Heat Transfer and Fluid Circulation of Thermoelectric Fluid through the Fractional Approach Based on Local Kernel

A thermoelectric effect occurs when a material's intrinsic property directly converts temperature differences applied across its body into electric voltage. This manuscript presents the prediction for maximum and optimal heat transfer efficiency of a thermoelectric fluid via the non-classical approach of the differential operator. The fractionalized mathematical model is also established to analyze the efficiency and characteristics of thermoelectric fluid through a temperature distribution and velocity field. The comprehensive analytical approach of integral transforms and Cardano's method are applied to provide analytical solutions that include the dynamic investigation of the temperature distribution and velocity field. A dynamic investigation of the temperature distribution and velocity field of the thermoelectric fluid is explored on the basis of magnetization and anti-magnetization, which describe the behavior for sine and cosine sinusoidal waves. The rheological parameter, i.e., magnetization, suggests that by employing varying magnetic fields, the magnetized intensity generates 34.66% of the magnetic hysteresis during the thermoelectric effect.