Mass transfer inside spiral coils under laminar flow and possible applications

ABSTRACT

Rates of mass transfer in a spiral coil were measured by a technique involving the diffusion-controlled dissolution of copper in acidified dichromate. The variables studied were solution velocity, spiral tube pitch, and physical properties of the solution. The data were correlated by the equation

$\mathrm{S}\mathrm{h}=0.189\mathrm{S}{\mathrm{c}}^{0.33}\mathrm{D}{\mathrm{e}}^{0.55}{\left(\frac{\mathrm{P}}{\mathrm{d}}\right)}^{0.29}$

For a given set of conditions, the mass transfer coefficient predicted from the above equation was found to be much higher than that of the straight tube. Comparison of the ratio between the mass transfer coefficient and pressure drop for spiral tubes and straight tubes has revealed that $\frac{\mathrm{k}}{\mathrm{\Delta }\mathrm{p}}$ for spiral tubes is much higher than that of a straight tube under the present range of conditions. The possibility of using the above equation in predicting the rate of diffusion-controlled corrosion and the corrosion allowance needed to design a spiral tube heat exchanger was noted. Other possible applications in heterogeneous reactor design and membrane processes are reported.

KEYWORDS:

• Mass transfer
• spiral tubes
• heat transfer
• diffusion controlled corrosion
• membrane processes

List of symbols

A	=	Inner area of the spiral coil, cm2
$a,a_1,a_2$	=	Constant
Co, C	=	Initial dichromate concentration and concentration at any time t, mol cm−3
$C_p$	=	Specific heat of the solution, cal g−1 °C−1
D	=	Diffusivity of transferring Cu2+, cm2 s−1
d	=	Inner diameter of the coil tube, cm
${\mathrm{d}}_{\mathrm{a}\mathrm{v}}$	=	Average coil diameter, cm
f	=	Fanning friction factor
g	=	Acceleration due to gravity, cm s−2
h	=	Heat transfer coefficient, cal s−1 cm−2ºC−1
k	=	Mass transfer coefficient, cm s−1
L	=	Pipe length, cm
P	=	Spiral coil pitch, cm
Q	=	Solution volume, cm3
V	=	Solution velocity, cm s−1
De	=	Dean number $\mathrm{R}\mathrm{e}\sqrt{\frac{\mathrm{d}}{{\mathrm{d}}_{\mathrm{c}}}}$
Nu	=	Nusselt number $\left(\frac{\mathrm{h}\mathrm{d}}{\kappa }\right)$
Pr	=	Prandtle number $\left(\frac{\mu C_p}{\kappa }\right)$
Re	=	Reynolds number $\left(\frac{\rho \mathrm{V}\mathrm{d}}{\mu }\right)$
Sc	=	Schmidt number $\left(\frac{\mu }{\rho \mathrm{D}}\right)$
Sh	=	Sherwood number $\left(\frac{\mathrm{k}\mathrm{d}}{\mathrm{D}}\right)$
$\kappa$	=	Thermal conductivity of the solution, cal s−1 cm−1ºC−1
$\mu$	=	Solution viscosity, g cm−1 s−1
$\nu$	=	Kinematic viscosity, cm2 s −1
$\rho$	=	Average solution density, g cm−3
$\mathrm{\Delta }\rho$	=	Density difference between solution bulk and interfacial solution, g cm−3
Δp	=	Pressure drop