The Effect of Random Roughness on the Electromagnetic Flow in a Micropipe

Abstract

The features of stationary random processes and the small parameter expansion approach are used in this work to examine the impact of random roughness on the electromagnetic flow in cylindrical micropipes. Utilizing the perturbation method, the analytical solution until second order velocity is achieved. The analytical expression of the roughness function ζ, which is defined as the deviation of the flow rate ratio with roughness to the case having no roughness in a smooth micropipe, is obtained by integrating the spectral density. The roughness function can be taken as the functions of the Hartmann number Ha and the dimensionless wave number λ. Two special corrugated walls of micropipes, i.e., sinusoidal and triangular corrugations, are analyzed in this work. The results reveal that the magnitude of the roughness function rises as the wave number increases for the same Ha. The magnitude of the roughness function decreases as the Ha increases for a prescribed wave number. In the case of sinusoidal corrugation, as the wave number λ increases, the Hartmann number Ha decreases, and the value of ζ increases. We consider the λ ranging from 0 to 15 and the Ha ranging from 0 to 5, with ζ ranging from −2.5 to 27.5. When the λ reaches 15, and the Ha is 0, ζ reaches the maximum value of 27.5. At this point, the impact of the roughness on the flow rate reaches its maximum. Similarly, in the case of triangular corrugation, when the λ reaches 15 and the Ha is 0, ζ reaches the maximum value of 18.7. In addition, the sinusoidal corrugation has a stronger influence on the flow rate under the same values of Ha and λ compared with triangular corrugation.

Self-Powered Flow Rate Sensing via a Single-Electrode Flowing Liquid Based Triboelectric Nanogenerator

“…Additionally, the transit time or Doppler effect is utilized in ultrasonic flow meters [ 14 , 15 ]. However, each of these technologies has inherent drawbacks, such as fluid flow disturbances, pressure drops, high costs, and limitations in applications with millimeter-scale pipes [ 16 , 17 ]. Furthermore, these technologies necessitate a continuous external power supply and ample internal space for integration into the device.…”

Alternating Current Electroosmotic Flow of Maxwell Fluid in a Parallel Plate Microchannel with Sinusoidal Roughness

“…In addition, the EMHD of transverse and longitudinal roughness have been studied [ 31 , 32 ]. Recently, the effect of small-amplitude random lateral wall roughness on EMHD flow in microchannels in parallel plates [ 33 ] and cylindrical [ 34 ] microchannels was studied using the perturbation method of stationary random function theory. Hosham et al [ 35 ] studied the heat and mass transfer effects in EOF based on the viscoplastic Bingham fluid model in complex corrugated microchannels.…”