In this paper, the effect of surface radiation in a square cavity containing an absorbing, emitting and scattering medium with four heated boundaries is investigated, numerically. Lattice Boltzmann method (LBM) is used to solve the energy equation of a transient conduction–radiation heat transfer problem and the radiative heat transfer equation is solved using finite-volume method (FVM). In this work, two different heat flux boundary conditions are considered for the east wall: a uniform and a sinusoidally varying heat flux profile. The results show that as the value of conduction–radiation decreases, the dimensionless temperature in the medium increases. Also, it is clarified that, for an arbitrary value of the conduction–radiation parameter, the temperature decreases with decreasing scattering albedo. It is observed that when the boundaries reflect more, a higher temperature is achieved in the medium and on boundaries.

This study presents numerical and experimental investigation on breast cancer tumour parameters by inverse heat transfer method using genetic algorithm (GA) and image processing (IP) to determine the depth and rate of heat generation of a breast cancer tumour. To simulate the problem, using the energy equation in acylinder including a heater, the surface temperature distribution was obtained. Then, the temperature surface of the cylinder was analysed by the GA in MATLAB software to determine the depth and rate of heat generation of heater. The validity of the numerical method was evaluated using the IP from a laboratory sample. A thermal heater was placed inside a cylinder and was covered by a tissue similar to the human body tissue. According to the obtained results, it was determined that the results of the laboratory sample and the numerical method were in agreement with each other. Finally, these steps were applied on the thermal image of a patient’s cancer breast to determine the depth and rate of heat generation of the breast tumour. It is shown that the average computational error between numerical and experimental results in this method to determine the depth of the tumour isabout 8–10% and to determine the rate of tumour heat generation is about 0.01–1%.