# Two and Three Dimensional Steady-State Heat Conduction - MCQs

## Two and Three Dimensional Steady-State Heat Conduction – MCQs

1. Consider an element with finite dimensions. In general which among the following equations is correct for change in energy of element during a time span dt?

a. [Heat generated in the element during time dt] + [Heat flow into the element during time dt] + [Heat flow out of the element during time dt]
b. [Heat generated in the element during time dt] + [Heat flow into the element during time dt] – [Heat flow out of the element during time dt]
c. [Heat generated in the element during time dt] – [Heat flow into the element during time dt] – [Heat flow out of the element during time dt]
d. none of the above

ANSWER: b. [Heat generated in the element during time dt] + [Heat flow into the element during time dt] – [Heat flow out of the element during time dt]

2. What is the general heat conduction equation which gives the temperature distribution and conduction heat flow in an isotropic solid?

a. (∂T/∂x2) + (∂T/∂y2) + (∂T/∂z2) = (∂T/∂t)
b. (∂T/∂x2) + (∂T/∂y2) + (∂T/∂z2) = (1/α)(∂T/∂t)
c. (∂T/∂x2) + (∂T/∂y2) + (∂T/∂z2) + (q̇/k) = (∂T/∂t)
d. (∂T/∂x2) + (∂T/∂y2) + (∂T/∂z2) + (q̇/k) = (1/α)(∂T/∂t)

Where,
= rate of heat generation
k = thermal conductivity
= (k/ρc) thermal diffusivity
ρ = density of the element
c = specific heat of the element

ANSWER: d. (∂T/∂x2) + (∂T/∂y2) + (∂T/∂z2) + (q̇/k) = (1/α)(∂T/∂t)

3. If the body or element does not produce heat, then the general heat conduction equation which gives the temperature distribution and conduction heat flow in an isotropic solid reduces to

(∂T/∂x2) + (∂T/∂y2) + (∂T/∂z2) = (1/α)(∂T/∂t)

this equation is known as

a. Laplace equation
b. Fourier equation
c. Poisson equation
d. none of the above

4. If the body or element is in steady-state but has heat generation then the general heat conduction equation which gives the temperature distribution and conduction heat flow in an isotropic solid reduces to

(∂T/∂x2) + (∂T/∂y2) + (∂T/∂z2) + (q̇/k) = 0

this equation is known as

a. Laplace equation
b. Fourier equation
c. Poisson equation
d. none of the above

5. When does the general heat conduction equation which gives the temperature distribution and conduction heat flow in an isotropic solid reduce to Laplace equation?

a. if the body or element is in unsteady-state with heat generation
b. if the body or element is in steady-state with heat generation
c. if the body or element is in unsteady-state with no heat generation
d. if the body or element is in steady-state with no heat generation