# Heat transfer coefficient: a review of measurement techniques

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## Abstract

Heat transfer coefficient is a basic parameter used in the calculation of convective heat transfer problems. Due to the importance of the experimental measurements for the development of convective heat transfer, this review identifies, classifies and describes the experimental methods used for the measurement of heat transfer coefficient. The methods were classified into five major groups: (1) direct method, (2) transient method, (3) Wilson method, (4) heat/momentum/mass transfer analogy method and (5) boundary layer thickness method. Their applications, limitations and the reported accuracy were evaluated in the context of new developments in temperature and heat flux measurement techniques. Finally, this review provides criteria for the selection of the most suitable technique for measurements of heat transfer coefficient according to the aspects of spatial resolution, geometric scale, intrusiveness, fluid type, response time and accuracy.

## Keywords

Heat transfer coefficient Temperature Heat flux Convection Experimental measurements## List of symbols

- 1D
One-dimensional

- 2D
Two-dimensional

*A*Surface area (m

^{2})*A*_{e}Outer tube surface area (m

^{2})*A*_{i}Inner tube surface area (m

^{2})*A*_{s}Surface area (m

^{2})*C*_{e}Thermal resistances outside the tube and the tube wall (K/W) (constant)

*C*_{i}Constant

*C*_{f}Fanning friction factor (–), \(C_{\text{f}} = \frac{{\tau_{\text{s}} }}{{\rho V^{2} /2}}\)

*c*Constant (–)

*c*_{p}Specific heat capacity (J/kg K)

*c*_{p,i}Specific heat capacity at constant pressure (J/kg K)

*d*Diameter (m)

*d*_{e}Outer tube diameter (m)

*d*_{i}Inner tube diameter (m)

*D*_{m}Mass diffusivity (m

^{2}/s)*f*Darcy friction factor (–), \(f = 4 \cdot C_{\text{f}}\)

*G*Mass velocity (kg/s m

^{2})*h*Heat transfer coefficient (W/m

^{2}K)*h*_{i}Internal convection heat transfer coefficient (W/m

^{2}K)*h*_{e}External convection heat transfer coefficient (W/m

^{2}K)*I*Electric current (A)

*i*Local enthalpy (J/kg)

*i*_{in}Inlet enthalpy of the point at which the applied heat flux starts (J/kg)

*i*_{l}Enthalpy of liquid (J/kg)

*i*_{lat}Latent heat of phase change (J/kg)

*i*_{lv}Enthalpy of vaporization (J/kg)

*j*Colburn

*j*-factor (–), \(j = St\,Pr^{2/3}\)*j*_{m}Mass transfer Colburn

*j*-factor (–), \(j_{\text{m}} = St_{\text{m}} Sc^{2/3}\)*k*Thermal conductivity (W/m K)

*k*_{f}Fluid thermal conductivity (W/m K)

*k*_{p}Constant related to the heat flux (1/s)

*k*_{w}Tube thermal conductivity (W/m k)

*Le*Lewis number (–), \(Le = Sc/Pr\)

*L*_{tr}Length, from the inlet position to the flow pattern transition position (m)

*L*_{w}Tube length (m)

*m*Mass of the system (kg)

- \(\dot{m}\)
Mass flow rate (kg/s)

- \(\dot{m}_{\text{i}}\)
Inner mass flow rate (kg/s)

- \(\dot{m}_{\text{pc}}\)
Phase changing mass flow rate (kg/s)

*n*Normal direction (–)

*n*Velocity exponent (–)

*Nu*Nusselt number (–), \(Nu = h \cdot D/k\)

*Pr*Prandtl number, \(Pr = c_{\text{p}} \cdot \mu /k\)

*q*Thermal energy rate (W)

*q*″Surface/fluid interface heat flux (W/m

^{2})*R*Electrical resistance (Ω)

*R*_{e}Thermal resistance of external convection (K/W)

*Re*Reynolds number (–), \(Re = G \cdot D /\mu\)

*R*_{i}Thermal resistance of internal convection (K/W)

*R*_{T}Total thermal resistance (K/W)

*R*_{W}Tube wall thermal resistance (K/W)

*Sc*Schmidt number (–), \(Sc = \frac{\nu }{{D_{\text{m}} }}\)

*Sh*Sherwood number (–), \(Sh = \frac{{h_{\text{m}} L}}{{D_{\text{m}} }}\)

*St*Stanton number (–), \(St = \frac{Nu}{Re\,Pr}\)

*St*_{m}Mass transfer Stanton number (–), \(St_{\text{m}} = \frac{Sh}{Re\,Sc}\)

*T*Temperature (K)

*t*Time (s)

*T*_{i},_{in}Inlet temperature (K)

*T*_{i,out}Outlet temperature (K)

*T*_{s}Wall surface temperature (K)

*T*_{∞}Temperature under free-flow conditions (K)

- V
Electric potential difference (V)

*v*Fluid velocity (m/s)

*x*_{tr}Vapor quality of flow pattern transition (–)

## Greek symbols

*β*Seebeck coefficient (V/K)

*δ*Thermal boundary layer thickness, liquid film thickness (m)

- Δ
*e* Seebeck voltage (V)

- Δ
*T* Temperature difference (K)

- Δ
*T*_{LM} Logarithmic mean temperature difference of the fluids (K)

*ρ*_{v}Vapor density (kg/m

^{3})*Τ*Time constant (s)

*τ*_{s}Shear stress on the wall (N/m

^{2})- ∇
*T* Temperature gradient (K/m)

## Notes

### Acknowledgements

The authors acknowledge the financial support of FAPESP (São Paulo Research Foundation) contract numbers 2016/16849-3 and 2018/06057-4, CAPES (Coordination for the Improvement of Higher Education Personnel) and CNPq (National Council for Scientific and Technological Development).

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