crystals, and certain polymeric fluids. The concept of boundary layer in micropolar fluids was first introduced by Willson [3] to study the steady, incompressible laminar flow over 2-dimensional bodies. The steady boundary layer flow of micropolar fluids at the stagnation point of a 2-dimensional body has been considered by Peddieson and McNitt [4]. Ahmadi [5] considered the steady boundary layer flow of micropolar fluids over a semi-infinite flat plate and obtained a self-similar solution. The thermal boundary layer in micropolar fluids at the stagnation point of a 2dimensional body was considered recently by Ramachandran et al [6] and Gorla [7]. Hossain et al [8, 9] investigated two-dimensional mixed convection and natural convection flow of a viscous incompressible thermomicropolar fluid with uniform spin-gradient over a flat plate
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