Analytical solution of MHD bioconvection Williamson nanofluid flow over an exponentially stretching sheet with the impact of viscous dissipation and gyrotactic microorganism

• Siva Sankari,

  Roles Writing – original draft

  Affiliation Department of Mathematics, Saveetha School of Engineering, SIMATS, Chennai, Tamil Nadu, India

  ⨯
• M. Eswara Rao ,

  Roles Investigation

  * E-mail: mannerieswar99@gmail.com (MER); wariskhan758@yahoo.com (WH)

  Affiliation Department of Mathematics, Saveetha School of Engineering, SIMATS, Chennai, Tamil Nadu, India

  ⨯
• Awatif M.A. Elsiddieg,

  Roles Data curation, Formal analysis, Writing – review & editing

  Affiliation Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, P.O. Box 710, Al-Kharj 11942, Saudi Arabia

  ⨯
• Waris Khan ,

  Roles Software

  * E-mail: mannerieswar99@gmail.com (MER); wariskhan758@yahoo.com (WH)

  Affiliation Department of Mathematics and Statistics, Hazara University, Mansehra 21120, Khyber Pakhtunkhwa, Pakistan

  https://orcid.org/0000-0002-4286-5403

  ⨯
• O. D. Makinde,

  Roles Methodology, Supervision

  Affiliation Faculty of Military Science, Stellenbosch University, Saldanha, South Africa

  https://orcid.org/0000-0002-3991-4948

  ⨯
• Taoufik Saidani,

  Roles Conceptualization, Data curation, Resources

  Affiliation Center for Scientific Research and Entrepreneurship, Northern Border University, Arar, Saudi Arabia

  ⨯
• Naoufel Kraiem,

  Roles Data curation, Funding acquisition, Project administration, Resources

  Affiliation College of Computer Science, King Khalid University, Abha, Saudi Arabia

  ⨯
• Hakim AL Garalleh

  Roles Formal analysis, Resources, Validation, Visualization, Writing – review & editing

  Affiliation Department of Mathematical Science, College of Engineering, University of Business and Technology, Jeddah 21361, Saudi Arabia

  https://orcid.org/0000-0003-3917-2339

  ⨯