Asian Research Journal of Mathematics

Aims: To investigate how temperature-dependent (Arrhenius) viscosity affects buoyancy-driven natural convection and heat transfer of diesel fuel in cylindrical storage geometries, and how this, in turn, shapes derived quantities such as the Reynolds number and pumping power. The work addresses the limitations of classical constant-viscosity models, which may misestimate flow resistance, wall shear stress, heat-transfer rate, and pumping power when the stored fuel is thermally non-uniform.

Study Design: Theoretical and numerical (computational) study.

Methodology: An Arrhenius viscosity law is embedded in the complete natural-convection governing equations: continuity; momentum with Boussinesq buoyancy and the temperature-dependent viscosity retained inside the diffusion term; and energy with thermal conduction and viscous dissipation. A similarity transformation reduces the coupled nonlinear partial differential equations to two ordinary differential equations for the dimensionless stream function f(η) and temperature θ(η), governed by the Grashof number Gr, Prandtl number Pr, viscosity parameter λ, and Eckert number Ec. The reduced system is solved by a fourth-order Runge-Kutta scheme with a secant-based shooting technique to a tolerance of 10⁻⁶. The Reynolds number is treated as a derived diagnostic rather than a primary governing variable. The model is not validated against experimental measurements; the findings should be read within the stated assumptions.

Results: Over 5-35°C, the diesel viscosity falls from about 3.5 to 0.95 mPa·s (a factor of roughly 3.7). A reference Reynolds number rises by the same factor (from about 1000 to about 3700), crossing the laminar-transitional value (Re ≈ 2300) near 25°C. The natural-convection velocity profile rises from zero at the wall to an internal peak and decays to the quiescent far field; warmer fuel (higher effective Grashof number and lower viscosity) produces a thinner, faster boundary layer. Higher Prandtl numbers and viscosity parameters thin the thermal boundary layer and raise the wall temperature gradient −θ′(0), which is proportional to the local Nusselt number. The pumping power falls to about 27% of its 5°C value at 35°C.

Conclusion: Incorporating temperature-dependent viscosity materially changes the predicted natural-convection flow and heat transfer relative to constant-viscosity models. The findings are model-based and require experimental validation before strong engineering recommendations can be made.