In a heat exchanger, heat is transferred from hot fluid to cold fluid through metal wall, which generally separates these two fluids. Heat transfer through metal wall is always by conduction while on both sides of metal wall it is by convection. Generally, resistance offered to heat transfer by the metal wall is negligible as compared to resistance offered by convection. The wall temperature is always between local temperatures of the two fluids. The actual value depends upon the individual film heat transfer coefficient on either sides.

At low Reynolds number (Re < 2100), the flow pattern is laminar and the fluid flows in an ordered manner along generally parallel “Filament like” streams which do not mix. It follows that in this type of flow that the heat transferred to and through the fluid is essentially by conduction.

When heat is transferred through resistances in series, the total resistance to heat transfer is the sum of individual resistances in series. Thus, for heat exchanger, one can write,

$$ \begin{equation} \frac{1}{U_iA_i} = \frac{1}{h_iA_i} + \frac{Δx}{KA_{lm}} + \frac{1}{h_oA_o} \tag{1} \end{equation} $$

$$ or $$

$$ \begin{equation} \frac{1}{U_i} = \frac{1}{h_i} + \frac{\Delta xA_i}{KA_{lm}} + \frac{A_i}{h_oA_o} \tag{2} \end{equation} $$

Once the heat exchanger material and its geometry are fixed, then the metal wall resistance [Δx/KA_lm] becomes constant. Similarly, if the flow rate of cold fluid is fixed and its mean temperature does not differ much for different flow rates of hot fluid, then the resistance by the outside film will remain almost constant. Thus, the overall heat transfer coefficient will depend upon the value of inside film heat transfer coefficient alone. If flow through inner tube is in the laminar flow regime, then Sieder-Tate equation can be used to predict the inside film heat transfer coefficient.

$$ \begin{equation} Nu = 1.86 × (Re)^{1/3} × (Pr)^{1/3} \tag{3} \end{equation} $$

If the bulk mean temperature does not differ much for different flow rates, then all the physical properties will remain nearly the same and equation (3) can be re-written as:

$$ \begin{equation} Nu = Constant \ \ t × (Velocity)^{1/3} \tag{4} \end{equation} $$

Substituting equation (4) in equation (2), one can write it as:

$$ \frac{1}{U_i} = \frac{Constant \ \ t - 1}{U^{1/3}} + Constant \ \ t - 2 \tag{5} $$

Thus, the graph of 1/U_i vs 1/U^1/3 (which is known as Wilson plot) should be a straight line with a slope equal to constant-1 and intercept equal to constant-2. From this graph, inside film heat transfer coefficient can be calculated which can be used to verify Sieder-Tate equation.