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The present study communicates with the thermal analysis of an incompressible micropolar fluid by considering two different prescribed conditions corresponding to two different surfaces. On the porous surface of two different stretchable sheets, the unsteady flow problem of a micropolar fluid is explored by taking the variable impacts of the magnetic field. For both considered sheets, the prescribed thermal analysis is carried out with the contribution of joule heating, viscous dissipation, and radiation. Two prescribed cases of surface temperature and heat flux are discussed for linear stretched surface. Similarly, prescribed cases of exponential surface temperature and exponential heat flux are investigated for the case of an exponential stretchable surface. An effective technique of bvp4c in MATLAB is utilized to numerically tackle the governing equations of the problem. Both the distributions of temperature and velocity and the field of microrotation are graphically scrutinized relative to different geometries and several pertinent parameters. This study of thermal analysis with prescribed conditions elucidates that for an exponential surface, three distributions of flow phenomenon (temperature, microrotation, velocity) manifest more prominent results in comparison to the stretchable surface with linear velocity.

Due to realistic implementations of heat transfer flows, this study communicates with the two cases of the prescribed thermal process. A comparative analysis of the time-dependent flow of a micropolar fluid between two problems of linear stretching sheet and exponential stretching sheet is demonstrated. In the context of the linear stretching sheet, the investigation covers situations involving prescribed surface temperature (PST) and prescribed heat flux (PHF). Likewise, for the exponential stretching sheet, the study examines cases of prescribed exponential order temperature (PEST) and prescribed exponential order heat flux (PEHF). For both problems, the two cases of the thermal process are examined for heat transfer analysis considering joule heating and nonlinear thermal radiation. The two-dimensional flow in the presence of a variable magnetic field is explored for both the linear and exponential stretching sheet problems. Graphical representations are employed to provide a comparative illustration of flow properties concerning relevant parameters for both cases. From the graphical and tabular analysis, we deduce that an exponential stretching sheet provides more consequential results as compared to a linear stretching sheet. Furthermore, the material parameter demonstrates an increase in the velocity field for both of the considered sheets.