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

Natural convection is the heat transfer process that occurs due to the movement of fluid caused by buoyancy forces generated by temperature differences within the fluid. In forced convection, heat transfer takes place due to the forced movement of a fluid, which is usually caused by an external force like a pump, fan, or a moving object.

To determine whether natural convection can be neglected or not, we need to compare the relative importance of natural and forced convection. We can do this using two dimensionless numbers: the Grashof number (Gr) and the Reynolds number (Re). The Grashof number is a measure of the importance of buoyancy forces due to natural convection relative to viscous forces, and it is given by: Gr = (g * beta * (T_s - T_inf) * L^3) / (nu^2) Where g is the acceleration due to gravity, beta is the thermal expansion coefficient, T_s is the surface temperature, T_inf is the ambient temperature, L is a characteristic length, and nu is the kinematic viscosity of the fluid. The Reynolds number is a measure of the ratio of inertial forces to viscous forces and is mainly used to determine the flow regime (laminar or turbulent) in forced convection. It is given by: Re = (rho * U * L) / mu Where rho is the fluid density, U is the velocity of the fluid, and mu is the dynamic viscosity of the fluid.

To compare the importance of natural and forced convection in a situation, we can use the ratio of the Grashof number to the Reynolds number squared (Gr/Re^2), which is also known as the Richardson number. If this ratio is much less than 1, the forced convection is dominant, and natural convection can be neglected. If the ratio is greater than 1, natural convection is more significant, and both natural and forced convection need to be considered in the analysis.

Natural convection is negligible in forced convection heat transfer if the Grashof number is much smaller than the Reynolds number squared (Gr/Re^2 << 1). Under these conditions, forced convection is the dominant mode of heat transfer, and the effect of natural convection can be disregarded in the analysis.

Natural convection is not negligible in forced convection heat transfer if the Grashof number is comparable to or greater than the Reynolds number squared (Gr/Re^2 ≥ 1). In this situation, both natural and forced convection are significant in the heat transfer process, and both factors must be considered in the analysis. In conclusion, the importance of natural convection relative to forced convection in a heat transfer situation can be assessed using the ratio of the Grashof number to the Reynolds number squared (Gr/Re^2). If this ratio is much smaller than 1, natural convection can be neglected. If it is greater than or equal to 1, both natural and forced convection need to be considered.