Quick Algebraic Estimate of the Thickness of Insulation for the Design of Process Pipelines with Allowable Heat Losses to Ambient Air

Adequate control of the total heat losses from in-tube fluid streams to neighboring ambient air is an important problem in heat transfer engineering. In this regard, the primary goal of this article is to demonstrate that an iterative solution of a nonlinear algebraic equation might allow thermal design engineers to estimate quickly the thickness of insulation of round tubes. The calculation methodology begins with the adoption of a powerful 1-D extended lumped energy model in favor of the customary 2-D differential energy model. The principal advantage of the former model is its ability to produce concise analytic expressions for the axial variation of the mean bulk temperature and also for the total heat transfer in the entire length of the tube. Particular attention was given to realistic situations in industry that account for laminar or turbulent velocities of single-phase viscous fluid flows in horizontal tubes rejecting heat by natural or forced cross flow of the ambient air. The total heat transfer to the air is the constraint design parameter in the set of design parameters. Once the magnitude of the total heat transfer was prespecified, the thickness of insulation of the round tube was easily computed numerically, exploiting the fixed-point iteration procedure for the solution of an adjoint nonlinear algebraic equation. Starting with a judicious guess of a root of the nonlinear algebraic equation, the correct root was surprisingly obtained in two or three iterations, thus furnishing immediately the required size of the thickness of the insulation annulus.