Question

The relationship between the rate of heat transfer per unit area \(\dot{q}_s\)=-(k∇T). Where, k is a scalar value of thermal conductivity and ∇T is the gradient of temperature. Which of these following is wrong according to the above equation?

(a) Heat transfer is different in different directions

(b) The rate of heat transfer depends upon the temperature gradient

(c) Heat transfer is in the opposite direction of increasing temperature

(d) k is the proportionality constant

I got this question in exam.

I'm obligated to ask this question of Energy Equation in section Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer 1

Correct choice is (a) Heat transfer is different in different directions

Easiest explanation: The statement “Heat transfer is different in different directions” is wrong. k is a scalar means that the heat transfer is the same in all directions and the material is isotropic. For different heat transfers in different directions (anisotropic material), the proportionality constant should be a tensor.