The Equations of Convective Heat Transfer

In order to be able to predict convective heat transfer rates there are, in general, three variables whose distributions through the flow field must be determined. These variables (see Fig. 2.1) are  

Once the distributions of these quantities are determined, the variation of any other required quantity, such as the heat transfer rate, can be obtained. 

In order to determine the distributions of pressure, velocity, and temperature the principles of conservation of mass, conservation of momentum (Newton s Law) and conservation of energy (first law of Thermodynamics) are applied. These conservation principles represent empirical models of the behavior of the physical world. They do not, of course, always apply, e.g., there can be a conversion of mass into energy in some circumstances, but they are adequate for the analysis of the vast majority of engineering problems. These conservation principles lead to the so-called Continuity, Navier-Stokes and Energy equations respectively. These equations involve, beside the basic variables mentioned above, certain fluid properties, e.g., density, p viscosity, p conductivity, k and specific heat, cp. Therefore, to obtain the solution to the equations, the relations between these properties and the pressure and temperature have to be known. (Non-Newtonian fluids in which p depends on the velocity field are not considered here.) As discussed in the previous chapter, there are, however, many practical problems in which the variation of these properties across the flow field can be ignored, i.e., in which the fluid properties can be assumed to be constant in obtaining fire solution. Such solutions are termed constant 

Variables required to determine convective heat transfer rates. 

In the present chapter, it will also be assumed that all body forces are negligible. A discussion of some flow s in which buoyancy forces are important will be given in Chapters 8 and 9. 

---

Equation (4.60) corresponds to discarding 0T/0t from the left-hand side of the equation of convective heat transfer, Eq. (4.56), which has an apparent physical significance for fast thermal tuning. 

---