Heat transfer enhancement due to properly managing the distribution of the heat flux: Exact solutions

This work seeks for the maximum possible heat transfer enhancement in laminar channel flow due to properly distributing the heat flux over the boundaries. The considered heat flux distributions are (A) Periodic step, (B) Periodic sinusoidal (C) Linear, and the (D) Exponential distribution. All of these distributions have the same average heat flux value. Appropriate dimensionless governing energy equations are solved using various complex analysis methods. Different energy performance factors computed to completely characterize the problem. Comparisons with numerical solutions are performed and excellent agreement is obtained. Various correlations are identified. A parametric study of all involved parameters is presented graphically. It is found that the maximum heating source excess temperature for case (D) is at most 22.4% lower than that with uniform heat flux distribution. The previous percentage changes to 18% and 10.7% for the cases (C) and (B), respectively. These results are capable of increasing heat flux by 21.35%, 15.98% and 10.22%, respectively, to attain the same maximum temperature of the uniform heat flux distribution. Finally, this work proves that properly managing the heat flux distribution can transfer additional noticeable heat under same maximum temperatures.