Abstract
The present study provides the heat transfer analysis of a viscous fluid in the presence of bioconvection with a Caputo fractional derivative. The unsteady governing equations are solved by Laplace after using a dimensional analysis approach subject to the given constraints on the boundary. The impact of physical parameters can be seen through a graphical illustration. It is observed that the maximum decline in bioconvection and velocity can be attained for smaller values of the fractional parameter. The fractional approach can be very helpful in controlling the boundary layers of the fluid properties for different values of time. Additionally, it is observed that the model obtained with generalized constitutive laws predicts better memory than the model obtained with artificial replacement. Further, these results are compared with the existing literature to verify the validity of the present results.
Highlights
A variety of researchers dedicate their resources to revealing bioconvection characteristics, like Khan et al [2], who conducted their research on the dynamics of the Cattaneo–Christov theory of heat and mass flow with bioconvection Oldroyd-B nanofluid
The unsteady bioconvection effect is studied in this investigation with a fractional derivative for a vertical surface
The Caputo fractional explains the memory of the function and further shows dual behavior for long and short times due to the power law kernel that appears in its definition
Summary
Academic Editors: Miklós Rontó, András Rontó, Nino Partsvania, Bedřich Půža and Hriczó Krisztián. Note that the conventional PDEs cannot decipher the dynamical behavior of physical flow parameters and retention effects To remove these defects, researchers focused on the fractional dynamic systems of heat transfer in simple and complex fluid models. Many researchers have worked on the application of fractional calculus but they have not considered the unsteady effect of bioconvection in those heat transfer models. Vieru et al [46] applied a Caputo fractional derivative to heat and mass transfer flow over a flat plate They used the Laplace transform method to find exact solutions. Shah et al [25] studied analytical solutions for time-fractional boundary layer flow of viscous fluid over a vertical heat transfer surface including Caputo and Caputo–Fabrizio derivatives. A graphical discussion of flow parameters is presented through graphics
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