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Let us consider a non-isothermal flow where an inlet temperature Ti is imposed, while a temperature Tw is imposed on an adjacent wall. A conflict may exist at the intersection point between the inlet and the wall. How to handle this?
The temperature condition should be selected for the inlet, where the value Ti is assigned. For the wall, the temperature condition can be replaced by a convective heat flux alpha.[T-Talpha], where Tlapha is the outside world temperature, while alpha is the heat transfer coefficient. For the present purpose, Talpha should receive the assigned value Tw, while the coefficient alpha should receive a sufficiently large value, that would lead to a quick temperature jump from Ti to Tw. A value of 10000 W/m2/°C or more could be considered [good to remember that the heat exchange coefficient in boiling oil is of about 1000 W/m2/°C].
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