Graetz problem for the casson fluid model with prescribed heat flux in a circular duct

This article aims to discuss the Graetz problem for the Casson fluid model under the influence of prescribed heat flux in a circular duct. For this purpose, we employed the separation of variables and the principle of superposition methods to obtain the solution to the problem. The resulting boundary value problem is numerically tackled with MATLAB function bvp4c. The impact of the Brinkman number is also taken into account. Results are presented graphically to show how the prescribed heat flux affects fully developed temperature, average temperature, wall temperature, and the local Nusselt number in the presence of the Casson parameter and viscous dissipation. The analysis reveals that the local Nusselt number is higher for the negative Brinkman number and lower for the positive Brinkman number as compared to the no dissipation function. Moreover, the Casson parameter enhances the local Nusselt number. The findings of this investigation may be beneficial in the improvement of several types of thermal apparatus.