Onset modules of heat source and generalized Fourier’s law on Carreau fluid flow over an inclined nonlinear stretching sheet

ABSTRACT

The motivation for this comparative examination is to verify and account for the appropriate source of heat energy needed in production industries, and to expunge the contradictions between Fourier’s law and the theory of relativity. In heat management such as in engineering systems, the required heat for effective melting, production rate, etc. dictates the appropriate heat generation/injection module to be deployed. However, the material medium of heat transmission can be a hindering factor for a successful convection process, to this, an investigation of the instantaneous heat propagation paradox is required. An assumption of induced flow due to stretching characteristics is made, and an appropriate similarity transformation is deployed for the governing systems. By means of the Galerkin-weighted residual method, numerical solutions to the system of equations are approximated and validated. In a limited case, the solution compares favourably with existing literature, while the novel comparative investigation predicts the dominance of the Temperature-Dependent Heat Source (TDHS) capable of weakening the fluid cohesive force and upsurging the energy rate in short time in contrast to the Space-Dependent Heat Source (SDHS) module. The material relaxation phenomenon indicated that more time will be needed for prosperous/equal heat energy transfer. Further heat transfer enhancement is called for higher discharge of radiation and boosting of thermal conductivity, while TDHS module is strongly recommended in highly required heat systems.

KEYWORDS:

• Carreau fluid
• temperature jump
• Cattaneo-Christov
• heat source/sink
• nonlinear convection
• nonlinear stretching sheet

Nomenclature

Table

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Mojeed T. Akolade

Mojeed T. Akolade obtained his first degree in Pure and Applied Mathematics from Ahmadu Bello University Zaria, Nigeria, and a Master of Science in Applied Mathematics from the University of Ilorin, Ilorin, Nigeria. He is currently a Ph.D. student at the same University, his research interest includes, fluid mechanics, thermodynamics analysis, squeezing flow, non-Newtonian fluid flow, sensitivity, numerical, and statistical analysis of fluid flow problems. He has published more than 10 international articles through various reputable journals as author/co-author.

Samson A. Agunbiade

Dr. Samson A. Agunbiade is currently working as Lecturer II in the department of basic sciences, Babcock university Ilishan-Rome, Ogun state, Nigeria. He obtained his Ph.D. in fluid mechanics from the University of Ilorin, Ilorin, Nigeria in 2019. His research interests are directed towards heat and mass transfer, Newtonian and non-Newtonian boundary layer flows.

Timothy L. Oyekunle

Dr. Timothy L. Oyekunle was born and bred in Kwara State, Nigeria. He schooled in Nigeria up to the University level and presently works as a lecturer at the University of Ilorin, Ilorin, Nigeria.