Numerical heat and solutal transfer simulation of fluid flowing via absorptive shrinkable sheet with Ohmic heat resistance

Abstract

This work mainly deals with the effect of heat, mass transmission, and heat generating (sinking) on the time-independent two-dimensional boundary-layer flowing of radiative MHD over a sheet, which is dwindling including Joule heating. The governing formulas have been converted into nonlinear ordinary differential equations (NLODE). The final step aims to obtain the graphical numerical illustrations from the set of NLODE; this method is namely as shooting using MATLAB. The accuracy of the outcomes from this study are examines and the comparison have been made by using bvp4c routine of MATLAB. The effect of different material factors on the flow speed, energy, and concentricity have been depicted in diagrams and tables and also discussed in detail. It is found that velocity is enhanced by increasing suction, whereas temperature is increased due to radiation, heat source/sink, and Eckert number. Meanwhile, concentration profile is always being suppressed by magnetic fields, suction, Schmidt number, and chemical reaction parameter. The streamline of the velocity is intensified at the region close to the dwindling surface, whereas the density is the highest for the thicker boundary layer thickness for the temperature and concentration streamlines.

Keywords:

• Heat source
• Joule heating
• magnetic field
• numerical simulation
• shrinking sheet

Disclosure statement

No potential conflict of interest was reported by the authors.

Figure 1. Schematic diagram of the model of flow.

Figure 2. Methodology of the shooting method.

Figure 3. (a) The outcome of the velocity distribution against $M.$ (b) Impression of $M$ on the velocity contour plot.

Figure 4. (a) The outcome of the velocity distribution against $S.$ (b) Impression of $S$ on velocity contour plot.

Figure 5. (a) The outcome of the temperature distribution against $M.$ (b) Impression of $M$ on temperature contour plot.

Figure 6. (a) The outcome of the temperature distribution against $S.$ (b) Impression of $S$ on temperature contour plot.

Figure 7. (a) The outcome of the temperature distribution against $R.$ (b) Influence of $R$ on temperature contour plot.

Figure 8. (a) The outcome of the temperature distribution against $Q.$ (b) Influence of $Q$ on temperature contour plot.

Additional information

Funding

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through large group Research Project under grant number RGP2/251/44.