Introduction to Convective Heat Transfer

6One‐Dimensional Solutions in Convective Heat Transfer

6.1 Introduction

In this chapter, one‐dimensional flow and heat transfer problems will be considered. In one‐dimensional flows, the streamlines are straight lines. In one‐dimensional rectilinear flows, u = u(x) and v = w = 0. In axisymmetric rectilinear flows, v_z = v_z(r) and v_r = v_θ = 0. We will discuss these points shortly. One‐dimensional solutions may be found in [1–3]. Although the applications of one‐dimensional problems are restrictive, conclusions that we draw from the solutions of one‐dimensional flow problems are very instructive to understand the fundamental concepts. The reader will develop an appreciation for the physical significance of each term in the governing equations of the problem and gain insight to identify the conditions under which the terms may be neglected. The meaningful simplification of the governing equations is critical to obtaining solutions. Energy, continuity, and momentum equations are not coupled in general. For this reason, velocity distribution is obtained first. With velocities known, temperature distribution may be obtained. We will make certain simplifying assumptions in the solution of the problems, and here are some of these assumptions:

1. Flow is laminar.
2. Steady flow, ∂/∂t = 0.
3. In general, the fluid properties are constant.
4. In general, energy, momentum, and continuity equations are decoupled. This means that velocity field can be determined independently from the temperature field. ...