Question

A fluid is flowing over a heated plate. The viscosity of flowing fluid is 0.001 Pa s and they specific heat at constant pressure is 1 kJ/kgk. The thermal conductivity of the heated plate is 1 W/m⋅k. (a) calculated the prand +1 numbes (b) comment on the relationship b/w hydrodyransic and thermal boundorylayer

Answer 1

(a) Prandtl number:Prandtl number is a dimensionless quantity, and it represents the ratio of momentum diffusivity to thermal diffusivity. It is usually represented as Pr = v/α, where v is kinematic viscosity and α is thermal diffusivity. It is one of the key parameters that determine the flow characteristics of fluids. The Prandtl number can be determined by the following formula:Pr = μ*Cp/k = 0.001 * 1000 / 1 = 1The Prandtl number is 1.(b) Hydrodynamic and Thermal Boundary Layer:Thermal boundary layer and hydrodynamic boundary layer are the two types of boundary layers. The thermal boundary layer and hydrodynamic boundary layer have different lengths in fluid flow over a flat plate, and the thermal boundary layer is always longer than the hydrodynamic boundary layer because of the low thermal conductivity of the fluid.The ratio of the length of the thermal boundary layer to the length of the hydrodynamic boundary layer can be expressed as:δt/δ = (Pr)^1/2Where δt is the length of the thermal boundary layer, δ is the length of the hydrodynamic boundary layer, and Pr is the Prandtl number. The Prandtl number is greater than 1 for fluids with high viscosity and low thermal conductivity, and the thermal boundary layer is larger than the hydrodynamic boundary layer.Therefore, there is a relationship between the hydrodynamic and thermal boundary layer, and it is directly proportional to the square root of the Prandtl number. In summary, the thermal boundary layer and hydrodynamic boundary layer are related, and the Prandtl number plays a key role in their relationship.