A note on the temperature distribution in a channel bounded by two co-axial cylinders

Abstract

If we neglect the viscous dissipation, the temperature distribution in an incompressible fluid flowing in the annulus between two coaxial cylinders with radii r₁ and r₂ (> r₁) is determined by the equation ∂T/∂t = 1/ρc_v × ∂Q/∂t + k'(∂²T/∂r² + 1/r × ∂T/∂r), k' = k/ρc_v. Initial conditions Q(0) = Q_o, T(r, 0)=0. Boundary conditions T(r₁, t) = T₁(t), T(r₂, t) = T₂(t), where ∂Q/∂t is a function of time alone representing the rate of heat generation per unit volume per unit time in the fluid.