Abstract
The present article analyzes the effect of viscous dissipations on natural convection heat transfer. The power law model for non-Newtonian fluid with heat generation or absorption effect along a sinusoidal wavy surface with isothermal boundary condition is investigated. A simple coordinate transform is employed to map the wavy surface into a flat surface, and also, the fully implicit finite difference method is incorporated for the numerical solution. The findings of this study can help better understand the effect of parameters such as the Brinkman number, heat generation/absorption, wave amplitude magnitude, and generalized Prandtl number on convective heat transfer in dilatant and pseudoplastic non-Newtonian. Results show that as the Brinkman number increases, the amount of heat transfer decreases. This is physically justifiable considering that the fluid becomes warmer due to the viscous dissipation, decreasing its temperature difference with the constant temperature surface. Also, the effect of the power law viscosity index is surveyed. It is demonstrated that the magnitude of the local Nusselt number in the plane leading edge has the smallest quantity for pseudoplastic fluids compared to dilatant Newtonian fluids. Additionally, as the distance from the plane leading edge increases, the heat transfer declines.
Highlights
Because of its wide practical application in different contexts, free convection heat transfer of non-Newtonian fluids on the wavy vertical surface has received great attention
Since the study of heat transfer from wavy surfaces is more practically widespread and a wavy surface interferes with the development of a boundary layer, enhancing the heat transfer in the applications such as solar collectors and condensers, this article is aimed at further understanding their heat transfer characteristics
One of the early researches on the free convection heat transfer of non-Newtonian fluids on wavy surfaces accompanied by the magnetic effect is accomplished by Yang et al [3]
Summary
Because of its wide practical application in different contexts, free convection heat transfer of non-Newtonian fluids on the wavy vertical surface has received great attention. One of the early researches on the free convection heat transfer of non-Newtonian fluids on wavy surfaces accompanied by the magnetic effect is accomplished by Yang et al [3] They solved a converted set of equations by the cubic spline method and showed that the temperature gradient for dilatant fluids is more than that for pseudoplastic fluids. Kim [4] numerically investigated the natural convection along a vertical wavy plate for non-Newtonian fluids He analyzed the effect of parameters like flow index, Prandtl number, and surface amplitude on the velocity and thermal boundary layer. Applying mapping of the wavy surface onto the flat surface, they proceeded with solving boundary layer equations by a spline alternating-direction implicit method They showed that with the increase in surface wave length and amplitude, the local Nusselt number and skin
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