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Thermal and rheological effects in a classical Graetz problem using a nonlinear Robertson‐Stiff fluid model
Author(s) -
Khan Muhammad Waris Saeed,
Ali Nasir,
Asghar Zeeshan
Publication year - 2021
Publication title -
heat transfer
Language(s) - English
Resource type - Journals
eISSN - 2688-4542
pISSN - 2688-4534
DOI - 10.1002/htj.21980
Subject(s) - nusselt number , mechanics , heat transfer , radius , mathematics , thermodynamics , physics , reynolds number , computer science , turbulence , computer security
The present article elaborates the Graetz problem for the Robertson‐Stiff fluid model with imposed iso‐thermal conditions. The closed‐form expression of Robertson‐Stiff fluid velocity is obtained. Employing the classical separation of variables approach, the energy equation of the said problem is reduced into an eigenvalue problem. The solution of the eigenvalue problem is developed numerically via the MATLAB built‐in algorithm BVP4C. The constants appearing in series solutions are computed by Simpson's rule. The special case of this analysis with appropriate scaling is also applicable for the Bingham, power‐law, and Newtonian fluid models. The impact of the dissipation function on Nusselt numbers and mean temperature is also considered. The pictorial representation of average temp7erature and Nusselt number are discussed in the presence of the plug radius, power‐law index, and Brinkman number. It is observed that the presence of the plug radius and power‐law index delay the prevalence of fully developed conditions for the Nusselt number. Moreover, the local Nusselt number for channel confinement attains higher values as compared with tube confinement. The present investigation has numerous applications in the field of engineering, nanotechnology, biomedical sciences, and development of several thermal types of equipment or microfluidic devices.