in solving mathematical problems we consider momentum equation energy equation as well as concentration equation to model our physical problem but why homo-hetro? what they describe physically? and how it help us?
The homogeneous reactions happen in the whole fluid bulk, e.g. a stirred tank with two feeds with the reagents A and B. The chemical reaction will happen in the fluid as the two streams are mixed. This happens in the whole reactor, there is no special place where we have the chemical reactions, it is homogeneous.
Consider now a tube covered by a catalytic surface. As the fluid flows in the tube chemical reactions take place on the tube wall - the catalytic surface, and only there. The bulk only transports the reagents and products. And the chemical reaction is part of the boundary contour. As the reaction does not happen in the entire domain, this reaction is called as heterogeneous.
This is the distinction among them. I hope help to understand, Bests!
To answer your question it is worthwhile first to draw the distinction between what we mean by homogeneous versus heterogeneous reactions. Consider first a homogeneous reaction,. This type of chemical reaction occurs in a single phase.The two most familiar homogeneous reactions are those that occur in a liquid phase or a gas phase. The reactants, products and any catalyst used form one continuous phase;. In contrast, the reactants in a heterogeneous reaction are components of two or more phases (solid and gas, solid and liquid, or two immiscible liquids). Recall a catalyst is a substance that, without itself undergoing any permanent chemical change, increases the rate of a reaction.
Now the overriding problem in reactor design is to promote mass transfer between the phases. Thus to design and size a reactor requires detailed knowledge of the mass transfer environment of the reactor, which in turns requires knowledge of the fluid mechanics and the heat transfer environment. For example in a continuous stirred reactor (CSTR) the overriding assumption is that the reactor is well mixed so that the temperature and concentration of the relevant species are both only a function of time. The fluid mechanics is reduced to knowledge of the residence time of the reactor ( reactor volume/volumetric flow rate). In a plug flow reactor, the fluid velocity at any cross-section is assumed to be a constant. So once again the fluid mechanics is trivial. In microfluidic reactors this is not the case and so the fluid momentum equations and the thermal energy equation must be solved in conjunction with the species balances with appropriate kinetic expressions for the reactions, whether they are homogeneous reactions or heterogeneous reactions.