UNIT 2

Partial differentiation

1. A rod of length l has its ends a A and B kept at 00 and 1000 respectively until steady state condition prevail. If the temperature at B is reduced suddenly to 00c and kept so while that of A is maintained. Find the temperature u(x,t) at a distance x from A and at time t.
2. A road of length of 30 cms has its ends A and B kept at 200C and 800respoectivrly until steady state condition prevail. The temperature at each end is then suddenly reduced to 00C and kept so. Find the resulting temperature function taking x=0 at A.
3. A long rectangular plate of width 10cms with insulated surface has its temperature u equal to zero on both long side and one short edge so that u(0,y)=0, u(10,y)=0,u(x,=x(10-x) for all x between 0-10. Find the temperature u(x,y) at any point of the plates in steady state
4. A homogenous rod of conducting material of length l and has kept at zero temperature and the temperature at the centre is T and falls uniformly at zero at the two ends. Find the temperature.
5. Find the transient state of temperature of a non -radiating rod of length pi whose ends are kept at iced cold temperature, the temperature of the rod being initially (pix-x2) at a distance x from an end .

UNIT 2

Partial differentiation

1. A rod of length l has its ends a A and B kept at 00 and 1000 respectively until steady state condition prevail. If the temperature at B is reduced suddenly to 00c and kept so while that of A is maintained. Find the temperature u(x,t) at a distance x from A and at time t.
2. A road of length of 30 cms has its ends A and B kept at 200C and 800respoectivrly until steady state condition prevail. The temperature at each end is then suddenly reduced to 00C and kept so. Find the resulting temperature function taking x=0 at A.
3. A long rectangular plate of width 10cms with insulated surface has its temperature u equal to zero on both long side and one short edge so that u(0,y)=0, u(10,y)=0,u(x,=x(10-x) for all x between 0-10. Find the temperature u(x,y) at any point of the plates in steady state
4. A homogenous rod of conducting material of length l and has kept at zero temperature and the temperature at the centre is T and falls uniformly at zero at the two ends. Find the temperature.
5. Find the transient state of temperature of a non -radiating rod of length pi whose ends are kept at iced cold temperature, the temperature of the rod being initially (pix-x2) at a distance x from an end .