Given information:
- Ratio of laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness for fluid P: 1/2
- Ratio of laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness for fluid Q: 2
- Reynolds number based on plate length for both fluids: 104
- Prandtl number for fluid P: 1/8
- Nusselt number for fluid P: 35

We need to find the Prandtl and Nusselt numbers for fluid Q.

Explanation:
1. Understanding the laminar hydrodynamic boundary layer thickness and thermal boundary layer thickness:
- The hydrodynamic boundary layer thickness is the distance from the surface of the flat plate where the velocity of the fluid flow is significantly affected by the presence of the plate.
- The thermal boundary layer thickness is the distance from the surface of the flat plate where the temperature of the fluid flow is significantly affected by the presence of the plate.

2. Reynolds number:
- The Reynolds number (Re) is a dimensionless quantity that represents the ratio of inertial forces to viscous forces in a fluid flow. It is given by the formula Re = ρVL/μ, where ρ is the density of the fluid, V is the velocity of the fluid flow, L is the characteristic length (in this case, the length of the flat plate), and μ is the dynamic viscosity of the fluid.
- The Reynolds number helps classify the flow regime as laminar or turbulent. For Re < 2300,="" the="" flow="" is="" laminar,="" and="" for="" re="" /> 4000, the flow is turbulent.

3. Ratio of laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness:
- For a laminar boundary layer flow, the ratio of the hydrodynamic boundary layer thickness (δ_h) to the thermal boundary layer thickness (δ_t) is given by the Prandtl number (Pr), which is the ratio of momentum diffusivity to thermal diffusivity. Pr = ν/α, where ν is the kinematic viscosity of the fluid and α is the thermal diffusivity of the fluid.

4. Calculation of the Prandtl and Nusselt numbers for fluid Q:
- Given that the ratio of laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness for fluid Q is 2, and the Reynolds number based on the plate length is 104, we can assume that the flow is laminar for fluid Q.
- Since the flow is laminar, we can use the Prandtl number (Pr) to find the thermal boundary layer thickness (δ_t) for fluid Q.
- The Prandtl number for fluid Q can be calculated as Pr = δ_h/δ_t = 2.
- Given that the Prandtl number for fluid P is 1/8, we can assume that the Prandtl number for fluid Q is also 1/8, as the Reynolds number is the same for both fluids.
- The Nusselt number (Nu) represents the ratio of convective heat transfer to conductive heat transfer at the surface of the flat plate. It is given by the formula Nu = hL/k, where h is the convective heat transfer coefficient, L is the characteristic length (in this case, the length of the flat plate), and k is the thermal conductivity of the fluid.
- The Nusselt number for fluid P is given as 35.
- Since the