MATHEMATICAL MODELING OF HEAT EXCHANGE IN DIRECT FLAT CHANNELS AND DIRECT ROUND PIPES WITH ROUGH WALLS UNDER THE SYMMETRIC HEAT SUPPLY

Abstract

Objectives. The aim of present work was to carry out mathematical modelling of heat transfer with symmetrical heating in flat channels and round pipes with rough walls.Methods. The calculation was carried out using the L'Hôpital-Bernoulli's method. The solution of the problem of intensified heat transfer in a round tube with rough walls was obtained using the Lyon's integral.Results. Different from existing theories, a methodology of theoretical computational heat transfer determination for flat rough channels and round pipes with rough walls is developed on the basis of the principle of full viscosity superposition in a turbulent boundary layer. The analysis of the calculated heat transfer and hydroresistivity values for flat rough channels and round rough pipes shows that the increase in heat transfer is always less than the corresponding increase in hydraulic resistance, which is a disadvantage as compared to channels with turbulators, with all else being equal. The results of calculating the heat transfer for channels with rough walls in an extended range of determinant parameters, which differ significantly from the corresponding data for the channels with turbulators, determine the level of heat exchange intensification.Conclusion. An increase in the calculated values of the relative average heat transfer Nu/NuGL for flat rough channels and rough pipes with very high values of the relative roughness is significantly contributed by both an increase in the relative roughness height and an increase in the Reynolds number Re. In comparison with empirical dependencies, the main advantage of solutions for averaged heat transfer in rough flat channels and round pipes under symmetrical thermal load obtained according to the developed theory is that they allow the calculation of heat exchange in rough pipes to be made in the case of large and very large relative heights of roughness protrusions, including large Reynolds numbers, typical for pipes of small diameters and narrow flat channels. An increase in the relative heat exchange in air due to an increase in the relative height of the roughness or the Reynolds number is accompanied by an even more significant increase in the hydraulic resistance. Calculated data on averaged heat transfer obtained in the work showed that in the range of determinant parameters for flat rough channels with symmetrical thermal loading, the average heat transfer is higher by (4.811.7)% as compared to round rough pipes – all other things being equal.

Keywords

• multilayer model
• flat channel
• round pipe
• roughness
• turbulence
• modelling
• heat exchange
• turbulent
• intensification
• heating
• heat supply
• symmetric