Question

2–25 Consider a medium in which the heat conduction equation is given in its simplest form as

d^2T/dx^2 + d^2T/dy^2 = 1/a dT/dt

(a) Is heat transfer steady or transient?
(b) Is heat transfer one-, two-, or three-dimensional?
(c) Is there heat generation in the medium?
(d) Is the thermal conductivity of the medium constant or variable?

Answer 1

d) Is the thermal conductivity of the medium constant or variable.

Step-by-step explanation:

As we know that

Heat equation with heat generation at unsteady state and with constant thermal conductivity given as

`(d^2T)/(dx^2)+(d^2T)/(dy^2)+(d^2T)/(dz^2)+\frac{\dot{q}_g}{K}=(1)/(\alpha )(dT)/(dt)`

With out heat generation

`(d^2T)/(dx^2)+(d^2T)/(dy^2)+(d^2T)/(dz^2)=(1)/(\alpha )(dT)/(dt)`

In 2 -D with out heat generation with constant thermal conductivity

`(d^2T)/(dx^2)+(d^2T)/(dy^2)=(1)/(\alpha )(dT)/(dt)`

Given equation

`(d^2T)/(dx^2)+(d^2T)/(dy^2)=(1)/(a )(dT)/(dt)`

So we can say that this is the case of with out heat generation ,unsteady state and with constant thermal conductivity.

So the option d is correct.

d) Is the thermal conductivity of the medium constant or variable.