ORCID Identifier(s)


Graduation Semester and Year




Document Type


Degree Name

Doctor of Philosophy in Mechanical Engineering


Mechanical and Aerospace Engineering

First Advisor

Ankur Jain

Second Advisor

Abdolhossein Haji-Sheikh


Bioheat transfer is the phenomenon of heat transfer in biological systems where the dominant modes of heat transfer are conduction and advection. Other factors such as rate of metabolism that are unique to biological systems contribute significantly towards bioheat transfer. In the present work, the Pennes bioheat equation has been solved for a multilayer system to derive steady state and transient temperature solutions in the multilayer skin tissue with a tumor. In nanoparticle based hyperthermia therapy, the body temperature elevates from the physiological core body temperature, 37 deg. C. Analytical solutions for three different therapeutic techniques have been developed to predict the steady state temperature distribution for a five-layer perfused skin tissue model. The transient bioheat model based on Pennes equation introduces an additional challenge for determining the temperature in a two dimensional multilayer skin tissue model. The existence of both real and imaginary eigenvalues in the temperature solution makes it different from classical transient heat conduction problems. This observation has been addressed by introducing a special transformation which modifies the temperature solution such that the transient solution agrees well with the results from the steady state model. The transient temperature model accounts for the specific absorption rate (SAR) as a function of both space and time. Finally, temperature in vascular tissue with a tumor of any arbitrary shape is derived. The equation for the tumor boundary can be determined using medical imaging techniques. In addition, different values for thermo-physical and physiological parameters are accounted for in the tissue and tumor region of the vasculature. This helps in determining the temperature distribution in the vascular tissue as a function of SAR for nanoparticle assisted hyperthermia therapy which is critical for planning nanoparticle assisted thermal based therapy for cancer. Another fundamental heat transfer problem is that of the cooling of a cylinder, such as temperature in a Li-ion cell is examined when subject to variable heat transfer. In particular, a general solution for the temperature distribution in the cylinder is derived, accounting for circumferential varying convective heat transfer coefficient around the cylinder, and orthotropic thermal conductivity of the cylinder. This solution procedure is later extended to derive an analytical temperature in an orthotropic and partially orthotropic sphere subject to circumferential varying heat transfer coefficient. A general solution for temperature can provide very fast and highly accurate solutions for different functionally graded materials, heat generation/dissipation rates subject to different cooling loads. Finally, the mathematical procedure derived earlier is applied to estimate the error in steady- state heat transfer measurements due to lateral conduction effects in the heater foil. The error due to lateral conduction effects is quantified by a heat flux correction factor. Correlations for peak error as a function of non-dimensional parameters such as Biot number, ratio of maximum to minimum heat transfer and gradient of shear layer, for both slot and radial jets are obtained. These correlations can help experimentalists estimate error during measurement of steady-state heat transfer coefficient.


Analytical modeling, Heat conduction, Bioheat transfer, Photothermal therapy, Hyperthermia, Cryotherapy, Variable heat transfer coefficient, Lateral conduction


Aerospace Engineering | Engineering | Mechanical Engineering


Degree granted by The University of Texas at Arlington