Combined convection assisting flow

E. Combined Forced and Free Laminar Convection from Vertical Surfaces When Both Are in the Same Direction (Assisting Flows)... 

It is difficult to solve the system of Eqs. (39)—(41) for these boundary conditions. However, certain simplifying assumptions can be made, if the Prandtl number approaches large values. In this case, the thermal boundary layer becomes very thin and, therefore, only the fluid layer near the plate contributes significantly to the heat transfer resistance. The velocity components in Eq. (41) can then be approximated by the first term of their Taylor series expansions in terms of y. In addition, because the nonlinear inertial terms are negligible near the wall, one can further assume that the combined forced and free convection velocity is approximately equal to the sum of the velocities that would exist when these effects act independently. Therefore, for assisting flows at large Prandtl numbers (theoretically for Pr -> oo), Eq. (41) can be rewritten in the form ... 

FIGURE 9A Assisting and opposing combined convective flow. 

To illustrate the form of results obtained, consider assisting and opposing combined convective flow over a square cylinder at low Reynolds numbers (Fig. 9.13). A computer program, MIXSQCYL, that finds this solution can be obtained in the way discussed in the Preface. The program assumes that the flow over the cylinder is symmetrical about the vertical center-line of the cylinder. 

Consider assisting combined convective flow over a body. If the Grashof number is kept constant and the Reynolds number is varied, the variation of Xu with Re would resemble that shown in Fig. 9.17. This type of result could be obtained by considering a body of fixed size, kept at a fixed temperature (this would keep the Grashof number constant), that is placed in a fluid flow in which the velocity could be varied (this would allow the Reynolds number to be varied). 

Typical variation of Nusselt number with Reynolds number in assisting combined convective flow. 

When determining heat transfer under combined natural and forced convection conditions, it is tempting to add the contributions of natural and forced convection in assisting flows and to subtract them in opposing flows. However, the evidence indicates differently. A review of experimental data suggests a conelation of the form... 

Contact temperature measurement is based on a sensor or a probe, which is in direct contact with the fluid or material. A basic factor to understand is that in using the contact measurement principle, the result of measurement is the temperature of the measurement sensor itself. In unfavorable situations, the sensor temperature is not necessarily close to the fluid or material temperature, which is the point of interest. The reason for this is that the sensor usually has a heat transfer connection with other surrounding temperatures by radiation, conduction, or convection, or a combination of these. As a consequence, heat flow to or from the sensor will influence the sensor temperature. The sensor temperature will stabilize to a level different from the measured medium temperature. The expressions radiation error and conduction error relate to the mode of heat transfer involved. Careful planning of the measurements will assist in avoiding these errors. 

MHD-based models have been widely used in various magnetically assisted electrolyte flow investigations. 74,75 application of the pumping effect of combined electric and magnetic fields led to the development of MHD-pump electrode cells, where the concentration distribution, modeled by the classical convective diffusion equation... 

Combined forced and free convection at a vertical flat plate, where the forced convection velocity is in the same direction as the natural convection flow (the so-called assisting mixed convection case). Here, researchers have combined Sherwood numbers for the pure forced and natural convection cases in the following way [15, 24-26] ... 

---