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The theory of rheology of non-Newtonian fluids is based on the generalized Newtonian hypothesis of viscosity. The viscometers for non-Newtonian fluids should implement fluid flows with the known stress and strain state parameters distributions. Ideally, the distributions should be homogeneous in the flow domain. The idea of the proposed method is based on a combination of a capillary and a rotational viscometers implemented in the torus-shaped capillary viscometer. Analysis of the mathematical model of the inertial non-Newtonian fluid flow in the torus allowed to determine the conditions of homogeneity of the mechanical and thermal parameters in the flow domain and to develop method of viscosity measurement. The measured values are the shear rate on the inner surface of the capillary and the flow rate. The measurements are implemented with the computer vision system that processes data obtained from the high speed CMOS camera that records inertial flow in the transparent capillary illuminated with laser. The computer vision system is based on the application of deep convolutional neural network for laser speckle contrast imaging processing. During the experiments, the proposed viscometer was compared with the Brookfield rotational viscometer. The relative error of the proposed viscometer and method is less than 2 %. The inertial viscometer is compact, it allows to study the wide range of shear rates per one test in automatic mode, and it has low fluid capacity of approximately 1.87 ml. That makes it possible to use the viscometer as a point on care testing device in medicine to study the rheology of physiological fluids, in particular blood. [Display omitted] • Inertial flow in a torus-shape capillary is perfectly symmetrical and homogeneous. • Laser speckle-contrast imaging allows one to see flow velocity on an image. • Artificial intelligence allows computer vision to see shear rate of the fluid flow. • Inertial viscometer could be a novel point on care testing device in medicine. [ABSTRACT FROM AUTHOR]

• A comprehensive and detailed solution of double-diffusive natural convection of Casson fluids in an enclosure is obtained. • The influence of the governing parameters on fluid flow, morphology of yielded/unyielded regions, and heat and mass transfer are thoroughly examined. • The unyielded regions grow with decreasing buoyancy ratio and increasing the yield number. • The Lewis number has different effects on unyielded areas depending on the flow parameters. • Correlations for average Nusselt and Sherwood numbers are provided. This study investigates the double-diffusive natural convection of the non-Newtonian Casson fluid in a square cavity based on the original viscoplastic stress model without simplification. Therefore, yield stress plays an essential role in understanding fluid behavior. The finite element approach provided a numerical solution to continuity, momentum, energy, and species governing equations. The governing parameters for this problem are Rayleigh number, Ra , yield number, Y , buoyancy ratio number, Nr , and Lewis number, Le. The influence of these parameters on heat and mass transfer, the morphology of yielded/unyielded regions, and fluid flow are thoroughly examined. The results show that unyielded regions increase at high Rayleigh numbers, despite the increase in buoyancy force and consequently increased heat and mass transfer. On the other hand, as the buoyancy ratio drops, the flow's strength and heat and mass transmission diminish, leading to an increase in plug regions. Accordingly, the mechanisms influencing the growth of unyielded regions are complex and follow different patterns. However, the plug regions always grow with increasing Y. The results indicate that increasing the Lewis number (mass transfer) reduces the effect of the buoyancy ratio on flow, heat transfer, and the unyielded regions in every case. Quantitative analysis of the results indicates that, while buoyancy ratio affects heat and mass transfer almost equally, the Lewis number increases mass transfer up to three times the heat transfer. Meanwhile, changing the buoyancy ratio can increase the maximum yield stress to 400%, while changing the Lewis number has a maximum effect of 20%. [Display omitted] [ABSTRACT FROM AUTHOR]