Case study of entropy optimization with the flow of Non-Newtonian nanofluid past converging conduit with slip mechanism: An application of geothermal engineering

Abstract

Magneto hydrodynamic flow over a wedge-shaped channel is often seen in geothermal applications, microelectronic, energy systems, and pumping systems. The slip condition is a normally recognized condition for the fluid flow occurs along lubricated, coated, wall channels. The best examples of such flows are the blood flow in arteries with plaque layer arteries. Flow configuration within channel is anticipated by using Carreau nanofluid injection at inlet. The intersecting wall of channel is inclined with respect to horizontal plane to make convergent angle of −α and divergent angle of α. The mathematical equations for energy and nanofluid concentration are established using well-known Navier–Stokes Equation with conservation equations invoking modified Buongiorno model. The temperature differences between the wall and core region leads to entropy. By using distinguishing amendments, system of equations are remodeled into system of ordinary differential equations (ODE's), which are numerically solved by Bvp4c technique of MATLAB for realistic conditions of under discussed phenomena. Simple shear close to the wall admit compression in local flow topology in zones of channel (divergent). The temperature field increases along thermal radiation, Brinkman number, nanoscale effects and heat source. Entropy is minimal and can be minimized with optimal angle and slip velocity.

Keywords

• Entropy optimization
• Slip boundary conditions
• Convergent/divergent channel
• Carreau nanofluids
• Heat and mass transport
• Dual solutions