Heat transfer in gas-solid reactions

When a gas reacts with a solid, heat will be transferred from the solid to the gas when the reaction is exothermic, and from gas to solid during an endothermic reaction. The energy which is generated will be distributed between the gas and solid phases according to the temperature difference between the two phases, and their respective thermal conductivities. If the surface temperature of the solid is 7 at any given instant, and that of the bulk of the gas phase is Ti, the rate of convective heat transfer from the solid to the gas may be represented by the equation 

The value of the heat transfer coefficient of the gas is dependent on the rate of flow of the gas, and on whether the gas is in streamline or turbulent flow. This factor depends on the flow rate of the gas and on physical properties of the gas, namely the density and viscosity. In the application of models of chemical reactors in which gas-solid reactions are carried out, it is useful to define a dimensionless number criterion which can be used to determine the state of flow of the gas no matter what the physical dimensions of the reactor and its solid content. Such a criterion which is used is the Reynolds number of the gas. For example, the characteristic length in the definition of this number when a gas is flowing along a tube is the diameter of the tube. The value of the Reynolds number when the gas is in streamline, or linear flow, is less than about 2000, and above this number the gas is in turbulent flow. For the flow 

There are three dimensionless numbers used in these equations, and their definitions are  

The relation given above for streamline flow can therefore be expressed as 

In the definition of the Prandtl number, Cp is the heat capacity of the gas at constant pressure. 

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