False statement: Dynamic viscosity has to be decreased sixteen times.

Explanation:

Nusselt number (Nu) is a dimensionless number that relates the convective heat transfer coefficient (h) to the conductive heat transfer coefficient (k) for a given fluid flow. It is defined as:

Nu = hL/k

where L is the characteristic length of the system.

For laminar flow over a flat plate, the average value of Nusselt number is prescribed by the relation:

Nu = 0.664 (Re)0.5(Pr)0.33

where Re is the Reynolds number and Pr is the Prandtl number. The Reynolds number is a dimensionless number that relates the inertial forces to the viscous forces for a fluid flow, and it is defined as:

Re = ρUL/μ

where ρ is the density of the fluid, U is the velocity of the fluid, L is the characteristic length of the system, and μ is the dynamic viscosity of the fluid.

The Prandtl number is a dimensionless number that relates the momentum diffusivity to the thermal diffusivity of a fluid, and it is defined as:

Pr = μCp/k

where Cp is the specific heat of the fluid at constant pressure and k is the thermal conductivity of the fluid.

Now, let's consider each option:

a) Density has to be increased four times:

If the density of the fluid is increased four times, the Reynolds number will increase four times as well, assuming that the velocity and viscosity remain constant. This would result in a four-fold increase in Nusselt number.

b) Plate length has to be decreased four times:

If the plate length is decreased four times, the characteristic length (L) of the system will decrease four times as well. This would result in a four-fold decrease in Nusselt number.

c) Specific heat has to be increased four times:

If the specific heat of the fluid is increased four times, the Prandtl number will increase four times as well, assuming that the viscosity and thermal conductivity remain constant. This would result in a four-fold increase in Nusselt number.

d) Dynamic viscosity has to be decreased sixteen times:

If the dynamic viscosity of the fluid is decreased sixteen times, the Reynolds number will increase sixteen times as well, assuming that the velocity and density remain constant. This would result in a sixteen-fold increase in Nusselt number, which contradicts the prescribed relation for Nusselt number in laminar flow over a flat plate. Therefore, option d is the false statement.

In summary, for laminar flow over a flat plate, the average value of Nusselt number is prescribed by the relation Nu = 0.664 (Re)0.5(Pr)0.33. The false statement is that the dynamic viscosity has to be decreased sixteen times.