Arod of length l coincides with the interval [0, l] on the x-axis. set up the boundary-value problem problem for the temperature u(x, t) in the following scenarios:

(a) the left end is held at temperature u0, and the right end is held at temperature u1. the initial temperature is zero throughout.

(b) there is heat transfer from the left end into a surrounding medium at temperature 20◦ , and the right end is insulated. the initial temperature is f(x) throughout.

(c) the ends are insulated, and there is heat transfer from the lateral surface of the rod into the surrounding medium held at 50◦ . the initial temperature is 100◦ throughout.

When temperature of a substance increases, of its particles increase resulting in more between particles. real world applications of thermal expansion absolute zero (-273 degrees c) is the lowest possible temperature on the kelvin scale. it is a measure of where a substance has no kinetic energy. heat is a process of the . energy flows spontaneously from a object to a until equilibrium is reached. heat is measured in heat is transferred throughis a method of heat transfer that occurs between particles of matter that are in direct contact with each other. are poor conductors that impede / reduce the rate of heat transfer. is a method of heat transfer that occurs in fluids (non-solids) by means of currents. real world application of convectiona method of heat transfer through electromagnetic waves. when energy moves from one object to another inside a closed system, no energy is or in the system in the transaction. systems will spontaneously move to a state of organized energy or high disorder over time called