Analytical estimation of energy dissipations: Viscous,Joulian, and Darcy of viscoelastic fluid flow phenomena over a deformable surface

In this paper, analytical estimation of energy dissipations, such as viscous, Joulian, and Darcy dissipation of viscoelastic flow phenomena over a deformable surface has been presented. This supplement to the study of many transport processes, which occur in nature, and various experimental setups that are driven or modified by the composition of the various flow characteristics and material or phase constitution. These processes are very important and have received considerable attention in the literature. The estimation of dissipative energy in the process of transport energy is an important phenomenon to investigate. The present analysis is carried out on steady MHD viscoelastic liquid due to deformable domains. Moreover, the impact of internal heat sources and prescribed thermal conditions, such as surface temperature and heat flux, are carefully studied. Analytical solutions to governing equations are obtained with the help of Kummer's function. The solutions are presented graphically as well as in tables to estimate the energy losses and their effects on transport processes, which serve as the salient features of the current analysis. The outcomes serve as a guideline due to the process of transport properties as per the design requirements. Looking into the current scenario, dissipative heat energies have several applications in industries and technological processes, such as electric heaters, fuses, food processing, and several others.