A study on nanoliquid flow with irregular heat source and realistic boundary conditions: A modified Buongiorno model for biomedical applications

Abstract

Titanium dioxide plays a vital role in cancer therapy methods (including photothermal therapy and photodynamic therapy), skincare products, heat exchangers, and car radiators. Therefore, the dynamics of the TiO 2 nanomaterial with H 2 O as basefluid over a nonlinearly stretched surface is investigated. For realistic nanoliquid modeling, the conventional Buongiorno model has been improvised (called modified Buongiorno model [MBM]) by incorporating the effective thermophysical properties of the nanoliquid. Experimentally derived correlations of the thermal conductivity and dynamic viscosity of the nanofluid are utilized. The significance of passive control of nanoparticles is also studied. The heat transfer analysis includes the mechanism of Rosseland heat flux and exponential heat source. Similarity theory is used to obtain nonlinear ordinary differential equations (ODEs) from the governing partial differential equations which are solved numerically using bvp5c, a finite difference-based routine in MATLAB. Further, the heat transfer rate is statistically scrutinized for the consequence of magnetic field (0.5 ≤ 𝑀 ≤ 1.5), thermal radiation (0.5 ≤ 𝑅 𝑑 ≤ 1.5) and exponential heat source (0.2 ≤ 𝑄 𝐸 ≤ 0.4) by employing Response Surface Methodology (RSM) and sensitivity analysis. The temperature of nanofluid ascends with the exponential heat source, thermal radiation, and thermophoresis aspects. Furthermore, when the MBM is utilised, the thermal field of the nanofluid is greater than when the classic Buongiorno model is used. The rate of heat transfer correlates positively with radiative heat flux. The exponential heat source exhibits a negative sensitivity towards the rate of heat transfer.Nomenclature: 𝑢, 𝑣, velocity components; 𝑇, temperature; 𝐶, nanoparticle volume fraction; 𝑢 𝑤 , stretching velocity; 𝑥, 𝑦, Cartesian coordinates; 𝑇 𝑤 , wall temperature; 𝑇 ∞ , ambient temperature; 𝐶 ∞ , ambient nanoparticle volume fraction; 𝐷 𝑇 , thermophoretic diffusion coefficient; 𝑞 𝑟 , radiative heat flux; 𝐷 𝐵 , Brownian diffusion coefficient; 𝑓 ′ (𝜁), dimensionless velocity profile; 𝑄 * 𝑒 , coefficient of exponential space-based heat source; 𝑘 * , mean absorption coefficient; 𝑁𝑡, thermophoresis parameter; 𝑁𝑏, Brownian motion parameter; 𝑀, magnetic field parameter; 𝑄 𝐸 , Exponential space-based heat source parameter; 𝑓, dimensionless stream function;

Transport phenomena in hydromagnetic convective Carreau nanoliquid flow over an elongating cylinder: A statistical approach

“…The highly non-linear ordinary differential equations (ODEs), Equations ( 6)-( 8), along with the boundary condition, Equation ( 9), are solved by BVP5C using the MATLAB software (see [42] for more details). To accomplish this, assume…”

“…The highly non‐linear ordinary differential equations (ODEs), Equations ()–(), along with the boundary condition, Equation (), are solved by BVP5C using the MATLAB software (see [42] for more details). To accomplish this, assume $$$$\begin{equation} \def\eqcellsep{&}\begin{array}{@{}*{5}{c}@{}} { \def\eqcellsep{&}\begin{array}{*{20}{c}} { \def\eqcellsep{&}\begin{array}{*{20}{c}} {f\ = {S}_1\ }&{\ f^{\prime} = {S}_2\ } \end{array} }&{\ f^{\prime\prime} = {S}_3\ }&{ \def\eqcellsep{&}\begin{array}{*{20}{c}} {\ f^{\prime\prime\prime} = S_3^{\prime}\ }&{\theta \ = {S}_4\ } \end{array} } \end{array} }\\[6pt] { \def\eqcellsep{&}\begin{array}{*{20}{c}} { \def\eqcellsep{&}\begin{array}{*{20}{c}} {\ \theta ^{\prime} = {S}_5\ }&{\ \theta ^{\prime\prime} = S_5^{\prime}\ } \end{array} }&{\phi \ = {S}_6\ }&{ \def\eqcellsep{&}\begin{array}{*{20}{c}} {\ \phi ^{\prime} = {S}_7\ }&{\ \phi ^{\prime\prime} = S_7^{\prime}} \end{array} } \end{array} } \end{array} \end{equation}$$$$…”

Mathematical modelling of heat and solutal rate with cross‐diffusion effect on the flow of nanofluid past a curved surface under the impact of thermal radiation and heat source: Sensitivity analysis

“…Arrekara et al. [23] looked at a simulation of nanoliquid flow with an erratic heat source and realistic boundary conditions, where the rate of heat transfer is maximised using RSM. Rana and Gupta [24] discovered Von Kármán's swirling flow of nanoliquid throughout a revolving disc with Stefan blowing and many slip effects using the nonlinear Boussinesq Approximation Sensitivity computation.…”

“…Puneet and Gupta et al [22] used Response Surface Technique to optimise the FEM approach to the nonlinear convective and radiative flow of hybrid nanofluid across a revolving cone with Hall current. Arrekara et al [23] looked at a simulation of nanoliquid flow with an erratic heat source and realistic boundary conditions, where the rate of heat transfer is maximised using RSM. Rana and Gupta [24] discovered Von Kármán's swirling flow of nanoliquid throughout a revolving disc with Stefan blowing and many slip effects using the nonlinear Boussinesq Approximation Sensitivity computation.…”

Quadratic regression estimation of hybridized nanoliquid flow using Galerkin finite element technique considering shape of nano solid particles

“…Akram et al (Akram et al, 2022) analyzed the electroosmotic movement of silver-water HNF controlled by using two altered methods for NF including the MBNM. Areekara et al (Areekara et al, 2022) suggested a study on NF movement with asymmetrical heat foundation and representative boundary conditions with the application by MBNM.…”