Transient Couple Stress Fluid Past a Vertical Cylinder With Bejan’s Heat and Mass Flow Visualization for Steady-State

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
H. P. Rani ◽  
G. Janardhan Reddy ◽  
Chang Nyung Kim ◽  
Y. Rameshwar
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Flow Visualization ◽  
Boundary Layer Flow ◽  
Couple Stress ◽  
Vertical Cylinder ◽  
Couple Stress Fluid ◽  
Layer Flow ◽  
Flow Variables ◽  
Mass Functions

In the present study, the transient, free convective, boundary layer flow of a couple stress fluid flowing over a vertical cylinder is investigated, and the heat and mass functions for the final steady-state of the present flow are developed. The solution of the time dependent nonlinear and coupled governing equations is obtained with the aid of an unconditionally stable Crank–Nicolson type of numerical scheme. Numerical results for the time histories of the skin-friction coefficient, Nusselt number, and Sherwood number as well as the steady-state velocity, temperature, and concentration are presented graphically and discussed. Also, it is observed that time required for the flow variables to reach the steady-state increases with the increasing values of Schmidt and Prandtl numbers, while the opposite trend is observed with respect to the buoyancy ratio parameter. To analyze the flow variables in the steady-state, the heatlines and masslines are used in addition to streamlines, isotherms, and isoconcentration lines. When the heat and mass functions are properly made dimensionless, its dimensionless values are related to the local and overall Nusselt and Sherwood numbers. Boundary layer flow visualization indicates that the heatlines and masslines are dense in the vicinity of the hot wall, especially near the leading edge.

scholarly journals Computational study of unsteady couple stress magnetic nanofluid flow from a stretching sheet with Ohmic dissipation

2019 ◽  
Vol 233 (2-4) ◽  
pp. 49-63 ◽  
Author(s):  
Mahesh Kumar ◽  
G Janardhana Reddy ◽  
N Naresh Kumar ◽  
O Anwar Bég
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Couple Stress ◽  
Stretching Sheet ◽  
Magnetic Parameter ◽  
Aluminium Oxide ◽  
Ohmic Dissipation ◽  
Non Linear ◽  
Layer Flow ◽  
Sheet Stretching

To provide a deeper insight of the transport phenomena inherent to the manufacturing of magnetic nano-polymer materials, in the present work a mathematical model is developed for time-dependent hydromagnetic rheological nano-polymer boundary layer flow and heat transfer over a stretching sheet in the presence of a transverse static magnetic field. Joule heating (Ohmic dissipation) and viscous heating effects are included since these phenomena arise frequently in magnetic materials processing. Stokes’ couple stress model is deployed to simulate non-Newtonian microstructural characteristics. The Tiwari–Das nanoscale model is adopted which permits different nanoparticles to be simulated (in this article, both copper–water and aluminium oxide–water nanofluids are considered). Similarity transformations are utilized to convert the governing partial differential conservation equations into a system of coupled, non-linear ordinary differential equations with appropriate wall and free stream boundary conditions. The shooting technique is used to solve the reduced non-linear coupled ordinary differential boundary value problem via MATLAB symbolic software. Validation with published results from the literature is included for the special cases of non-dissipative and Newtonian nanofluid flows. Fluid velocity and temperature profiles for both copper and aluminium oxide (Al2O3) nanofluids are observed to be enhanced with greater non-Newtonian couple stress parameter and magnetic parameter, whereas the opposite trend is computed with greater values of unsteadiness parameter. The boundary layer flow is accelerated with increasing buoyancy parameter, elastic sheet stretching parameter and convection parameter. Temperatures are generally increased with greater couple stress rheological parameter and are consistently higher for the aluminium oxide nanoparticle case. Temperatures are also boosted with magnetic parameter and exhibit an overshoot near the wall when magnetic parameter exceeds unity (magnetic force exceeds viscous force). A decrease in temperatures is induced with increasing sheet stretching parameter. Increasing Eckert number elevates temperatures considerably. With greater nanoparticle volume fraction, both skin friction and Nusselt number are elevated, and copper nanoparticles achieve higher magnitudes than aluminium oxide.

scholarly journals Heat transport by laminar boundary layer flow with polymers

2012 ◽  
Vol 696 ◽  
pp. 330-344 ◽  
Author(s):  
Roberto Benzi ◽  
Emily S. C. Ching ◽  
Vivien W. S. Chu
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Heat Transport ◽  
Boundary Layer Flow ◽  
Effective Viscosity ◽  
Iterative Scheme ◽  
Streamwise Velocity ◽  
Heated Plate ◽  
State Boundary ◽  
Layer Flow

AbstractMotivated by recent experimental observations, we consider a steady-state boundary layer flow with polymers in forced convection above a heated plate and study how the heat transport might be affected by the polymers. We discuss how a set of equations can be derived for the problem and how these equations can be solved numerically by an iterative scheme. By carrying out such a scheme, we find that the effect of the polymers is equivalent to producing a space-dependent effective viscosity that first increases from the zero-shear value at the plate then decreases rapidly back to the zero-shear value far from the plate. We further show that such an effective viscosity leads to a decrease in the streamwise velocity near the plate, which in turn leads to a reduction in heat transport.

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