Question

In any forced or natural convection situation, the velocity of the flowing fluid is zero where the fluid wets any stationary surface. The magnitude of heat flux where the fluid wets a stationary surface is given by (a) \(k\left(T_{\text {fluid }}-T_{\text {wall }}\right)\) (b) \(\left.k \frac{d T}{d y}\right|_{\text {wall }}\) (c) \(\left.k \frac{d^{2} T}{d y^{2}}\right|_{\text {wall }}\) (d) \(\left.h \frac{d T}{d y}\right|_{\text {wall }}\) (e) None of them

Short answer

Answer: (a) \(k\left(T_{\text {fluid }}-T_{\text {wall }}\right)\)

Step-by-step solution

Understanding heat flux

Heat flux is the rate of heat transfer per unit area. It gives us an idea of how much heat is being transferred where the fluid wets a stationary surface in forced or natural convection.

Understand the given options

We have been given several options for the equation of heat flux in this situation: (a) \(k\left(T_{\text {fluid }}-T_{\text {wall }}\right)\) is representing the heat flux using the temperature difference between the fluid and the wall, and the thermal conductivity k. (b) \(\left.k \frac{d T}{d y}\right|_{\text {wall }}\) is representing the heat flux using the temperature gradient at the wall, and the thermal conductivity k. (c) \(\left.k \frac{d^{2} T}{d y^{2}}\right|_{\text {wall }}\) is representing the heat flux using the second derivative of temperature with respect to y at the wall, and the thermal conductivity k. (d) \(\left.h \frac{d T}{d y}\right|_{\text {wall }}\) is representing the heat flux using the temperature gradient at the wall, and the heat transfer coefficient, h. (e) None of them means that none of the given options represent the correct equation for heat flux in this scenario.

Determine the correct equation

The key aspect of this problem is that we are dealing with convection heat transfer where fluid is flowing over a stationary surface. In convection heat transfer situations, the heat transfer is strongly dependent on the temperature difference between the surface and the fluid, and also the heat transfer coefficient which includes the effect of fluid velocity. Hence, the correct option for the problem would reflect the product of heat transfer coefficient and temperature difference. Therefore, the correct answer is: (a) \(k\left(T_{\text {fluid }}-T_{\text {wall }}\right)\)