Introduction and Modes of Heat Transfer

From the first law of thermodynamics in Chap. 2,

(4-1)

where U is internal energy, Q is heat, and W is work. For heat transfer, there must be a temperature difference ? T, which is a driving force. Heat can be transferred by different mechanisms; conduction, convection, and radiation.

In any system, energy is transferred from a high-temperature to a low-temperature region. We will calculate heat transfer as a flux, which is power (heat per unit time) transferred per unit area in each of the three coordinate directions. The equation governing this transfer is Fourier's law

(4-2)

where i, are unit vectors in the x, y, and z direction, q' is the energy of heat flux in kJ/s-m ², k is the thermal conductivity in kJ/s-m-K, and T is temperature in K.

If the material has an internal heat source and if the heat transfer is unsteady (i.e., it varies with temperature), then the equation of energy is

(4-3)

where q is a heat source in units of energy generated per unit volume and unit time, r is density, C _p is the specific heat, and t is time.

The second mode of heat transfer, convection, involves at least one component in motion, for example, a liquid flowing past a solid or a gas and liquid both flowing. Convection is conduction together with motion. Because this a...