 ## Heat Transfer

#### I am running a closed system multiphase buoyancy problem in Fluent where the density of the liquid phase is described by the Boussinesq model. Is it possible to define a thermal expansion coefficient that varies with temperature? This property seems to only allow constant values. This is the case even when a UDF definition is available

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The Boussinesq model is the only variable density model that treats density as a constant in the equations. (The second term in the equation below is implemented as a momentum source term.) rho(T) = rho(To) + [d(rho)/d(T)]@To * (T – To) The assumption is that rho(T) can be expressed as above at a given reference temperature, To (entered in operating conditions). The corresponding density is rho(To) (entered in materials) and the corresponding thermal expansion coefficient is beta(To). The derivative in the second term, [d(rho)/d(T)]@To is related to the thermal expansion coefficient by -1*beta(To)*rho(To). The Boussinesq approximation for density is is part of a Taylor series expansion, and would theoretically stop making sense if the derivative were taken at arbitrary T instead of prescribed To. To is generally set at the midpoint of the temperature range for the problem. Unless the temperature range is very large, using a single-valued beta at the evaluated at the midpoint is normally quite accurate. Since the second term, -1*beta(To)*rho(To)* (T – To) is treated as a momentum source term in the Boussinesq model, it would be possible to isolate this and implement your own using a DEFINE_SOURCE UDF. To to this: 1. Set the material density to constant rho(To) 2. Deactivate gravity so that the effect of the source term on the fluid phase is not duplicated 3. Define a source term equal to -g*beta(T)*rho(To)* (T – To) using DEFINE_SOURCE. NOTE: If the other phase has a slip velocity defined, this will have to be modified with DEFINE_VECTOR_EXCHANGE_PROPERTY UDF to account for the missing effect of gravity. 