Introduction to Convective Heat Transfer

2Fundamental Equations of Laminar Convective Heat Transfer

2.1 Introduction

Since we are considering moving media, in this chapter, we will present the fundamental equations applicable to the open systems or control volume. The Eulerian approach is preferred in the study of convective heat transfer in determining temperature, pressure, forces, etc. at a particular location in space. Motivation for the use of the control volume technique is that measurement sensors, such as thermometers and pressure transducers, are located at a fixed position. Measurements give Eulerian fluid properties, for example, temperature T (x, y, z, t). We described fluid properties and flow characteristics in terms of field (Eulerian) concept.

We will develop the integral form of the mass, momentum, and energy. In each development, the finite system approach will first be undertaken, and afterward, this finite system formulation will be converted to the case of finite control volume by means of the Reynolds transport theorem. The Reynolds transport theorem is repeated here for convenience.

The Reynolds transport theorem gives a relation between the time rate of change within the system volume and that within the control volume. Finite integral formulations of the laws of mass, momentum, and energy provide us average values of quantities but cannot provide us the details of the flow. Using these integral ...