Q1:  is called the __________ number

ANS:C - Graetz

The Graetz number, named after German engineer Ernst Graetz, is a dimensionless parameter used in the analysis of heat transfer in fluid flow through a pipe or conduit. It is commonly denoted as Gr or Grz. The Graetz number represents the ratio of the thermal diffusion timescale to the fluid flow timescale in a system. Mathematically, the Graetz number (Gr) is defined as: Gr=αLD​ Where:

• L is the characteristic length of the flow (typically the length of the pipe or conduit),
• D is the diameter of the pipe or conduit,
• α is the thermal diffusivity of the fluid.

The thermal diffusivity (α) is a material property that describes how quickly heat can diffuse through a substance relative to its ability to conduct heat. It is defined as the ratio of the material's thermal conductivity (k) to its volumetric heat capacity (ρCp​): α=ρCp​k​ In fluid flow through a pipe, the Graetz number is used to characterize the dominance of conduction compared to convection. A low Graetz number indicates that conduction dominates over convection, meaning that heat transfer occurs primarily through the pipe wall. On the other hand, a high Graetz number suggests that convection dominates, and heat transfer occurs primarily due to the fluid flow inside the pipe. The Graetz number is particularly important in analyzing situations where the fluid flow rate, fluid properties, and geometry of the system affect the balance between conduction and convection heat transfer. It is commonly used in the analysis of heat exchangers, reactors, and other industrial processes involving fluid flow and heat transfer.