## 4 Results and Discussion
This effect becomes more pronounced for fluids with higher viscosities, leading to an increased temperature difference. The heat transfer phenomenon for viscometers was also investigated through the numerical simulations using OpenFOAM. The simulations are shown in Figures 11 and 12. Figure 10: Time variation in non-uniform temperature field in flow visualization test cup. (**a**) Fluid A (100 cSt); (**b**) Fluid B (1000 cSt); (**c**) Fluid C (10,000 cSt). Figure 11: Thermal conduction when \(t=10\) min in top view: **(a)** Fluid A (100 cSt), **(b)** Fluid B (1000 cSt), **(c)** Fluid C (10,000 cSt) and projectile view, **(d)** Fluid A (100 cSt), **(e)** Fluid B (1000 cSt), **(f)** Fluid C (10,000 cSt). Figure 12: Thermal convection when \(t=10\) min in **(a)** Fluid A (100 cSt), **(b)** Fluid B (1000 cSt), **(c)** Fluid C (10,000 cSt). Figure 13 displays velocity field measurements within planar sections observed from the front and side of the test cup. These sections are taken through the center of Fluid A at the eight-minute mark, as captured during the current PIV experiment. The figure presents velocity vectors, magnitudes, and streamlines, providing insights into the flow dynamics within the test cup. Notably, the velocity magnitude (v) is depicted using color-coded bars. Importantly, it should be noted that the cell pattern exhibits asymmetry concerning the midplane. This asymmetry arises due to the considerable Rayleigh number of 6.6 \(\times\) 10\({}^{5}\), which induces flow instability [28]. Figures 14 and 15 show the velocity fields in the test cup for Fluids B and C, respectively, 8 min after the initiation of the heating. These results indicate that the magnitude of the thermal convection decreases as the viscosity of the fluid increases, corresponding to a decrease in the Rayleigh and Grashof numbers and an increase in the Prandtl number. Therefore, the influence of thermal convection becomes weaker for the highly viscous fluids and thermal conduction becomes the main method for the heat transfer. This result agrees well with the experimental observation of the temperature variations in the test cup and the estimates of the Rayleigh, Grashof and Prandtl numbers in Figure 6.  
Figure 14: Velocity field in test cup for Fluid B (1000 cSt) (\(t\) = 8 min). Figure 13: Velocity field in test cup for Fluid A (100 cSt). (**a**) \(t\) = 4 min, (**b**) \(t\) = 8 min. As a final discussion, _VME_ graphic that is presented in Figure 16 explains a lot about the serious problems in viscosity measurement during heat transfer. _VME_ is calculated by [29]  
\[\log\eta^{T}=\frac{763.1}{273+T}-2.559+\log\eta^{25}, \tag{5}\]  
where \(\eta^{T}\) is kinetic viscosity (mm\({}^{2}\)/s) at \(T\)\({}^{\circ}\)C and \(-25\)\({}^{\circ}\)C \(<T<-250\)\({}^{\circ}\)C.  
\[VME\ (\%)=\left(100-\left(\frac{\left(\eta^{T}{}_{IS8}\pi 100\right)}{\eta^{T}{}_{IS1}} \right)\ \right), \tag{6}\]  
where \(\eta^{T}{}_{IS8}\) and \(\eta^{T}{}_{IS1}\) imply the viscosity of Fluid A, B or C at the points where \(IS8\) (at the bottom) and \(IS1\) (at the surface) measure the temperature (\(T\)) at selected times. Owing to pronounced thermal convection, low-viscosity fluids offer a more thermally uniform environment, leading to reduced _VME_s. Nevertheless, even within these favorable circumstances, there is still a 15% occurrence of _VME_s. In the case of highly viscous fluids, the outcomes related to _VME_s are notably more severe. As the duration of heating extends, the incidence of _VME_s escalates, reaching levels as high as 30%, ultimately invalidating all viscosity measurements. Figure 9:0 Viscosity measurement error (_VME_). Figure 9:1 Velocity field in test cup for Fluid C (10,000 cSt) (\(t=8\) min). 5 The Proposal of a Non-Dimensional Parameter Called the Akpek Number as a Possible Solution for VME  
In the previous parts, the non-uniform temperature distribution problem was discussed. It is understood that this problem in viscometers is naturally caused by the thermal conduction and thermal convection.