## 4 Results and Discussion
In both industry and academia, capillary viscometers are widely used to obtain standard viscosity values. These values are universally accepted as highly accurate due to the absence of non-uniform temperature distribution issues in capillary viscometers. The temperature measurement error in these instruments is typically within the range of \(\pm\)0.02 \({}^{\circ}\)C, ensuring precise viscosity measurements. However, it is essential to note that capillary viscometers can only provide single-point viscosity measurements. To acquire data equivalent to continuous viscosity measurements, it often takes several days, requires a significant amount of labor force, and can be expensive. Despite the precision of capillary viscometers, the limitation in achieving continuous viscosity data has led to the exploration of alternative methods that strike a balance between accuracy and efficiency. Researchers and industries are continually working to develop innovative techniques that can provide more frequent and cost-effective viscosity measurements without compromising accuracy. In this section, a novel non-dimensional parameter is introduced to address the issue of non-uniform temperature distribution during fluid heating and its impact on viscosity measurements. The proposed concept suggests that there exists an optimal heating speed for a fluid, considering factors such as applied heat flux, viscosity change rate, fluid volume, and thermal diffusivity. By using this new concept, it becomes possible to eliminate the problem of non-uniform temperature distribution in viscometers. Consequently, any type of viscometer can provide viscosity measurements that are as accurate as those obtained with a capillary viscometer. To calculate the acceptable heating speed that can eliminate the non-uniform temperature distribution problem, certain parameters need to be considered. These parameters include:  
Figure 9:2  
In Equation (7),  
In Equation (10), \(t^{*}\) is called the Fourier number. When viscosity change in temperature (\(\dfrac{d\mu}{dT}\)) is non-dimensionalized,  
Figure 9:3  
In Figure 17, the centerline temperature of an infinite cylinder is plotted as a function of time. It can be observed that as the Fourier number increases, the temperature homogeneity also increases. In fluid mechanics, the Fourier number is a dimensionless parameter used to characterize heat conduction. Conceptually, the Fourier number represents the ratio of the conduction rate to the storage rate of heat and is derived from the non-dimensionalization of the heat conduction equation, as shown in Equation (12). The Fourier number plays a crucial role in understanding the heat transfer behavior in various systems. As it increases, it indicates that heat conduction becomes more dominant compared to heat storage effects, leading to a faster and more uniform temperature distribution within the system. This information is valuable for analyzing and solving heat conduction problems in different engineering and scientific applications. Figure 9:4  
The Fourier number includes the following parameters:  
Figure 9:5  
Figures 18 and 19 are presented as an example to the viscosity change in temperature (\(\dfrac{d\mu^{*}}{dT}\)) and the change in the temperature of the edge of the fluid in time (\(\dfrac{dT_{w}}{dt}\)). Figure 9:6 Heisler chart and centerline temperature as a function of time [30]. Based on the Heisler chart in Figure 17, temperature homogeneity (\(\theta^{*}\)) can be evaluated regarding to the change in the Fourier number. As an example, let us say we have a ratio of center temperature (\(T_{c}\)) to wall temperature (\(T_{w}\)) in percentage as the Fourier number increases as in Figure 19a. In this figure, an inverse Biot number is accepted as zero. This means we should have a temperature difference (\(1-\dfrac{T_{c}}{T_{w}}\)) as in Figure 19b. The viscosity change in temperature (\(\dfrac{d\mu^{*}}{dT}\)) and the wall temperature change in time (\(\dfrac{dT_{w}}{dt}\)) is directly proportional to the temperature difference.