# Modelling of transient heat transfer in annealing furnaces

• Tagelsir M. Abdelsalam

Student thesis: Doctoral ThesisDoctor of Philosophy

### Abstract

This is a study of heat transfer in a lift-off furnace which is employed in the batch annealing of a stack of coils of steel strip. The objective of the project is to investigate the various factors which govern the furnace design and the heat transfer resistances, so as to reduce the time of the annealing cycle, and hence minimize the operating costs.
The work involved mathematical modelling of patterns of gas flow and modes of heat transfer. These models are: Heat conduction and its conjectures in the steel coils;Convective heat transfer in the plates separating the coils in the stack and in other parts of the furnace; and Radiative and convective heat transfer in the furnace by using the long furnace model. An important part of the project is the
development of numerical methods and computations to solve the transient models.
A limited number of temperature measurements was available from experiments on a test coil in an industrial furnace. The mathematical model agreed well with these data. The model has been used to show the following characteristics of
annealing furnaces, and to suggest further developments which would lead to significant savings:
- The location of the limiting temperature in a coil is nearer to the hollow core than to the outer periphery.
- Thermal expansion of the steel tends to open the coils, reduces their thermal conductivity in the radial direction, and hence prolongs the annealing cycle. Increasing the tension in the coils and/or heating from the core would overcome this heat transfer resistance.
- The shape and dimensions of the convective channels in the plates have significant effect on heat convection in the stack. An optimal design of a channel is shown to be of a width-to-height ratio equal to 9.
- Increasing the cooling rate, by using a fluidized bed instead of the normal shell and tube exchanger, would shorten the cooling time by about 15%, but increase the temperature differential in the stack.
- For a specific charge weight, a stack of different-sized coils will have a shorter annealing cycle than one of equally-sized coils, provided that production constraints allow the stacking order to be optimal.
- Recycle of hot flue gases to the firing zone of the furnace would produce a. decrease in the thermal efficiency up to 30% but decreases the heating time by about 26%.
Date of Award Oct 1979 English D.A. Lihou (Supervisor)

• modelling
• conduction
• furnace
• radiation
• computation

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