Calculate the Nusselt number and see how large it is. Depending on the geometry of the situation this will guide you as to whether conductive or convective transport is happening.
Failing that, test it empirically!
(much more entertaining, and less likely to be wrong)
It all depends on the state of the crude. Is it stagnant or moving and if moving at what speed to see if it is laminar or turbulent flow. Then after defining the state a possible logical answer could be envisaged.
In general, heat is transferred through conduction process in a reservoir. However, if viscosity is high, after a certain time interval heat will decrease the viscosity of the fluid and hence the permeability will increase. This will in turn affect the pressure drop calculations. Hence constant heat flow should not be taken into consideration if the fluid is viscous enough. The initial and boundary conditions has to be changed.
Please indicate the state of the crude. Is it kept in a tank or flowing in a pipe.If the crude is stagnant and highly viscous then the mode is conduction heat transfer. If it is flowing then the mode is convective and we need to know at what speed. Then calculate the Reynauld number to determine whether the flow is turbulent or laminer..