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

Bhatnagar, P. L. ; Tikekara, V. G. (1966) A note on the temperature distribution in a channel bounded by two co-axial cylinders Mathematical Proceedings of the Cambridge Philosophical Society, 62 (2). pp. 301-302. ISSN 0305-0041

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Related URL: http://dx.doi.org/10.1017/S0305004100039864

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/ρcv × ∂Q/∂t + k'(∂2T/∂r2 + 1/r × ∂T/∂r), k' = k/ρcv. Initial conditions Q(0) = Qo, 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.

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