Final answer:
To calculate the heat flux required to heat water by 5℃ in a tube, we use the conservation of energy and specific heat capacity formula, considering the water's density and velocity. However, without additional data on the tube's thermal properties and heat loss, the surface temperature of the tube at the exit cannot be determined.
Step-by-step explanation:
To find the heat flux required to raise the temperature of water by 5℃ as it flows through a tube, we can use the following relationship that comes from the conservation of energy and the specific heat capacity formula:
Q = mcΔT
where Q is the heat added, m is the mass flow rate of water, c is the specific heat capacity of water, and ΔT is the change in temperature. Assuming steady-state conditions and that the density (ρ) of water at 20℃ is close to 1000 kg/m³, and the specific heat capacity (c) is approximately 4186 J/kg·℃, we can express the mass flow rate m as:
m = ρAV
where A is the cross-sectional area of the tube, and V is the velocity of water. The cross-sectional area A for a tube with a diameter (D) of 0.02 m (2.00 cm) can be calculated using the formula for the area of a circle (A = π(D/2)^2). Then the heat flux q, considering the tube's length (L) and surface area (S), can be defined as:
q = Q/(SL)
Note that since the problem doesn't provide enough data to calculate the actual heat flux, additional information, such as the tube's thermal properties, would be needed to determine the surface temperature of the tube at the exit. Similarly, without knowing the amount of heat loss to the surroundings, it is challenging to provide an accurate value for the tube's surface temperature. Thus, the question cannot be answered accurately with the information provided and assumptions that need to be made.