conider one-dimeasional heat fow. take for a model a thin, laterally in with constant cross-sectional area a. start from scratch and derive the o insulated rod (4-1) as th by th (4-2 + f, where a and f are as given following (3-8 zero, then (0, t)-0 for t equation 2 if the left end of the rod in prob. 1 is held at temperature the fact that this end is insulated (i what boundary condition at x- l expresses heat crosses the end x ly? . the specific heat e and thermal conductivity k in fourier's law (3-7) become funct of position x when the heat-conducting medium is inhomogeneous. find the a of (3-8) for such a medium. t suppose that the left end of the rod in prob. 1 is in contact with air, held at a constant temperature to. newton's law of cooling, confirmed by experiment states that heat flow across the end x = 0 will be proportional to the temperature differ- ence aral)-to. what boundary condition does this law give for u at x = 0? suppose that a similar medium at the end x = l is held at temperature tl. condition atx l heat flows in a region d in space that is bounded by a surface b. within d heat flow is governed by (3-8. the surface b is surrounded by a medium held at the constant temperature ts. use newton's law of cooling to find an equation (boundary condition) find the boundar giving the heat flow across b case of the situation in prob. 5 1-4. diffusion-dispersion phenomena 6 suppose that the region d in prob. 5 has an insulated boundary. what is the boundary condition? explain briefly how this boundary condition can be regarded as a limiting