On prescribed thermal distributions of bioconvection Williamson nanofluid transportion due to an extending sheet with non-Fourier flux and radiation

Bio-convection, Cattaneo-Christov, and thermal radiation fluxes are accompanied by mixed convection flow of Williamson nano-fluids. The dynamics of the fluid occur due to an extendable surface with two thermal boundary constraints; the prescribed heat flux and surface temperature. The objective of this exploration pertains to effective and efficient thermal distributions. Theoretical layout is formulated in the form of a partial differential format. In order to attain the numerical resolution of this non-linear formulation, similarity transforms are employed to modify them into ordinary differential forms. The computational code for the Runga-Kutta procedure is developed in a MATLAB script. The temperature of fluids enhances with mounting strength of prescribed heat flux, thermophoresis, thermal radiation, magnetic field, Brownian motion and heat source but it descends against thermal relaxation time. The speed of fluids undergoes retardation against exceeding inputs of Williamson parameter lambda, parameters of porosity, and magnetic body force. The range of distinct parameters while computing graphically is taken as 0.0 <= M <= 1.5, 0.0 <= kp <= 1.5, 0.1 <= omega <= 0.7, 0.0 <= Nr <= 1.5, 1.0 <= Rb <= 4.0, 0.01 <= Nt <= 0.3, 0.2 <= Nb <= 0.5, 0.1 <= Rd <= 1.0, 2.0 <= Pr <= 5.0, 0.1 <= b <= 1.5, 0.0 <= Q <= 0.3, 0.1 <= E <= 1.5, 2.0 <= Sc <= 5.0, 0.05 <= Omega <= 0.2, 0.1 <= Lb <= 0.4 and 0.1 <= Pe <= 0.4.