General Equation for the Heat Flux

Substituting Equation 4.154 into Equation 4.294 and rearranging the terms yields 

Equation 4.297 is the exact expression for the HC heat flux from the CL. As discussed above, this expression is simplified to Equation 4.296 since in the HC regime, the parameter jolcL/((fpb) is large, therefore, the exponent in Equation 4.297 can be neglected. 

Equation 4.297 suggests the general expression for the heat flux from the CL, which is valid in the whole range of cell currents  

Equation 4.298 differs from Equation 4.297 by the factor 3 in the power of exponent. 

In the LC regime, the exponent in Equation 4.298 can be expanded in a series. Retaining the linear term, gives the LC equation (4.288). In the HC limit, the exponent in Equation 4.298 can be neglected, which leads to Equation 4.296. Thus, in the LC and HC limits. Equation 4.298 reduces to the respective exact expression and hence this equation interpolates between the limiting solutions. 

---