The mathematical principles of convective heat transfer are complex and outside the scope of this section. The problems are often so complicated that theoretical handling is difficult, and full use is made of empirical correlation formulas. These formulas often use different variables depending on the research methods. Inaccuracy in defining material characteristics, experimental errors, and geometric deviations produce noticeable deviations between correlation formulas and practice. Near the validity boundaries of the equations, or in certain unfavorable cases, the errors can be excessive.
The general forms of the convection equations are given below in a simple form. More accurate equations can be found from the latest research results presented in technical journals.
The general equation for the case of forced convection is Nu = /(Re, Pr). In the case of free convection it is Nu = f(Gr, Pr).
Nu = Nusselt number =
Gr = Grashof number = ^
& = M = a Q e = r _ j
Where Tp is the surface temperature.
A.. = —
Pr = Prandtl number = —
Re = Reynolds number =
The characteristic length L denotes the pipe diameter or the hydraulic diameter dhyd = 4A/P (A is the cross-sectional area and P is the wet periphery). If the cross-section is not circular, or in the case of a plane, the length is measured in the flow direction.
The temperature changes taking place through the surface of an exothermic body depend on the material characteristics and changes in the parameters. In formulas involving convection, either the solid surface temperature or the heat flow from the surface is assumed to be constant. The temperature 6 defines the material characteristics (c, p, v, etc.). Normally this temperature is the mixed temperature of the flowing fluid. The mean temperature of the boundary layer is the average temperature of the surface temperature and the undisturbed flow (Tm = (Tp + T„)/2). Sometimes the boundary layer temperature, which is the average of the mixing temperature and the surface temperature, is used.
Posted in INDUSTRIAL VENTILATION DESIGN GUIDEBOOK