The thermal management in Solid-State Electronics (SSE) has been one critical issue in design of modern electronic devices. The SSE's size reduction and the need for a better and efficient power dissipation has motived several studies about the temperature control.

Electronic components' thermal control aims to maintain the temperature equal to or below the manufacturer’s maximum specified service temperature. The knowledge of those values and their ideal operational ranges would ensure an effective performance and long service life. Chips with this type of configuration have a wide industrial performance from high-performance computers, solar energy conversion, nuclear plants and aircrafts.

The objective of this research is propose an analytical approach to estimate the temperature field in solid state electronics (SSE). The formulation considers several internal heat generation (HG) regions caused by Joule effect due to internal components, which can be applied in any layout of internal components in the SSE.

Heat Sinks are passive heat exchangers responsible for transferring the thermal energy from a heated component to a cooling fluid medium, often air or a liquid coolant. They are designed to significantly increase the contact surface area between solid and fluid, thereby increasing the heat transfer and, consequently, regulating the device's temperature at optimal levels.

In this research, the thermal analysis of heat sinks, for the cooling of solid-state electronics and photovoltaics components, is proposed using an analytical approach. Analytical solutions for the base and fins are obtained using the Classical Integral Transform Technique (CITT) and, then, they are coupled to obtain the temperature field for the heat sink. CFD simulations using the OpenFOAM software are also performed for verification purposes.

Solutions for advection-diffusion problems in ducts, known as Graetz problems, are presented using the Generalized Integral Transform Technique (GITT). The GITT is an established hybrid analytical-numerical methodology for heat transfer problems. Some industrial applications of extended Graetz analysis are the transportation of heavy oils and heat exchangers cooling process.