Convective Flow and Heat Transfer from Wavy Surfaces

Viscous Fluids, Porous Media, and Nanofluids

Aroon Shenoy, Mikhail Sheremet, Ioan Pop

• Publisher: CRC Press
• Year: 2016
• Print ISBN: 9780367877132
• eBook ISBN: 9781315350653
• Topic: Physical Sciences
• Subtopic: Thermodynamics

Convective Flow and Heat Transfer from Wavy Surfaces: Viscous Fluids, Porous Media, and Nanofluids addresses the wavy irregular surfaces in heat transfer devices. Fluid flow and heat transfer studies from wavy surfaces have received attention, since they add complexity and require special mathematical techniques. This book considers the flow and heat transfer characteristics from wavy surfaces, providing an understanding of convective behavioral changes.

Chapter 1

Governing Equations

Governing equations for flow from wavy surfaces are not truly different from those that are used when dealing with flat and smooth surfaces. The only difference lies in the use of an additional equation, which is needed for describing the profile of the wavy surface. Thus, the starting point is from the well-known Navier–Stokes equations. For example, for the simplest case of two-dimensional flow from a wavy wall, the relevant equations of continuity, momentum, and energy are written as follows:

$$\begin{array}{cc}\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0& (1.1)\end{array}$$

$$\begin{array}{cc}u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}=g_x-\frac{1}{\rho }\frac{\partial p}{\partial x}-\frac{1}{\rho }\left(\frac{\partial {\tau }_{xx}}{\partial x}+\frac{\partial {\tau }_{xy}}{\partial y}\right)& (1.2)\end{array}$$

$$\begin{array}{cc}u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}=g_y-\frac{1}{\rho }\frac{\partial p}{\partial y}-\frac{1}{\rho }\left(\frac{\partial {\tau }_{yx}}{\partial x}+\frac{\partial {\tau }_{yy}}{\partial y}\right)& (1.3)\end{array}$$

$$\begin{array}{cc}u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial y}=\frac{1}{\rho C_P}\left(\frac{{\partial }^{2}T}{\partial x^2}+\frac{{\partial }^{2}T}{\partial y^2}\right)& (1.4)\end{array}$$

where τ_ij, stress tensor, is related to the deformation tensor

$${\mathrm{\Delta }}_{ij}=[(\partial u_i/\partial x_j)+(\partial u_j/\partial x_i)]$$

through the rheological equation of state, thereby specifying the type under consideration. The stress components for two-dimensional flow of Newtonian fluids as well as non-Newtonian power-law fluids are given in Table 1.1.

Table 1.1. Shear Stress Components for Two-dimensional Flow in x, y Coordinate System

Newtonian Fluids	Non-Newtonian Power-law Fluids
${\tau }_{xx}=-{\mu }_0\left(2\frac{\partial u}{\partial x}\right)$	${\tau }_{xx}=-{\mu }^{*}{\left(\left|\sqrt{{\varphi }_v}\right|\right)}^{n-1}\left(2\frac{\partial u}{\partial x}\right)$
${\tau }_{yy}=-{\mu }_0\left(2\frac{\partial v}{\partial y}\right)$	${\tau }_{yy}=-{\mu }^{*}...$

Table of contents

• Cover
• Half title
• Title Page
• Copyright Page
• Contents
• Foreword I
• Foreword II
• Preface
• Nomenclature
• 1 Governing Equations
• 2 Steady Natural and Mixed Convection Flow in Viscous Fluids over Wavy Vertical Wall
• 3 Steady Natural Convection Flow in Fluid-Saturated Porous Media over Wavy Vertical Wall
• 4 Natural Convective Flow of a Viscous Fluid in a Wavy Vertical Channel
• 5 Forced Convective Flow in a Wavy Horizontal Channel
• 6 Convective Flow in a Wavy Tube
• 7 Natural Convection Flow Saturated with Nanoparticles in Wavy-Walled Cavities
• 8 Natural Convection Flow Saturated with Nanoparticles in Wavy-Walled Porous Cavities
• Concluding Remarks
• References
• Index