Question

After integration of the "Law" for unsteady state conduction you find the temperature profile to be:

T(x)=a+bx²+cx³

Where T is in K and x is in m.

a) what are the units for a, b, and c.

b)if qdot=1000 W/m³ , rho= 1600 kg/m³ , k=40 W/(m K), and Cp = 4 kJ/(kg K) waht is the rate of change of the temperature as a function of time? ($\partial$T/$\partial$t)

Answer 1

We need to use the equation of conduction to determine our final answer.

Solution:

We know from text book that unsteady state equation of conduction is given as following:

As given in question,

k = conductivity =40w/mk

T = a+ bx² + cx³ K

Density = Rho = 1600 Kg/m3

Cp = heat capacity = 4 Kj/Kg.K = 4000 J/kg.k

q = 1000 W/m3

So by putting all these variables in equation:

or K/sec

I hope i was very detailed in answering your query. Kindly let me know if you still have any further doubt. if you are satisfied then please rate me. Thanks for using homeworklib