Introduction to Convective Heat Transfer

8Laminar Momentum and Heat Transfer in Channels

8.1 Introduction

Internal laminar flow through channels, such as pipes and parallel plates, will be considered in this chapter. Fluid is constrained on all sides by solid boundaries. In these channels, continuum assumption is assumed to be valid. In many engineering devices, such as minichannels and microchannels, flow is laminar. We will emphasize on the analytical solutions, and I believe that students will gain insight provided by the analytical solutions.

There is a geometric length scale imposed on the flow in the cross‐stream direction, and the channel diameter D_H is the pertinent length scale. The Reynolds number for flow in a channel is defined as

(8.1)

where V is the mean velocity, D_H is the inside hydraulic diameter, ρ is the fluid density, and μ is dynamic viscosity of the fluid. Many engineering devices have noncircular cross sections; heat transfer and friction coefficients are needed for these configurations. For this reason, it is obvious that geometric length scale D_H has significant physical importance in internal flows, and therefore, it is common to use hydraulic diameter D_H for the length scale. Hydraulic diameter D_H is defined as

(8.2)

where A_c and P are the cross‐sectional flow area and wetted flow perimeter, ...