Final answer:
The most likely reason for the shape of temperature and heat-flux distribution in a system is that temperature distribution is affected by internal heat generation, while heat-flux distribution is influenced by thermal conductivity, as well as geometrical factors.
Step-by-step explanation:
The temperature distribution in a system is affected by various factors including internal heat generation and the thermal properties of the material, such as thermal conductivity and specific heat. The heat-flux distribution, or the rate at which heat is transferred through a material, is influenced by factors including the material's thermal conductivity, temperature difference across the material, as well as geometrical factors.
In regards to the options provided, the most likely option is b) Temperature distribution is primarily affected by internal heat generation, whereas heat-flux distribution is influenced by thermal conductivity. This is because internal heat generation will directly affect the temperature within a system, and the thermal conductivity of a material affects the rate at which heat is conducted through it. External factors can also play a role, but the materials' properties are fundamental.
Heat transfer occurs only via three methods: conduction, convection, and radiation. Conduction happens due to temperature differences within a material, convection involves the movement of fluid or air, and radiation is the transfer of energy via electromagnetic waves. The transfer of heat is thus always dependent on a temperature difference between systems or objects.