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 generally 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 individual film heat transfer coefficient on either sides.

At higher Reynolds number (Re > 10,000), the ordered flow pattern of laminar flow regime is replaced by randomly moving eddies thoroughly mixing the fluid and greatly assisting heat transfer. However, this enhancement of film heat transfer coefficient is accompanied by much higher pressure drop which demands higher pumping power. Thus, although desirable, turbulent flow is usually restricted to fluids of low viscosity.

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,

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

$$ or $$

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

Once the heat exchanger material and its geometry is fixed, then the metal wall resistance [ΔX / K × A_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 turbulent flow regime, then Dittus-Boelter equation can be used to find out inside film heat transfer coefficient.

$$ \begin{equation} Nu = 0.023× (Re)^{0.8}×(Pr)^n \tag{3} \end{equation} $$

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:

$$ \begin{equation} Nu = Constant \ \ \ t× (Velocity)^{0.8} \tag{4} \end{equation} $$

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

$$ \begin{equation} \frac{1}{U_i} = \frac{Constant \ \ t - 1}{(Velocity)^{0.8}} + Constant \ \ t - 2 \tag{5} \end{equation} $$

Thus, the graph of 1/U_i vs 1/(V)^0.8 (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 Dittus-Boelter equation.