The value of Tm is

Question

For flow through a pipe of radius R, the velocity and temperature distribution are as follows:

U(r,x)=$C_{1}$ and T(r,x)=$C_{2}$$\left [ 1-\left ( \frac{r}{R} \right )^{3} \right ]$

where $C_{1}$ and $C_{2}$ are constants.The bulk mean temperature is given by

$T_{m}=\frac{2}{U_{m}R^{2}}\int_{0}^{R}u\left ( r,x \right )T\left ( r,x \right )rdr$

With U_m being the mean velocity of flow.

The value of T_m is

     (a) $\frac{0.5C_{2}}{U_{m}}$                                                                        (b) 0.5C₂

      (c) 0.6$C_{2}$                                                                      (d) $\frac{0.6C_{2}}{U_{m}}$