Heat Transfer
Steady state one dimensional heat flow by conduction as given by Fourier's low does not assume that

There is no internal heat generation
Material is anisotropic
Constant temperature gradient exists
Boundary surfaces are isothermal

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Heat Transfer
Vacuum is generally maintained in the vapour space of an evaporator mainly to

Facilitate forward feeding in multiple effect evaporation
Concentrate heat sensitive materials
Achieve very high concentration of the final product
Get economical temperature difference by using moderate pressure steam

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