Heat transfer improvement due to the imposition of non-uniform wall heating for in-tube laminar forced convection

• Considered the bearing of non-uniform distribution of heat flux on the hot spots.
• Determined the optimal distribution of heat flux that minimizes the hot spots.
• Results are compared with those obtained by EGM method.

This paper explores the bearing that a non-uniform distribution of heat flux used as a wall boundary condition exerts on the heat transfer improvement in a round pipe. Because the overall heat load is considered fixed, the heat transfer improvement is viewed through a reduction in the maximum temperature (‘hot spot’) by imposing optimal distribution of heat flux. Two cases are studied in detail 1) fully developed and 2) developing flow. Peak temperatures in the heated pipe wall are calculated via an analytical approach for the fully developed case, while a numerical simulation based on CFD is employed for the developing case. By relaxing the heat flux distribution on the pipe wall, the numerical results imply that the optimum distribution of heat flux, which minimizes the peak temperatures corresponds with the ‘descending’ distribution. Given that the foregoing approach is quite different from the ‘ascending’ heat flux distribution recommended in the literature by means of the entropy generation minimization (EGM) method, it is inferred that the optimization of heat transfer and fluid flow, in comparison with the thermodynamic optimization, may bring forth quite different guidelines for the designs of thermal systems under the same constraints and circumstances.