Effect of Internal Heat Generation on Bioconvective Instability in a Nanofluid with Thermotactic Microorganisms

Thermotactic microorganisms play a vital role in bioremediation, biodegradation, and the food and agriculture industries. Their thermostable and thermoactive enzymes make them particularly suitable for moderate-temperature bioprocesses, thereby enhancing efficiency and overall performance. Building on these characteristics and practical relevance, this work explores how linear and nonlinear internal heat sources influence the onset of bioconvection in a nanofluid layer populated with thermotactic microorganisms. A mathematical model is developed using Buongiorno’s model for nanofluid together with Pedley’s model for microorganisms. Using normal-mode analysis, the dimensional flow equations are converted into a system of non-dimensional ordinary differential equations. The eigenvalue problem obtained is numerically solved using the finite difference scheme with MATLAB’s bvp4c solver, under the constraints of zero nanoparticle flux and rigid–rigid boundaries. The influence of key flow parameters on the onset of bioconvection is analyzed and presented in graphically and tabular form. A key novel insight of this study is that, under top heating in a nanofluid containing thermotactic microorganisms, linear internal heat generation destabilizes the system by driving microorganisms upward toward the hotter boundary, whereas nonlinear internal heat generation exerts a stabilizing influence by suppressing their accumulation near the heated wall. This contrasting behavior, not explicitly reported in earlier works, provides a new comparative perspective on the stability of bioconvective nanofluids. It is further observed that, in both cases, an increase in the Péclet number consistently promotes destabilization.