Question

When is natural convection negligible and when is it not negligible in forced convection heat transfer?

Short answer

Answer: Natural convection is considered negligible in forced convection heat transfer when the Grashof number (Gr) is much smaller than the Reynolds number (Re), i.e., Gr << Re. In this case, forced convection dominates the heat transfer process. However, natural convection is not negligible when Gr is comparable to or larger than Re, indicating that both natural and forced convection play significant roles in the heat transfer process.

Step-by-step solution

Understand natural convection and forced convection

Natural convection occurs as a result of differences in fluid density caused by temperature gradients. The fluid expands and becomes less dense as it heats up, causing it to rise and be replaced by cooler, denser fluid. This process leads to a continuous circulation of fluid and heat transfer. Forced convection is driven by external means, such as a fan or a pump, which creates a flow of fluid and the consequent transfer of heat between the fluid and a solid surface. Both natural and forced convection contribute to the overall heat transfer rate, but their relative importance depends on various factors.

Introduce the Grashof number and its importance

The Grashof number (Gr) is a dimensionless number that characterizes the relative importance of natural convection to forced convection. It is defined as: Gr = (g * β * ΔT * L^3) / ν^2 where g = acceleration due to gravity (9.81 m/s^2) β = thermal expansion coefficient of the fluid ΔT = temperature difference between the fluid and the surface L = characteristic length (typically the height or diameter of an object) ν = kinematic viscosity of the fluid The Grashof number compares the buoyancy forces (natural convection) to the viscous forces (forced convection).

Define when natural convection is negligible and when it is not negligible

Natural convection is considered negligible in forced convection heat transfer when the Grashof number is much smaller than the Reynolds number (Re). The Reynolds number is another dimensionless number that characterizes the flow regime and is defined as: Re = (ρ * V * L) / μ where ρ = fluid density V = fluid velocity μ = dynamic viscosity of the fluid If Gr << Re, then the effect of natural convection is considered negligible compared to forced convection. In this case, the forced convection dominates the heat transfer process, and the influence of natural convection can be ignored. On the other hand, if Gr is of the same order of magnitude as Re or larger, it implies that natural convection plays a significant role in the heat transfer process and cannot be neglected. In this situation, both natural and forced convection should be taken into account in order to accurately predict the heat transfer rate. In summary, natural convection is negligible in forced convection heat transfer when Gr << Re, and it is not negligible when Gr is comparable to or larger than Re.