Irreversibility analysis in Darcy-Forchheimer flow of CNTs with dissipation and Joule heating effects by a curved stretc
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ORIGINAL ARTICLE
Irreversibility analysis in Darcy‑Forchheimer flow of CNTs with dissipation and Joule heating effects by a curved stretching sheet T. Hayat1 · Sohail A. Khan1 · A. Alsaedi2 · Q. M. Zaigham Zia3 Received: 30 July 2020 / Accepted: 24 September 2020 © King Abdulaziz City for Science and Technology 2020
Abstract Here, heat transfer analysis in convection magnetohydrodynamic flow of carbon nanotube-based Darcy–Forchheimer flow by a curved stretched surface is addressed. Carbon nanotubes (Single and multiple walls) are assumed to be nanoparticles and blood as a base fluid. The mathematical modeling for the nanoparticles transportation is accomplished through Xue model. Thermal radiation, dissipation and Joule heating are addressed in heat equation. Physical features of irreversibility in the isolated thermal system are deliberated. Entropy generation instigated as a result of irreversibility due to heat transfer, porosity irreversibility, irreversibility due to Joule heating and dissipation irreversibility by a curved stretched sheet. Mathematical formulation of entropy generation is developing by a second law of thermodynamics. The principal equation is developed in a curvilinear coordinate system. The nonlinear system is altered to ordinary differential system through compatible transformation. The proposed system is numerically solved by ND-solve technique. Variations of Bejan number, entropy rate, temperature and velocity against several interesting parameters for both carbon nanotubes are scrutinized. Nusselt number and gradient of velocity are examined for both carbon nanotubes in tabulated form. For higher magnetic variable, velocity is augmented for both CNTs. Velocity field reduces against higher porosity parameter for both carbon nanotubes. Temperature distribution rises against porosity and radiation variables. Entropy rate is boosted versus radiation and magnetic parameters for both SWCNTs and MWCNTs. Bejan number and entropy have reverse trend for solid volume fraction for both nanotubes. Higher Brinkman number raises the entropy rate for both SWCNTs and MWCNTs. Larger estimation of porosity variable reduces the Bejan number, while opposite effect is noticed for radiation parameter. Larger magnetic variable boosts up velocity gradients for both carbon nanotubes. But the drag force of SWCNTs is less than MWCNTs. Heat transfer rate is enhanced against curvature variable. Clearly we observed that amplification of heat transference processes is higher for SWCNTs than MWCNTs. Comparative studies are also present and found an excellent agreement. Keywords Curved stretching surface · Darcy–Forchheimer medium · Cnts/blood · Joule heating · Bejan number · Entropy generation · Mixed convection · Viscous dissipation and thermal radiation
Introduction
* Sohail A. Khan [email protected] 1
Department of Mathematics, Quaid-I-Azam University, 45320, Islamabad 44000, Pakistan
2
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz Unive
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