Dear Mr.swami

heat transfer due to the applications and conditions, depends on to many parameters. it is better to add some details to your question.

There are three methods for heat transfer, each of which is of great importance.

You can earn more details about these methods from the links.

1. Conduction : https://en.wikipedia.org/wiki/Thermal_conduction

2. Convection : https://en.wikipedia.org/wiki/Convective_heat_transfer

3. Radiation : https://en.wikipedia.org/wiki/Thermal_radiation

It will depend upon the type of applications.

From the question, it is not clear where to use heat transfer and why? Pl. explain your question. .

Solutions of the heat diffusion equation

see paper

[Mathematical Engineering] Analytical Methods for Heat Transfer and Fluid Flow Problems || Heat Transfer in Pipe and Channel Flows (Parabolic Problems)

Weigand, Bernhard

https://booksc.xyz/book/43340935/b06ae4

Abdellah LAMNII thank you for giving me direction for this problem but as far as I know the solution of diffusion equation gives the methods to solve the given heat transfer problem, but it does not explains which heat transfer mode is effective if all modes are under same condition.

Which heat transfer mode is effective will depend on the temperatures of the contacting bodies and fluid involved in heat transfer. Generally, radiation is not effective for temperaures less than 300 oC but conduction and convection modes of heat transfer will always be effective in every heat transfer problems.

Dear Mr.swami

heat transfer due to the applications and conditions, depends on to many parameters. it is better to add some details to your question.

Hi

Among the three types of heat transfer methods, usually conjugate heat transfer( both conduction and convection) is used in different applications but depend on conditions each type can be efficient.