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

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?

• (1) Is there a reason you cannot use experiment? (2) Do you have a preferred style of heat exchanger e.g. shell and tube? Is your shear thinning fluid on the tube side? (3) This abstract suggests it is a hard problem, probably beyond the scope of a Q&A website: dx.doi.org/10.1111/j.1745-4530.2008.00321.x Jan 28, 2015 at 10:16
• 1) no ressources (plus admittedly I can delegate the problem to a supplier but I'm curious) 2) shell an tube, yes 3) lemme have a look ...
– mart
Jan 28, 2015 at 10:40
– Air
Mar 17, 2015 at 19:55
• If you don't mind, asking out of curiosity - what are you using that shear-thinning liquid for? I've read about them a little but I couldn't find anything on applications outside of food industry (stick sauces to food).
– SF.
Mar 31, 2015 at 20:13
• My company build biogas plants, and the thick slurries we have are shear thinning. We only sometimes use HX, mostly we heat our plants with pipes in the tanks, if we use HX we let the suppliers do the sizing. I just want to see if I land in a similiar ballpark.
– mart
Apr 1, 2015 at 5:09

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. $$Re = \frac{\rho \bar{U} D}{\eta_w}$$ $$\eta_w = K^{\frac{1}{n}} \frac{\tau_w}{(\tau_w - \tau_y)^{1/n}}$$ $$\tau_w \approx \frac{4}{D} \frac{\Delta p}{L}$$