How to size a heat exchanger for a shear thinning fluid?

Question

To size a heat exchanger, I need to know (among other things) the Reynolds number (Re) as an indication of the flow conditions. The Re number depends on the viscosity. In a shear thinning fluid, I can't assume a constant viscosity, instead it will depend on the shear rate that is not constant throughout the pipe. I've asked on Physics SE about the shear rate in turbulent shear thinning fluid flow in a pipe, but received no helpful answer.

Here at Engineering.SE, I am not looking for an in-depth examination of the beauty of the Navier-Stokes equation, but for a practical approach to sizing a heat exchange for such a fluid. How to go about it?

Answer 1

First, as Arthur notes, even the best Nusselt number correlations are often as much as 20% off, so don't expect any analytical method to give results that are much better than approximate.

With that said, there are ways to compute the Reynolds number for shear thinning fluids. Rudman, Blackburn, et al suggest using the effective viscosity for the mean wall shear stress. If you have a fluid that can be modeled as a Herschel-Bulkley Fluid, then the Reynolds number equation takes the following form. $$ Re = \frac{\rho \bar{U} D}{\eta_w} $$ $$ \eta_w = K^{\frac{1}{n}} \frac{\tau_w}{(\tau_w - \tau_y)^{1/n}} $$ $$ \tau_w \approx \frac{4}{D} \frac{\Delta p}{L} $$

The authors note that other formulations of the Reynolds number exist for shear thinning flows, and there is no "perfect" Reynolds number for shear thinning flows, but state that this formulation takes the dynamics near the walls of the pipe into account well.

Answer 2

Any heat exchanger has different values for the viscosity along its length, since it depends on the fluid's temperature. You should use an average value for the viscosity. Surely if it varies too much it is going to be harder to estimate this value, but it can be done. You can do it by knowing the shear rate in the different regions of your stream, and then prorate how much of your fluid goes though each region (in percentage).

You have to keep in mind that with the best Nusselt number correlation you will have at least a 20% error, so it is always a little uncertain