Forced convection analytical expressions

There are very many situations in which well-defined patterns of convection can be established, and analytical expressions for vf derived. Such situations usually involve forced convection, in which the movement of the liquid is determined by rotation, agitation, forced flow over a flat surface, etc. Once the functional form of vf is known, solutions for c as a function of x are sought so that values of the current can be found and compared with those obtained experimentally. 

The local heat transfer coefficient for forced convection inside tubes is determined from experiments conducted with electrically heated tubes. This coefficient requires that the inner temperature of the tube walls Tt be known. However, T turns out to be more difficult to measure than the outer temperature of the tube walls, To. The usual practice is to measure To and relate it to 7i by an analytical expression. We wish to obtain this expression in terms of a tube with an inner radius J i, an outer radius f 2> and internal energy generation u ". 

In Chapter 5, we learned the foundations of convection. Integrating the governing equations for laminar boundary layers, we obtained expressions for the heat transfer associated with forced convection over a horizontal plate and natural convection about a vertical plate. We also found analytically, as well as by the analogy between heat and momentum, that the thermal and momentum characteristics of laminar flow over a flat plate are related by... 

Analytical expressions for the heights at which impulsive and convective forces are acting are available from hydrodynamics, represented also in graphical form in Fig. 7. 

For the heated vertical plate and horizontal cylinder, the flow results from natural convection. The stagnation configuration is a forced flow. In each case the flow is of the boimdai7 Kiyer type. Simple analytical solutions can be obtained when the thickness of the du.st-free space is much smaller than that of the boundary layer. In this case the gas velocity distribution can be approximated by the first term in an expansion in the distance norroal to the surface. Expressions for the thickness of the dust-free space for a heated vertical surface and a plane stagnation flow are derived below. 

In free convection, there is a new complexity in that fluid motion arises from buoyancy forces due to the density differences, and the momentum, heat and mass balance equations are therefore coupled. The published analytical results for heat transfer from plates, cylinders and spheres involve significant approximations. This work has been reviewed by Shenoy and Mashelkar [1982] and Irvine and Kami [1987] the simple expressions (which are also considered to be reliable) for heat transfer coefficients are given in the following sections. 

Many formulations based upon these assumptions can be derived. One formulation can be converted into another using the definitions of density, internal energy and the ideal gas law. Though equivalent analytically, these formulations differ in their numerical properties. Each formulation can be expressed in terms of mass and enthalpy flow. These rates represent the exchange of mass and enthalpy between zones due to physical phenomena such as plumes, natural and forced ventilation, convective and radiative heat transfer, and so on. For example, a vent exchanges mass and enthalpy between zones in connected rooms, a fire plume typically adds heal to the upper layer and transfers entrained mass and enthalpy from the lower to the upper layer, and convection transfers enthalpy from the gas layers to the surrounding walls. 

---