# Internal forced convection

Internal heat and mass transfer have significant applications in a variety of technologies, including heat exchangers and electronic cooling. Internal convective heat and mass transfer can be classified as either forced or natural convection. An initial simple approach to internal convective heat transfer is to utilize the dimensional analysis presented in Chapter 1 to obtain important parameters and dimensionless numbers for the steady laminar flow of an incompressible fluid in a convectional tube, i.e.,

 h = f(k,μ,cp,ρ,u,D,x,ΔT) (1)

The local heat transfer coefficient is a function of the fluid properties (viscosity, μ; thermal conductivity, k; density, ρ; specific heat, cp), geometry (D), temperature (ΔT), and flow velocity (u). In dimensionless form, as shown in Chapter 1,

 $\text{Nu}=g(\operatorname{Re},\Pr ,x/D)$ (2)

The above relation indicates that the local Nusselt number for flow in a circular tube is a function of the Reynolds number, Prandtl number, and x/D. The goal of this chapter is to develop the heat and mass transfer coefficients for various internal flow configurations under different operating conditions. The objective of this chapter is to present fundamental models, and analytical and numerical solutions of both laminar and turbulent internal forced convections. Section 5.2 introduces the basic definitions, terminologies, and governing equations for internal flow; followed by discussions on uncoupled fully developed laminar flow and the thermal entry effects in Section 5.3 and 5.4. The fully developed laminar flow with coupled thermal and concentration entry effects is taken up in Section 5.5. While the flow in Sections 5.3 – 5.5 is assumed to be fully developed, the combined hydrodynamic, thermal, and concentration entry effects are discussed in Section 5.6. The full numerical solution of internal forced convection problem based on full Navier-Stokes equations using the finite volume method is discussed in Section 5.7; this is followed by a discussion on forced convection in microchannels.