Heat flux local dimensionless

In a heat exchanger, air flows through a pipe of length, l. The air enters the pipe at a temperature, Tt. The heat flux at the wall of this pipe increases linearly from zero at the inlet of the pipe to a value of qw at the end of the pipe. The velocity in the pipe is such that HRe PrD — 0.07 where D is the diameter of the pipe and Re is the Reynolds number. Determine how the Nusselt number based on the local wall heat transfer rate and on the difference between the local wall temperature and the inlet temperature varies with the dimensionless distance. Z, along the pipe. 

Before proceeding to other topics, it is worthwhile to reflect briefly on the results of Sections ll.C and ll.D. In particular, let us focus our attention on the two results in (11-53) and (11-91) for the local temperature gradient in the case of a horizontal flat plate, with x = 0. These correspond to correlations for the local dimensionless heat flux... 

Heat flux and the Nusselt number. By differentiating (3.3.4) and using the numerical value /"(0) = 0.332, we obtain the dimensionless local heat flux to the plate surface ... 

The corresponding dimensionless local jr and total It heat fluxes have the form [269]... 

Uniform and Equal Heat Flux at Both Walls. Thermally developing flow in a parallel plate duct with uniform and equal heat flux at both walls has been investigated by Cess and Shaffer [132] and Sparrow et al. [133] in terms of a series format for the local and mean Nus-selt numbers. The dimensionless thermal entrance length for this problem has been found by Shah and London [1] to be as follows ... 

Local heat transfer measurements were carried out in the once-through system for the same aqueous polyacrylamide solutions used in the friction factor and viscosity measurements shown in Figs. 10.22 and 10.23 [37, 93]. These heat transfer studies involving a constant heat flux boundary condition required the measurement of the fluid inlet and outlet temperatures and the local wall temperature along the tube. These wall temperatures are presented in terms of a dimensionless wall temperature 0 in Fig. 10.27 for four selected concentrations. Here 0 is defined as... 

The Desert Tortoise included heat-flux sensors buried just beneath the surface, and Nielsen and Ott (1999) fitted a solution of the suh-surface flux measured at the centerline on 100 m downstream of the source in trial DT3. The best lit indicated that the dimensionless exposure time was F 0.24, implying that the local surface flux decreased to 62% of its initial value (po. 

The modeling procedure can be sketched as follows. First an approximate description of the velocity distribution in the turbulent boundary layer is required. The universal velocity profile called the Law of the wall is normally used. The local shear stress in the boundary layer is expressed in terms of the shear stress at the wall. From this relation a dimensionless velocity profile is derived. Secondly, a similar strategy can be used for heat and species mass relating the local boundary layer fluxes to the corresponding wall fluxes. From these relations dimensionless profiles for temperature and species concentration are derived. At this point the concentration and temperature distributions are not known. Therefore, based on the similarity hypothesis we assume that the functional form of the dimensionless fluxes are similar, so the heat and species concentration fluxes can be expressed in terms of the momentum transport coefficients and velocity scales. Finally, a comparison of the resulting boundary layer fluxes with the definitions of the heat and mass transfer coefficients, indiates that parameterizations for the engineering transfer coefficients can be put up in terms of the appropriate dimensionless groups. 

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