## 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

View Answer / Hide Answer **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/∂x*^{2}) + (∂T/∂y^{2}) + (∂T/∂z^{2}) = (∂T/∂t)b.

*(∂T/∂x*^{2}) + (∂T/∂y^{2}) + (∂T/∂z^{2}) = (1/α)(∂T/∂t)c.

*(∂T/∂x*^{2}) + (∂T/∂y^{2}) + (∂T/∂z^{2}) + (q̇/k) = (∂T/∂t)d.

*(∂T/∂x*^{2}) + (∂T/∂y^{2}) + (∂T/∂z^{2}) + (q̇/k) = (1/α)(∂T/∂t)Where,

*q̇* = rate of heat generation

*k* = thermal conductivity

*/α* = (k/ρc) thermal diffusivity

*ρ* = density of the element

*c* = specific heat of the element

View Answer / Hide Answer **ANSWER: d. (∂T/∂x**^{2}) + (∂T/∂y^{2}) + (∂T/∂z^{2}) + (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/∂x*^{2}) + (∂T/∂y^{2}) + (∂T/∂z^{2}) = (1/α)(∂T/∂t)

this equation is known asa. Laplace equation

b. Fourier equation

c. Poisson equation

d. none of the above

View Answer / Hide Answer **ANSWER: b. Fourier equation **

**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/∂x*^{2}) + (∂T/∂y^{2}) + (∂T/∂z^{2}) + (q̇/k) = 0

this equation is known asa. Laplace equation

b. Fourier equation

c. Poisson equation

d. none of the above

View Answer / Hide Answer **ANSWER: c. Poisson equation **

**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

View Answer / Hide Answer **ANSWER: d. if the body or element is in steady-state with no heat generation **