Question

Which expression is used to determine the heat flux for convection? (a) \(-k A \frac{d T}{d x}\) (b) \(-k \operatorname{grad} T\) (c) \(h\left(T_{2}-T_{1}\right)\) (d) \(\varepsilon \sigma T^{4}\) (e) None of them

Short answer

a) -k A (dT/dx) b) -k grad T c) h(T2-T1) d) εσT^4 e) None of them Answer: c) h(T2-T1)

Step-by-step solution

Option (a) Analysis

The expression \(-k A \frac{d T}{d x}\) represents heat flux due to conduction in a solid, where \(k\) is the thermal conductivity, \(A\) is the area through which heat is transferred, and \(\frac{d T}{d x}\) is the temperature gradient. Thus, this option is not the correct answer.

Option (b) Analysis

The expression \(-k \operatorname{grad} T\) is a more general form of heat conduction which includes the temperature gradient in all three dimensions. Just like option (a), it represents heat transfer due to conduction, and therefore, is not the correct answer.

Option (c) Analysis

The expression \(h\left(T_{2}-T_{1}\right)\) represents heat flux due to convection. Here, \(h\) is the convection heat transfer coefficient, and \(T_{2}-T_{1}\) is the temperature difference between the fluid medium and the surface in contact. This option is the correct answer.

Option (d) Analysis

The expression \(\varepsilon \sigma T^{4}\) is used for the heat transfer rate due to radiation, where \(\varepsilon\) is the emissivity of the surface, \(\sigma\) is the Stefan-Boltzmann constant, and \(T\) is the absolute temperature of the radiating surface. This option does not represent convection heat transfer; thus, it's not the correct answer.

Option (e) Analysis

The statement "None of them" could be a correct answer if none of the prior expressions represented heat flux due to convection. However, as we have identified option (c) as the correct expression, this option is incorrect.

Final Answer

The correct expression to determine the heat flux for convection is (c) \(h\left(T_{2}-T_{1}\right)\).